含光生化反应的多孔介质内流动及传输特性的格子Boltzmann模拟
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摘要
由于人类过度开发利用传统的化石能源，同时新能源体系尚未建立，造成了全球环境污染、能源危机以及严重的生态环境破坏。未来经济的可持续发展要求我们开发和利用清洁的可再生能源来代替化石能源，从而建立人类与自然的和谐关系。在众多可代替能源中，氢能是目前最理想的能源，它具有热值高、燃烧稳定性好及清洁高效的优点。在各种制氢方法和技术中，光生物制氢技术是微生物利用太阳能通过降解有机物来供给自身生长，同时产生氢能的一种新技术。该技术反应条件温和、能耗低、能妥善解决能源与环境的矛盾，被认为是一种具有广泛应用前景的绿色能源技术。
目前，对光生物制氢已经展开了大量的实验研究，并将基于膜生物法和凝胶颗粒包埋法的细胞固定技术应用到生物制氢中，从而提高反应器内的生物量及运行的稳定性。同时，也有许多学者采用数值方法对反应器内的流动及传输现象进行理论研究。但是，这些数值方法主要是基于宏观传统算法，对于反应器内的微细观流动及传输过程不能够较好的反映，并且对于复杂边界条件其难以达到较高的数值精度和稳定性。近年来，一种新型的介观尺度算法——格子Boltzmann方法出现，它具有算法简单、天然的并行性及容易处理复杂边界条件的优势。本研究以圆柱体管束和玻璃珠堆积颗粒的膜生物反应器、以及包埋颗粒填充床反应器为背景，利用格子Bolzmann方法对这些多孔介质内的流动、传输及光生化反应过程进行研究。本文的主要研究内容和结论如下：
①首先，从连续Boltzmann方程出发，推导得到了时间、空间和速度上完全离散的格子Boltzmann方程；利用Chapman-Enskog展开技术，从格子Boltzmann方程反演得到宏观方程，进而建立了介观模型参数和宏观物理量间的关系。然后，根据所研究的物理问题设计了合适的格子Boltzmann传质模型及边界处理格式，且通过算例的模拟计算，证明了格子Boltzmann方法的可行性。
②利用2D格子Boltzmann传质模型研究了溶液横掠具有光生化表面的单圆柱及圆柱体管束构成的规则多孔介质内的流动及传输特性。得到了不同条件下的流场及浓度场分布，并研究分析了进口流速、管间距及管束排列方式对平均阻力系数、平均Sherwood数及平均降解效率的影响。模拟结果表明：进口流速增加，平均Sherwood数增大、平均阻力系数及降解效率降低；管间距减小，平均阻力系数、平均Sherwood数及降解效率均增大；管束采用叉排排列时，平均Sherwood数和降解效率均增大，平均阻力系数略有降低，说明叉排排列方式更有利于传质及光生化反应过程。
③利用3D格子Boltzmann传质模型研究了具有光生化表面的单颗粒及堆积颗粒构成的规则多孔介质内的流动、传输及光生化反应过程，该研究从二维拓展到三维。在计算中，将格子Boltzmann模型与多块模型耦合来提高计算效率。研究了光照强度、进口流速及颗粒堆积方式对流场、浓度场分布的影响，并且对其产氢性能也进行了评估。结果表明：光照强度为6000lx时，产氢性能最高；进口流速的增大，产氢性能降低；体心立方结构的颗粒堆积方式，阻力系数略低，但产氢性能较高。
④用表征体元尺度的格子Boltzmann模型研究了有机废水溶液绕流多孔包埋颗粒的流动、传输及其内部的光生化反应过程。计算中，将该模型与多块模型耦合来提高计算效率，研究了光照强度、进口流速、多孔包埋颗粒的渗透率及孔隙率的影响。结果表明：光照强度为6000lx时，光能转化效率最高，产氢性能最佳；进口流速增大，产氢性能明显降低；随着多孔包埋颗粒渗透率的增大，产氢得率增加，而底物降解效率减小；随着多孔包埋颗粒孔隙率的增大，产氢得率略有降低，而底物降解效率增加，并且在孔隙率大于0.5时，趋于稳定状态。
⑤用格子Boltzmann模型在孔隙尺度上研究了光合细菌单包埋颗粒反应器内的光生化反应过程。计算中，利用四参数随机生长法重构了包埋颗粒内的不规则多孔结构。研究了包埋颗粒的孔隙率对流动、传质及产氢性能的影响，且模拟结果与实验结果吻合得较好。此外，提出了一种格子Boltzmann多尺度模型，用该模型跨尺度研究了包埋颗粒填充床反应器内的光生化反应过程，既获得了包埋颗粒内微细观的流动及传输特性，又节约了计算成本。同时，考虑了反应器内的光衰减，模拟结果表明：光衰减主要发生在包埋颗粒内，且LB模拟的出射光强与实验值吻合得较好，并且产氢性能的模拟结果与实验结果也有较好的吻合度，从而证明了该格子Boltzmann多尺度模型用于模拟光生化反应系统是可行的。
Due to the over-exploitation of traditional fossil energy by human, as well as theunestablishment of the new energy system, this causes global environmental pollution,energy crisis and severe damage of ecological environment. The substainabledevelopment of economy in future requires the development and the use of cleanrenewable energy instead of the fossil energy, so as to build the harmonious relationbetween human and nature. In many alternative energy sources, hydrogen energy is themost ideal energy at present, attributed to its advantages of high energy content, goodstability of combustion, cleanness and high efficiency. In many hydrogen productionmethods and technologies, the photo biohydrogen production method is a newtechnology that the microorganisms degrade the organic matter for their own growth,and meanwhile generate hydrogen energy. The biohydrogen production method hasadvantages of mild reaction conditions, low energy consumption, proper treatment ofthe contradiction between energy and environment. Therefore, the photo biohydrogenproduction technology has been recognized as a green energy technology with a broadapplication prospect.
Recently, lots of experimental studies have been carried out, and theimmobilized-cell method based on biofilm and gel granule immobilized-cell has beenapplicated to the biohydrogen production, which can improve the biomass in the reactorand the stability of operation. Meanwhile, many researchers have implemented somenumerical methods to investigate the flow and mass transfer in the bioreactor.Unfortunately, these numerical methods are mainly on macro-scale, and it is difficult toreflect the flow and mass transfer on micro-scale, and achieve good stability and highnumerical precision for complex boundaries. In last decades, the lattice Boltzmannmethod (LBM) on mesoscale has emerged, and it has some advantages, such as simplealgorithm, nature parallelism and ease of handling with the complex boundary. Thisstudy is based on the biofilm bioreactor filled with tube bundles or packed particles withphotosynthetic bacteria (PSB) biofilm, and packed bed reactor filled with porousgranule immobilized PSB-cell, and the lattice Boltzmann method is used to investigatethe flow and mass transfer in these porous media with photo-bioreaction. The mainstudies and conclusions in this paper are as follows:
①First, the detail derivation of the transformation from consecutive Boltzmann equation to the lattice Boltzmann equation descrete on time, space and velocity, ispresented. Then, through Chapman-Enskog expansion, the macro equations can beobtained from the lattice Boltzmann equation, which establishes the relationship ofmodel parameters on meso-scale and macro physical quantities. The lattice Boltzmannmodel for mass transfer and the boundary treament methods are properly designedaccording to the physical problem in this study. Additionally, the feasibility of thelattice Boltzmann method is validated by simulations of some cases.
②The2D lattice Bolzmann mass transfer model is implemented to simulate theflow and mass transfer for substrate solution around a cylinder and a porous media oftube bundles with photo bioreaction surface. The flow and concentration fields areobtained under various conditions, and the effects of influent velocity, tube spacing andtube arrangement are investigated by these parameters of average drag coefficient,average Sherwood number and substrate consumption efficiency. The numerical resultsdemonstrate that the increasing influent velocity leads to high average Sherwoodnumber, while low average drag coefficient and substrate consumption efficiency. Withdecreasing tube spacing, these parameters both increase. For staggered arrangement oftube bundle, the average Sherwood number as well as substrate consumption efficiencyincrease, but the average drag coefficient decrease somewhat, implying that thisarrangement is benefit for the mass transfer and bioreaction.
③The flow and mass transfer of substrate solution around a particle and porousmedia of packed particles with photo-bioreaction surface are simulated with3D latticeBoltzmann model for mass transfer, which tends the2D to3D study. In the simulation, amulti-block strategy is coupled to improve the computational efficiency. The effects onflow and concentration fields by illumination intensity, influent velocity and particleaccumulation mode are investigated. Furthermore, the hydrogen productionperformance is evaluated. The numerical results indicate that when illuminationintensity is6000lx, the hydrogen production performance achieves maximum; withincreasing influent velocity, the hydrogen production performance decreases; thechoosing of body-centered structure particle accumulation mode leads to a betterhydrogen production performance, but lower average drag coefficient.
④The lattice Boltzmann model at Representative elementary volume (REV) scaleis used to simulate the flow and mass transfer of substrate solution through a porousgranule immobilized PSB-cell for photo biohydrogen production. In the simulation, themulti-block model is coupled with the lattice Boltzmann model, and the effects of illumination intensity, influent velocity, permeability and porosity of porous granule areinvestigated. The numerical results show that for6000lx, the light energy conversionefficiency is highest, and thus the hydrogen production performance reaches maximum;with increasing influent velocity, the hydrogen production performance decreases; withincreasing permeability of porous granule, the hydrogen yield increases, while thesubstrate consumption efficiency decreases; with increasing porosity of porous granule,the hydrogen yield slightly decreases, and substrate consumption efficiency increases,and they tend to be stable for porosity over0.5.
⑤The bioreaction in a photo bioreactor with a porous granule immobilizedPSB-cell is investigated with lattice Boltzmann model coupled with the multi-blockmodel at pore-scale. In the simulation, the porous structure of the granule is generatedby Quartet Structure Generation Set,(QSGS). The effect of porosity on flow, masstransfer and hydrogen production performance is studied, and the LB numerical resultsand experimental results have a good agreement. Furthermore, a multi-scale latticeBoltzmann model is proposed to simulate the photo bioreaction in packed bedbioreactor filled with porous granule immobilized PSB-cell, which can obtain the flowand mass transfer in the porous granule on micro-level, as well as save thecomputational cost. Furthermore, the light attenuation in bioreator is considered in thesimulation. The numerical results indicate that the light attenuation mainly occurs in theporous granule, and the output illumination intensity between the LB numerical solutionand the experimental result has a good agreement. Additionally, the hydrogenproduction performance is evaluated, and they agree well with the experimental results,which prove that the multi-scale lattice Boltzmann is viable for simulation of photobioreaction system.
目前，对光生物制氢已经展开了大量的实验研究，并将基于膜生物法和凝胶颗粒包埋法的细胞固定技术应用到生物制氢中，从而提高反应器内的生物量及运行的稳定性。同时，也有许多学者采用数值方法对反应器内的流动及传输现象进行理论研究。但是，这些数值方法主要是基于宏观传统算法，对于反应器内的微细观流动及传输过程不能够较好的反映，并且对于复杂边界条件其难以达到较高的数值精度和稳定性。近年来，一种新型的介观尺度算法——格子Boltzmann方法出现，它具有算法简单、天然的并行性及容易处理复杂边界条件的优势。本研究以圆柱体管束和玻璃珠堆积颗粒的膜生物反应器、以及包埋颗粒填充床反应器为背景，利用格子Bolzmann方法对这些多孔介质内的流动、传输及光生化反应过程进行研究。本文的主要研究内容和结论如下：
①首先，从连续Boltzmann方程出发，推导得到了时间、空间和速度上完全离散的格子Boltzmann方程；利用Chapman-Enskog展开技术，从格子Boltzmann方程反演得到宏观方程，进而建立了介观模型参数和宏观物理量间的关系。然后，根据所研究的物理问题设计了合适的格子Boltzmann传质模型及边界处理格式，且通过算例的模拟计算，证明了格子Boltzmann方法的可行性。
②利用2D格子Boltzmann传质模型研究了溶液横掠具有光生化表面的单圆柱及圆柱体管束构成的规则多孔介质内的流动及传输特性。得到了不同条件下的流场及浓度场分布，并研究分析了进口流速、管间距及管束排列方式对平均阻力系数、平均Sherwood数及平均降解效率的影响。模拟结果表明：进口流速增加，平均Sherwood数增大、平均阻力系数及降解效率降低；管间距减小，平均阻力系数、平均Sherwood数及降解效率均增大；管束采用叉排排列时，平均Sherwood数和降解效率均增大，平均阻力系数略有降低，说明叉排排列方式更有利于传质及光生化反应过程。
③利用3D格子Boltzmann传质模型研究了具有光生化表面的单颗粒及堆积颗粒构成的规则多孔介质内的流动、传输及光生化反应过程，该研究从二维拓展到三维。在计算中，将格子Boltzmann模型与多块模型耦合来提高计算效率。研究了光照强度、进口流速及颗粒堆积方式对流场、浓度场分布的影响，并且对其产氢性能也进行了评估。结果表明：光照强度为6000lx时，产氢性能最高；进口流速的增大，产氢性能降低；体心立方结构的颗粒堆积方式，阻力系数略低，但产氢性能较高。
④用表征体元尺度的格子Boltzmann模型研究了有机废水溶液绕流多孔包埋颗粒的流动、传输及其内部的光生化反应过程。计算中，将该模型与多块模型耦合来提高计算效率，研究了光照强度、进口流速、多孔包埋颗粒的渗透率及孔隙率的影响。结果表明：光照强度为6000lx时，光能转化效率最高，产氢性能最佳；进口流速增大，产氢性能明显降低；随着多孔包埋颗粒渗透率的增大，产氢得率增加，而底物降解效率减小；随着多孔包埋颗粒孔隙率的增大，产氢得率略有降低，而底物降解效率增加，并且在孔隙率大于0.5时，趋于稳定状态。
⑤用格子Boltzmann模型在孔隙尺度上研究了光合细菌单包埋颗粒反应器内的光生化反应过程。计算中，利用四参数随机生长法重构了包埋颗粒内的不规则多孔结构。研究了包埋颗粒的孔隙率对流动、传质及产氢性能的影响，且模拟结果与实验结果吻合得较好。此外，提出了一种格子Boltzmann多尺度模型，用该模型跨尺度研究了包埋颗粒填充床反应器内的光生化反应过程，既获得了包埋颗粒内微细观的流动及传输特性，又节约了计算成本。同时，考虑了反应器内的光衰减，模拟结果表明：光衰减主要发生在包埋颗粒内，且LB模拟的出射光强与实验值吻合得较好，并且产氢性能的模拟结果与实验结果也有较好的吻合度，从而证明了该格子Boltzmann多尺度模型用于模拟光生化反应系统是可行的。
Due to the over-exploitation of traditional fossil energy by human, as well as theunestablishment of the new energy system, this causes global environmental pollution,energy crisis and severe damage of ecological environment. The substainabledevelopment of economy in future requires the development and the use of cleanrenewable energy instead of the fossil energy, so as to build the harmonious relationbetween human and nature. In many alternative energy sources, hydrogen energy is themost ideal energy at present, attributed to its advantages of high energy content, goodstability of combustion, cleanness and high efficiency. In many hydrogen productionmethods and technologies, the photo biohydrogen production method is a newtechnology that the microorganisms degrade the organic matter for their own growth,and meanwhile generate hydrogen energy. The biohydrogen production method hasadvantages of mild reaction conditions, low energy consumption, proper treatment ofthe contradiction between energy and environment. Therefore, the photo biohydrogenproduction technology has been recognized as a green energy technology with a broadapplication prospect.
Recently, lots of experimental studies have been carried out, and theimmobilized-cell method based on biofilm and gel granule immobilized-cell has beenapplicated to the biohydrogen production, which can improve the biomass in the reactorand the stability of operation. Meanwhile, many researchers have implemented somenumerical methods to investigate the flow and mass transfer in the bioreactor.Unfortunately, these numerical methods are mainly on macro-scale, and it is difficult toreflect the flow and mass transfer on micro-scale, and achieve good stability and highnumerical precision for complex boundaries. In last decades, the lattice Boltzmannmethod (LBM) on mesoscale has emerged, and it has some advantages, such as simplealgorithm, nature parallelism and ease of handling with the complex boundary. Thisstudy is based on the biofilm bioreactor filled with tube bundles or packed particles withphotosynthetic bacteria (PSB) biofilm, and packed bed reactor filled with porousgranule immobilized PSB-cell, and the lattice Boltzmann method is used to investigatethe flow and mass transfer in these porous media with photo-bioreaction. The mainstudies and conclusions in this paper are as follows:
①First, the detail derivation of the transformation from consecutive Boltzmann equation to the lattice Boltzmann equation descrete on time, space and velocity, ispresented. Then, through Chapman-Enskog expansion, the macro equations can beobtained from the lattice Boltzmann equation, which establishes the relationship ofmodel parameters on meso-scale and macro physical quantities. The lattice Boltzmannmodel for mass transfer and the boundary treament methods are properly designedaccording to the physical problem in this study. Additionally, the feasibility of thelattice Boltzmann method is validated by simulations of some cases.
②The2D lattice Bolzmann mass transfer model is implemented to simulate theflow and mass transfer for substrate solution around a cylinder and a porous media oftube bundles with photo bioreaction surface. The flow and concentration fields areobtained under various conditions, and the effects of influent velocity, tube spacing andtube arrangement are investigated by these parameters of average drag coefficient,average Sherwood number and substrate consumption efficiency. The numerical resultsdemonstrate that the increasing influent velocity leads to high average Sherwoodnumber, while low average drag coefficient and substrate consumption efficiency. Withdecreasing tube spacing, these parameters both increase. For staggered arrangement oftube bundle, the average Sherwood number as well as substrate consumption efficiencyincrease, but the average drag coefficient decrease somewhat, implying that thisarrangement is benefit for the mass transfer and bioreaction.
③The flow and mass transfer of substrate solution around a particle and porousmedia of packed particles with photo-bioreaction surface are simulated with3D latticeBoltzmann model for mass transfer, which tends the2D to3D study. In the simulation, amulti-block strategy is coupled to improve the computational efficiency. The effects onflow and concentration fields by illumination intensity, influent velocity and particleaccumulation mode are investigated. Furthermore, the hydrogen productionperformance is evaluated. The numerical results indicate that when illuminationintensity is6000lx, the hydrogen production performance achieves maximum; withincreasing influent velocity, the hydrogen production performance decreases; thechoosing of body-centered structure particle accumulation mode leads to a betterhydrogen production performance, but lower average drag coefficient.
④The lattice Boltzmann model at Representative elementary volume (REV) scaleis used to simulate the flow and mass transfer of substrate solution through a porousgranule immobilized PSB-cell for photo biohydrogen production. In the simulation, themulti-block model is coupled with the lattice Boltzmann model, and the effects of illumination intensity, influent velocity, permeability and porosity of porous granule areinvestigated. The numerical results show that for6000lx, the light energy conversionefficiency is highest, and thus the hydrogen production performance reaches maximum;with increasing influent velocity, the hydrogen production performance decreases; withincreasing permeability of porous granule, the hydrogen yield increases, while thesubstrate consumption efficiency decreases; with increasing porosity of porous granule,the hydrogen yield slightly decreases, and substrate consumption efficiency increases,and they tend to be stable for porosity over0.5.
⑤The bioreaction in a photo bioreactor with a porous granule immobilizedPSB-cell is investigated with lattice Boltzmann model coupled with the multi-blockmodel at pore-scale. In the simulation, the porous structure of the granule is generatedby Quartet Structure Generation Set,(QSGS). The effect of porosity on flow, masstransfer and hydrogen production performance is studied, and the LB numerical resultsand experimental results have a good agreement. Furthermore, a multi-scale latticeBoltzmann model is proposed to simulate the photo bioreaction in packed bedbioreactor filled with porous granule immobilized PSB-cell, which can obtain the flowand mass transfer in the porous granule on micro-level, as well as save thecomputational cost. Furthermore, the light attenuation in bioreator is considered in thesimulation. The numerical results indicate that the light attenuation mainly occurs in theporous granule, and the output illumination intensity between the LB numerical solutionand the experimental result has a good agreement. Additionally, the hydrogenproduction performance is evaluated, and they agree well with the experimental results,which prove that the multi-scale lattice Boltzmann is viable for simulation of photobioreaction system.
引文
[1] K.Y. Show, Z.P. Zhang, J.H. Tay, D.T. Liang, D.J. Lee, W.J. Jiang. Production of hydrogen in agranular sludge-based anaerobic continuous stirred tank reactor [J]. International Journal ofHydrogen Energy,2007,32(18):4744-4753.
[2] G. Frenette, D. Forthoffer. Economic&commercial viability of hydrogen fuel cell vehiclesfrom an automotive manufacturer perspective [J]. International Journal of Hydrogen Energy,2009,34(9):3578-3588.
[3] V.A. Goltsov, T.N. Veziroglu, L.F. Goltsova. Hydrogen civilization of the future--A newconception of the IAHE [J]. International Journal of Hydrogen Energy,2006,31(2):153-159.
[4] I.P. Jain. Hydrogen the fuel for21st century [J]. International Journal of Hydrogen Energy,2009,34(17):7368-7378.
[5] D.B. Levin, L. Pitt, M. Love. Biohydrogen production: prospects and limitations to practicalapplication [J]. International Journal of Hydrogen Energy,2004,29(2):173-185.
[6] S. Meher Kotay, D. Das. Biohydrogen as a renewable energy resource--Prospects and potentials[J]. International Journal of Hydrogen Energy,2008,33(1):258-263.
[7] D. Das, T.N. Veziro lu. Hydrogen production by biological processes: a survey of literature [J].International Journal of Hydrogen Energy,2001,26(1):13-28.
[8] X.Y. Shi, H.Q. Yu. Response surface analysis on the effect of cell concentration and lightintensity on hydrogen production by Rhodopseudomonas capsulata [J]. Process Biochemistry,2005,40(7):2475-2481.
[9] J. Miyake, M. Miyake, Y. Asada. Biotechnological hydrogen production: research for efficientlight energy conversion [J]. Journal of Biotechnology,1999,70(1):89-101.
[10] I. Akkerman, M. Janssen, J. Rocha, R.H. Wijffels. Photobiological hydrogen production:photochemical efficiency and bioreactor design [J]. International Journal of Hydrogen Energy,2002,27(11-12):1195-1208.
[11] C.Y. Chen, J.S. Chang. Enhancing phototropic hydrogen production by solid-carrier assistedfermentation and internal optical-fiber illumination [J]. Process Biochemistry,2006,41(9):2041-2049.
[12] J. Ding, B.F. Liu, N.Q. Ren, D.F. Xing, W.Q. Guo, J.F. Xu, G.J. Xie. Hydrogen production fromglucose by co-culture of Clostridium Butyricum and immobilized Rhodopseudomonas faecalisRLD-53[J]. International Journal of Hydrogen Energy,2009,34(9):3647-3652.
[13] I.K. Kapdan, F. Kargi. Bio-hydrogen production from waste materials [J]. Enzyme andMicrobial Technology,2006,38(5):569-582.
[14] J.O. Kim, Y.H. Kim, J.Y. Ryu, B.K. Song, I.H. Kim, S.H. Yeom. Immobilization methods forcontinuous hydrogen gas production biofilm formation versus granulation [J]. ProcessBiochemistry,2005,40(3-4):1331-1337.
[15] Q. Liao, Y.J. Wang, Y.Z. Wang, X. Zhu, X. Tian, J. Li. Formation and hydrogen production ofphotosynthetic bacterial biofilm under various illumination conditions [J]. BioresourceTechnology,2010,101(14):5315-5324.
[16] C.N. Lin, S.Y. Wu, J.S. Chang. Fermentative hydrogen production with a draft tube fluidizedbed reactor containing silicone-gel-immobilized anaerobic sludge [J]. International Journal ofHydrogen Energy,2006,31(15):2200-2210.
[17] X. Tian, Q. Liao, W. Liu, Y.Z. Wang, X. Zhu, J. Li, H. Wang. Photo-hydrogen production rate ofa PVA-boric acid gel granule containing immobilized photosynthetic bacteria cells [J].International Journal of Hydrogen Energy,2009,34(11):4708-4717.
[18] C.M. Lee, P.C. Chen, C.C. Wang, Y.C. Tung. Photohydrogen production using purple nonsulfurbacteria with hydrogen fermentation reactor effluent [J]. International Journal of HydrogenEnergy,2002,27(11–12):1309-1313.
[19] Y.J. Wang, Q. Liao, Y.Z. Wang, X. Zhu, J. Li. Effects of flow rate and substrate concentrationon the formation and H2production of photosynthetic bacterial biofilms [J]. BioresourceTechnology,2011,102(13):6902-6908.
[20] G. Kars, U. Gündüz. Towards a super H2producer: Improvements in photofermentativebiohydrogen production by genetic manipulations [J]. International Journal of Hydrogen Energy,2010,35(13):6646-6656.
[21] Z.P. Zhang, K.Y. Show, J.H. Tay, D.T. Liang, D.J. Lee. Biohydrogen production with anaerobicfluidized bed reactors--A comparison of biofilm-based and granule-based systems [J].International Journal of Hydrogen Energy,2008,33(5):1559-1564.
[22] C. Zhang, X. Zhu, Q. Liao, Y.Z. Wang, J. Li, Y.D. Ding, H. Wang. Performance of agroove-type photobioreactor for hydrogen production by immobilized photosynthetic bacteria[J]. International Journal of Hydrogen Energy,2010,35(11):5284-5292.
[23] Y.Z. Wang, Q. Liao, X. Zhu, X. Tian, C. Zhang. Characteristics of hydrogen production andsubstrate consumption of Rhodopseudomonas palustris CQK01in an immobilized-cellphotobioreactor [J]. Bioresource Technology,2010,101(11):4034-4041.
[24] X. Tian, Q. Liao, X. Zhu, Y.Z. Wang, P. Zhang, J. Li, H. Wang. Characteristics of a biofilmphotobioreactor as applied to photo-hydrogen production [J]. Bioresource Technology,2010,101(3):977-983.
[25] Y.Y. Yan. Recent advances in computational simulation of macro-, meso-, and micro-scalebiomimetics related fluid flow problems [J]. Journal of Bionic Engineering,2007,4(2):97-107.
[26] I. Banerjee, J.M. Modak, K. Bandopadhyay, D. Das, B.R. Maiti. Mathematical model forevaluation of mass transfer limitations in phenol biodegradation by immobilized Pseudomonasputida [J]. Journal of Biotechnology,2001,87(3):211-223.
[27] A.Y. Dursun, O. Tepe. Internal mass transfer effect on biodegradation of phenol by Ca-alginateimmobilized Ralstonia eutropha [J]. Journal of Hazardous Materials,2005,126(1-3):105-111.
[28] T.Y. Hsien, Y.H. Lin. Biodegradation of phenolic wastewater in a fixed biofilm reactor [J].Biochemical Engineering Journal,2005,27(2):95-103.
[29] Q. Liao, D.M. Liu, D.D. Ye, X. Zhu, D.J. Lee. Mathematical modeling of two-phase flow andtransport in an immobilized-cell photobioreactor [J]. International Journal of Hydrogen Energy,2011,36(21):13939-13948.
[30] Y.H. Lin, J.Y. Leu, C.R. Lan, P.H.P. Lin, F.L. Chang. Kinetics of inorganic carbon utilization bymicroalgal biofilm in a flat plate photoreactor [J]. Chemosphere,2003,53(7):779-787.
[31] O. Tepe, A.Y. Dursun. Combined effects of external mass transfer and biodegradation rates onremoval of phenol by immobilized Ralstonia eutropha in a packed bed reactor [J]. Journal ofHazardous Materials,2008,151(1):9-16.
[32] J. Obeid, J.P. Magnin, J.M. Flaus, O. Adrot, J.C. Willison, R. Zlatev. Modelling of hydrogenproduction in batch cultures of the photosynthetic bacterium Rhodobacter capsulatus [J].International Journal of Hydrogen Energy,2009,34(1):180-185.
[33] X. Wang, J. Ding, N.Q. Ren, B.F. Liu, W.Q. Guo. CFD simulation of an expanded granularsludge bed (EGSB) reactor for biohydrogen production [J]. International Journal of HydrogenEnergy,2009,34(24):9686-9695.
[34] D. Das, P.K. Badri, N. Kumar, P. Bhattacharya. Simulation and modeling of continuous H2production process by Enterobacter cloacae IIT-BT08using different bioreactor configuration[J]. Enzyme and Microbial Technology,2002,31(6):867-875.
[35] G. Spigno, M. Zilli, C. Nicolella. Mathematical modelling and simulation of phenol degradationin biofilters [J]. Biochemical Engineering Journal,2004,19(3):267-275.
[36] Q. Liao, Y.J. Wang, Y.Z. Wang, R. Chen, X. Zhu, Y.K. Pu, D.J. Lee. Two-dimensionmathematical modeling of photosynthetic bacterial biofilm growth and formation [J].International Journal of Hydrogen Energy,2012,37(20):15607-15615.
[37] Y. Pomeau.20Years of Lattice Dynamics: A Personal View [J]. International Journal of ModernPhysics C,2007,18(4):437.
[38] S. Succi. The lattice Boltzmann equation For Fluid Dynamics and Beyond [M]. Oxford: OxfordUniversity Press,2001.
[39]郭照立，郑楚光.格子Boltzmann方法的原理及应用[M].北京;科学出版社.2008.
[40]郭照立，郑楚光，李青，王能超.流体动力学的格子Boltzmann方法[M].武汉;湖北科学技术出版社.2002.
[41]何雅玲，王勇，李庆.格子Boltzmann方法的理论及应用[M].北京;科学出版社.2008.
[42] J. Hardy, O. De Pazzis, Y. Pomeau. Molecular dynamics of a classical lattice gas: Transportproperties and time correlation functions [J]. Physical Review A,1976,13(5):1949-1961.
[43] J. Hardy, Y. Pomeau, O. De Pazzis. Time evolution of a two-dimensional model system. I.Invariant states and time correlation functions [J]. Journal of Mathematical Physics,1973,14(12):1746-1759.
[44] U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet. Lattice gashydrodynamics in two and three dimensions [J]. Complex Systems,1987,1(4):649-707.
[45] U. Frisch, B. Hasslacher, Y. Pomeau. Lattice-gas automata for the Navier-Stokes equation [J].Physical Review Letters,1986,56(14):1505-1508.
[46] G.R. McNamara, G. Zanetti. Use of the Boltzmann equation to simulate lattice-gas automata [J].Physical Review Letters,1988,61(20):2332-2335.
[47]F.J. Higuera, J. Jimenez. Boltzmann approach to lattice gas simulations [J]. Europhysics Letters,2007,9(7):663-668.
[48] F.J. Higuera, S. Succi, R. Benzi. Lattice gas dynamics with enhanced collisions [J]. EurophysicsLetters,2007,9(4):345-349.
[49] S. Chen, H. Chen, D. Martnez, W. Matthaeus. Lattice Boltzmann model for simulation ofmagnetohydrodynamics [J]. Physical Review Letters,1991,67(27):3776-3779.
[50] Y.H. Qian, D. d'Humieres, P. Lallemand. Lattice BGK models for Navier-Stokes equation [J].Europhysics Letters,1992,17(6):479.
[51] P.L. Bhatnagar, E.P. Gross, M. Krook. A model for collision processes in gases. I. Smallamplitude processes in charged and neutral one-component systems [J]. Physical Review A,1954,94(3):511-525.
[52] C. Chang, C.H. Liu, C.A. Lin. Boundary conditions for lattice Boltzmann simulations withcomplex geometry flows [J]. Computers&Mathematics with Applications,2009,58(5):940-949.
[53] R.R. Nourgaliev, T.N. Dinh, T.G. Theofanous, D. Joseph. The lattice Boltzmann equationmethod: theoretical interpretation, numerics and implications [J]. International Journal ofMultiphase Flow,2003,29(1):117-169.
[54] D. Raabe. Overview of the lattice Boltzmann method for nano-and microscale fluid dynamicsin materials science and engineering [J]. Modelling and Simulation in Materials Science andEngineering,2004,12(6): R13.
[55] M.C. Sukop, D.T. Thorne. Lattice Boltzmann modeling: An introduction for geoscientists andengineers [M]. Springer Verlag,2006.
[56] L. Amaya Bower, T. Lee. Numerical simulation of single bubble rising in vertical and inclinedsquare channel using lattice Boltzmann method [J]. Chemical Engineering Science,2011,66(5):935-952.
[57] H.X. Bai, P. Yu, S.H. Winoto, H.T. Low. Lattice Boltzmann method for flows in porous andhomogenous fluid domains coupled at the interface by stress jump [J]. International Journal forNumerical Methods in Fluids,2009,60(6):691-708.
[58] L. Biferale, P. Perlekar, M. Sbragaglia, F. Toschi. Convection in multiphase fluid flows usinglattice Boltzmann methods [J]. Physical Review Letters,2012,108(10):104502.
[59] Z. Chai, Z. Guo, B. Shi. Study of electro-osmotic flows in microchannels packed with variableporosity media via lattice Boltzmann method [J]. Journal of Applied Physics,2007,101(10):104913-104913-8.
[60] Z. Dong, W. Li, Y. Song. A numerical investigation of bubble growth on and departure from asuperheated wall by lattice Boltzmann method [J]. International Journal of Heat and MassTransfer,2010,53(21-22):4908-4916.
[61] M.M. Dupin, I. Halliday, C.M. Care. A multi-component lattice Boltzmann scheme: towards themesoscale simulation of blood flow [J]. Medical Engineering&Physics,2006,28(1):13-18.
[62] M.M. Dupin, I. Halliday, C.M. Care, L. Alboul, L.L. Munn. Modeling the flow of densesuspensions of deformable particles in three dimensions [J]. Physical Review E,2007,75(6):066707.
[63] Z. Guo, T.S. Zhao. A lattice Boltzmann model for convection heat transfer in porous media [J].Numerical Heat Transfer, Part B,2005,47(2):157-177.
[64] Z.L. Guo, T.S. Zhao. Lattice Boltzmann model for incompressible flows through porous media[J]. Physical Review E,2002,66(3):036304.
[65] A. H lzer, M. Sommerfeld. Lattice Boltzmann simulations to determine drag, lift and torqueacting on non-spherical particles [J]. Computers&Fluids,2009,38(3):572-589.
[66] X.Y. Kang, Q. Liao, X. Zhu, Y.X. Yang. Non-equilibrium extrapolation method in the latticeBoltzmann simulations of flows with curved boundaries (non-equilibrium extrapolation ofLBM)[J]. Applied Thermal Engineering,2010,30(13):1790-1796.
[67] F. Khan, F. Enzmann, M. Kersten, A. Wiegmann, K. Steiner.3D simulation of the permeabilitytensor in a soil aggregate on basis of nanotomographic imaging and LBE solver [J]. Journal ofSoils and Sediments,2012,12(1):86-96.
[68] N. Verma, D. Mewes, A. Luke. Lattice Boltzmann study of velocity, temperature, andconcentration in micro-reactors [J]. International Journal of Heat and Mass Transfer,2010,53(15):3175-3185.
[69] Y.X. Yang, Q. Liao, X. Zhu, H. Wang, R. Wu, D.J. Lee. Lattice Boltzmann simulation ofsubstrate flow past a cylinder with PSB biofilm for bio-hydrogen production [J]. InternationalJournal of Hydrogen Energy,2011,36(21):14031-14040.
[70] T. Zeiser, P. Lammers, E. Klemm, Y.W. Li, J. Bernsdorf, G. Brenner. CFD-calculation of flow,dispersion and reaction in a catalyst filled tube by the lattice Boltzmann method [J]. ChemicalEngineering Science,2001,56(4):1697-1704.
[71] B. Chopard, P.O. Luthi. Lattice Boltzmann computations and applications to physics [J].Theoretical Computer Science,1999,217(1):115-130.
[72] S. Chen, G.D. Doolen. Lattice Boltzmann method for fluid flows [J]. Annual Review of FluidMechanics,1998,30(1):329-364.
[73] O. Filippova, D. H nel. Grid refinement for lattice-BGK models [J]. Journal of ComputationalPhysics,1998,147(1):219-228.
[74] R.W. Mei, D.Z. Yu, W. Shyy, L.S. Luo. Force evaluation in the lattice Boltzmann methodinvolving curved geometry [J]. Physical Review E,2002,65(4):041203.
[75] Y. Xu, Y. Liu, Y. Xia, F. Wu. Lattice-Boltzmann simulation of two-dimensional flow over twovibrating side-by-side circular cylinders [J]. Physical Review E,2008,78(4):046314.
[76] A. Mussa, P. Asinari, L.S. Luo. Lattice Boltzmann simulations of2D laminar flows past twotandem cylinders [J]. Journal of Computational Physics,2009,228(4):983-999.
[77] X.W. Shan. Simulation of Rayleigh-Benard convection using a lattice Boltzmann method [J].Physical Review E,1997,55(3):2780.
[78] G.W. Yan, Y.S. Chen, S.X. Hu. Simple lattice Boltzmann model for simulating flows with shockwave [J]. Physical Review E,1999,59(1):454-459.
[79] Y. Liu, J. Cui, Y.X. Jiang, W.Z. Li. A numerical study on heat transfer performance ofmicrochannels with different surface microstructures [J]. Applied Thermal Engineering,2011,31(5):921-931.
[80] Y.Y. Yan, Y.Q. Zu. Numerical simulation of heat transfer and fluid flow past a rotatingisothermal cylinder-A LBM approach [J]. International Journal of Heat and Mass Transfer,2008,51(9-10):2519-2536.
[81] M. Wang, J.K. Wang, N. Pan, S.Y. Chen. Mesoscopic predictions of the effective thermalconductivity for microscale random porous media [J]. Physical Review E,2007,75(3):036702.
[82] E.G. FlekkZy. Lattice Bhatnagar-Gross-Krook models for miscible fluids [J]. Physical ReviewE,1993,47(6):4247.
[83] N. Jeong, D.H. Choi, C.L. Lin. Estimation of thermal and mass diffusivity in a porous mediumof complex structure using a lattice Boltzmann method [J]. International Journal of Heat andMass Transfer,2008,51(15):3913-3923.
[84] Q. Li, K. Zhao, Y.M. Xuan. Simulation of flow and heat transfer with evaporation in a porouswick of a CPL evaporator on pore scale by lattice Boltzmann method [J]. International Journalof Heat and Mass Transfer,2011,54(13-14):2890-2901.
[85] S. Bekri, P.M. Adler. Dispersion in multiphase flow through porous media [J]. InternationalJournal of Multiphase Flow,2002,28(4):665-697.
[86] S.H. Kim, H. Pitsch, I.D. Boyd. Lattice Boltzmann modeling of multicomponent diffusion innarrow channels [J]. Physical Review E,2009,79(1):016702.
[87] J. Onishi, Y. Chen, H. Ohashi. Dynamic simulation of multi-component viscoelastic fluidsusing the lattice Boltzmann method [J]. Physica A: Statistical Mechanics and its Applications,2006,362(1):84-92.
[88] X. Shan, H. Chen. Lattice Boltzmann model for simulating flows with multiple phases andcomponents [J]. Physical Review E,1993,47(3):1815.
[89] X. Shan, G. Doolen. Diffusion in a multicomponent lattice Boltzmann equation model [J].Physical Review E,1996,54(4):3614.
[90] Z.L. Yang, T.N. Dinh, R.R. Nourgaliev, B.R. Sehgal. Numerical investigation of bubble growthand detachment by the lattice-Boltzmann method [J]. International Journal of Heat and MassTransfer,2001,44(1):195-206.
[91] J.G. Zhou. A lattice Boltzmann method for solute transport [J]. International Journal forNumerical Methods in Fluids,2009,61(8):848-863.
[92] X. He, S. Chen, R. Zhang. A lattice Boltzmann scheme for incompressible multiphase flow andits application in simulation of Rayleigh-Taylor instability [J]. Journal of ComputationalPhysics,1999,152(2):642-663.
[93] X. Shan, G. Doolen. Multicomponent lattice-Boltzmann model with interparticle interaction [J].Journal of Statistical Physics,1995,81(1):379-393.
[94] Y. Gao, X. Zhang, P. Rama, Y. Liu, R. Chen, H. Ostadi, K. Jiang. Calculating the AnisotropicPermeability of Porous Media Using the Lattice Boltzmann Method and X-ray ComputedTomography [J]. Transport in Porous Media,2012,92(2):457-472
[95] N. Verma, D. Mewes. Lattice Boltzmann methods for simulation of micro and macrotransportin a packed bed of porous adsorbents under non-isothermal condition [J]. Computers&Mathematics with Applications,2009,58(5):1003-1014.
[96] X. Wang, B. Chen, J. Wu. A semianalytical solution of periodical electro-osmosis in arectangular microchannel [J]. Physics of Fluids,2007,19(12):127101.
[97] A. Gabrielli, S. Succi, E. Kaxiras. A lattice Boltzmann study of reactive microflows [J].Computer Physics Communications,2002,147(1-2):516-521.
[98] Z.W. Tian, C. Zou, H.J. Liu, Z.L. Guo, Z.H. Liu, C.G. Zheng. Lattice Boltzmann scheme forsimulating thermal micro-flow [J]. Physica A: Statistical Mechanics and its Applications,2007,385(1):59-68.
[99] M. Spasov, D. Rempfer, P. Mokhasi. Simulation of a turbulent channel flow with an entropicLattice Boltzmann method [J]. International Journal for Numerical Methods in Fluids,2009,60(11):1241-1258.
[100] D.Z. Yu, S.S. Girimaji. Multi-block Lattice Boltzmann method: Extension to3D andvalidation in turbulence [J]. Physica A: Statistical Mechanics and its Applications,2006,362(1):118-124.
[101] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman. Mechanisms of heat flow insuspensions of nano-sized particles (nanofluids)[J]. International Journal of Heat and MassTransfer,2002,45(4):855-863.
[102] R.M. MacMeccan, J.R. Clausen, G.P. Neitzel, C.K. Aidun. Simulating deformable particlesuspensions using a coupled lattice-Boltzmann and finite-element method [J]. Journal of FluidMechanics,2009,618(1):13-39.
[103] Z.G. Feng, E.E. Michaelides. Interparticle forces and lift on a particle attached to a solidboundary in suspension flow [J]. Physics of Fluids,2002,14(1):49-60.
[104] A.J.C. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmannequation. Part1. Theoretical foundation [J]. Journal of Fluid Mechanics,1994,271(1):285-309.
[105] A.J.C. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmannequation. Part2. Numerical results [J]. Journal of Fluid Mechanics,1994,271(1):311-339.
[106] S. Chen, S.P. Dawson, G.D. Doolen, D.R. Janecky, A. Lawniczak. Lattice methods andtheir applications to reacting systems [J]. Computers&Chemical Engineering,1995,19(6):617-646.
[107] H. Yu, L.S. Luo, S. Girimaji. Scalar mixing and chemical reaction simulations using latticeBoltzmann method [J]. International Journal of Computational Engineering Science,2002,3(1):73-87.
[108] X.M. Yu, B.C. Shi. A lattice Boltzmann model for reaction dynamical systems with timedelay [J]. Applied Mathematics and Computation,2006,181(2):958-965.
[109] A. Nabovati, E.W. Llewellin, A. Sousa. A general model for the permeability of fibrousporous media based on fluid flow simulations using the lattice Boltzmann method [J].Composites: Part A,2009,40(6):860-869.
[110] D. Gao, Z. Chen. Lattice Boltzmann simulation of natural convection dominated meltingin a rectangular cavity filled with porous media [J]. International Journal of Thermal Sciences,2011,50(4):493-501.
[111] H. Shokouhmand, F. Jam, M.R. Salimpour. The effect of porous insert position on theenhanced heat transfer in partially filled channels [J]. International Communications in Heatand Mass Transfer,2011,38(8):1162-1167.
[112] N. Verma, K. Salem, D. Mewes. Simulation of micro-and macro-transport in a packed bedof porous adsorbents by lattice Boltzmann methods [J]. Chemical Engineering Science,2007,62(14):3685-3698.
[113] M. Raúl. Numerical simulations of surface reaction in porous media with latticeBoltzmann [J]. Chemical Engineering Science,2012,69(1):628-643.
[114] S.P. Sullivan, L.F. Gladden, M.L. Johns.3D chemical reactor LB simulations [J].Mathematics and Computers in Simulation,2006,72(2-6):206-211.
[115] S.P. Sullivan, F.M. Sani, M.L. Johns, L.F. Gladden. Simulation of packed bed reactorsusing lattice Boltzmann methods [J]. Chemical Engineering Science,2005,60(12):3405-3418.
[116] K. Yamamoto, N. Takada, M. Misawa. Combustion simulation with Lattice Boltzmannmethod in a three-dimensional porous structure [J]. Proceedings of the Combustion Institute,2005,30(1):1509-1515.
[117] M. Selzer, M. Jainta, B. Nestler. A Lattice Boltzmann model to simulate the growth ofdendritic and eutectic microstructures under the influence of fluid flow [J]. Physica StatusSolidi B2009,246(6):1197-1205.
[118] D.A. von der Schulenburg, T.R.R. Pintelon, C. Picioreanu, M.C.M. Van Loosdrecht, M.L.Johns. Three‐dimensional simulations of biofilm growth in porous media [J]. AIChE Journal,2009,55(2):494-504.
[119] D. Alemani, F. Pappalardo, M. Pennisi, S. Motta, V. Brusic. Combining cellular automataand lattice Boltzmann method to model multiscale avascular tumor growth coupled withnutrient diffusion and immune competition [J]. Journal of Immunological Methods,2012,376(1-2):55-68.
[120] Q. Kang, D. Zhang, S. Chen. Unified lattice Boltzmann method for flow in multiscaleporous media [J]. Physical Review E,2002,66(5):056307.
[121] S. Succi, O. Filippova, G. Smith, E. Kaxiras. Applying the lattice Boltzmann equation tomultiscale fluid problems [J]. Computing in Science&Engineering,2001,3(6):26-37.
[122] M.A. Van der Hoef, M. van Sint Annaland, J.A.M. Kuipers. Computational fluid dynamicsfor dense gas-solid fluidized beds: a multi-scale modeling strategy [J]. Chemical EngineeringScience,2004,59(22):5157-5165.
[123] Y. Wang, J.G. Brasseur, G.G. Banco, A.G. Webb, A.C. Ailiani, T. Neuberger. A multiscalelattice Boltzmann model of macro-to micro-scale transport, with applications to gut function [J].Philosophical Transactions of the Royal Society A,2010,368(1921):2863-2880.
[124] T.D. Scheibe, A.M. Tartakovsky, D.M. Tartakovsky, G.D. Redden, P. Meakin, B.J. Palmer,K.L. Schuchardt. Hybrid numerical methods for multiscale simulations of subsurfacebiogeochemical processes [J]. Journal of Physics: Conference Series,2008,125(1):012054.
[125] W.C. Sun, J.E. Andrade, J.W. Rudnicki. Multiscale method for characterization of porousmicrostructures and their impact on macroscopic effective permeability [J]. InternationalJournal for Numerical Methods in Engineering,2011,88(12):1260-1279.
[126] X. He, L.S. Luo. A priori derivation of the lattice Boltzmann equation [J]. Physical ReviewE,1997,55(6):6333-6336.
[127] X. He, L.S. Luo. Theory of the lattice Boltzmann method: From the Boltzmann equation tothe lattice Boltzmann equation [J]. Physical Review E,1997,56(6):6811.
[128] Z.L. Guo, B.C. Shi, N.C. Wang. Lattice BGK model for incompressible Navier-Stokesequation [J]. Journal of Computational Physics,2000,165(1):288-306.
[129] S. Chen, D. Martinez, R. Mei. On boundary conditions in lattice Boltzmann methods [J].Physics of Fluids,1996,8(9):2527-2536.
[130] Z.L. Guo, C.G. Zheng, B.C. Shi. An extrapolation method for boundary conditions inlattice Boltzmann method [J]. Physics of Fluids,2002,14(6):2007.
[131] X. He, Q. Zou, L.S. Luo, M. Dembo. Analytic solutions of simple flows and analysis ofnonslip boundary conditions for the lattice Boltzmann BGK model [J]. Journal of StatisticalPhysics,1997,87(1):115-136.
[132] X.Y. He, G. Doolen. Lattice Boltzmann method on curvilinear coordinates system: flowaround a circular cylinder [J]. Journal of Computational Physics,1997,134(2):306-315.
[133] P.H. Kao, R.J. Yang. An investigation into curved and moving boundary treatments in thelattice Boltzmann method [J]. Journal of Computational Physics,2008,227(11):5671-5690.
[134] R. Mei, L.S. Luo, W. Shyy. An accurate curved boundary treatment in the latticeBoltzmann method [J]. Journal of Computational Physics,1999,155(2):307-330.
[135] G.H. Tang, W.Q. Tao, Y.L. He. Thermal boundary condition for the thermal latticeBoltzmann equation [J]. Physical Review E,2005,72(1):016703.
[136] Q. Zou, X. He. On pressure and velocity boundary conditions for the lattice BoltzmannBGK model [J]. Physics of Fluids,1997,9(6):1591-1598.
[137] D.P. Ziegler. Boundary conditions for lattice Boltzmann simulations [J]. Journal ofStatistical Physics,1993,71(5):1171-1177.
[138] D.R. Noble, S. Chen, J.G. Georgiadis, R.O. Buckius. A consistent hydrodynamic boundarycondition for the lattice Boltzmann method [J]. Physics of Fluids,1995,7(1):203-209.
[139] D.R. Noble, J.G. Georgiadis, R.O. Buckius. Direct assessment of lattice Boltzmannhydrodynamics and boundary conditions for recirculating flows [J]. Journal of StatisticalPhysics,1995,81(1):17-33.
[140]杨艳霞,廖强,朱恂,王宏,丁玉栋.绕流具有光合生化反应管束的格子Boltzmann模拟[J].化工学报,2012,63(8):2383-2391.
[141] M. Sch fer, S. Turek, F. Durst, E. Krause, R. Rannacher. Benchmark computations oflaminar flow around a cylinder [J]. Notes on numerical fluid mechanics,1996,52(547-566.
[142]刘大猛.含生化反应的固定化细胞光生物制氢反应器内的多相传输模型[D],2010.
[143] A. Dupuis, B. Chopard. Theory and applications of an alternative lattice Boltzmann gridrefinement algorithm [J]. Physical Review E,2003,67(6):066707.
[144] C.L. Lin, Y.G. Lai. Lattice Boltzmann method on composite grids [J]. Physical Review E,2000,62(2):2219.
[145] D.Z. Yu, R.W. Mei, W. Shyy. A multi‐block lattice Boltzmann method for viscous fluidflows [J]. International Journal for Numerical Methods in Fluids,2002,39(2):99-120.
[146] H. Farhat, W. Choi, J.S. Lee. Migrating multi-block lattice Boltzmann model forimmiscible mixtures:3D algorithm development and validation [J]. Computers&Fluids,2010,39(8):1284-1295.
[147] M. Pilotti. Generation of realistic porous media by grains sedimentation [J]. Transport inPorous Media,1998,33(3):257-278.
[148] R.S. Maier, D.M. Kroll, R.S. Bernard, S.E. Howington, J.F. Peters, H.T. Davis. Pore-scalesimulation of dispersion [J]. Physics of Fluids,2000,12(8):2065.
[149] M. Madadi, M. Sahimi. Lattice Boltzmann simulation of fluid flow in fracture networkswith rough, self-affine surfaces [J]. Physical Review E,2003,67(2):026309.
[150] H. Zhang, X. Ge, H. Ye. Randomly mixed model for predicting the effective thermalconductivity of moist porous media [J]. Journal of Physics D: Applied Physics,2005,39(1):220-226.
[151]王永忠.固定化光合细菌光生物制氢反应器传输与产氢特性[D];重庆大学,2008.
[2] G. Frenette, D. Forthoffer. Economic&commercial viability of hydrogen fuel cell vehiclesfrom an automotive manufacturer perspective [J]. International Journal of Hydrogen Energy,2009,34(9):3578-3588.
[3] V.A. Goltsov, T.N. Veziroglu, L.F. Goltsova. Hydrogen civilization of the future--A newconception of the IAHE [J]. International Journal of Hydrogen Energy,2006,31(2):153-159.
[4] I.P. Jain. Hydrogen the fuel for21st century [J]. International Journal of Hydrogen Energy,2009,34(17):7368-7378.
[5] D.B. Levin, L. Pitt, M. Love. Biohydrogen production: prospects and limitations to practicalapplication [J]. International Journal of Hydrogen Energy,2004,29(2):173-185.
[6] S. Meher Kotay, D. Das. Biohydrogen as a renewable energy resource--Prospects and potentials[J]. International Journal of Hydrogen Energy,2008,33(1):258-263.
[7] D. Das, T.N. Veziro lu. Hydrogen production by biological processes: a survey of literature [J].International Journal of Hydrogen Energy,2001,26(1):13-28.
[8] X.Y. Shi, H.Q. Yu. Response surface analysis on the effect of cell concentration and lightintensity on hydrogen production by Rhodopseudomonas capsulata [J]. Process Biochemistry,2005,40(7):2475-2481.
[9] J. Miyake, M. Miyake, Y. Asada. Biotechnological hydrogen production: research for efficientlight energy conversion [J]. Journal of Biotechnology,1999,70(1):89-101.
[10] I. Akkerman, M. Janssen, J. Rocha, R.H. Wijffels. Photobiological hydrogen production:photochemical efficiency and bioreactor design [J]. International Journal of Hydrogen Energy,2002,27(11-12):1195-1208.
[11] C.Y. Chen, J.S. Chang. Enhancing phototropic hydrogen production by solid-carrier assistedfermentation and internal optical-fiber illumination [J]. Process Biochemistry,2006,41(9):2041-2049.
[12] J. Ding, B.F. Liu, N.Q. Ren, D.F. Xing, W.Q. Guo, J.F. Xu, G.J. Xie. Hydrogen production fromglucose by co-culture of Clostridium Butyricum and immobilized Rhodopseudomonas faecalisRLD-53[J]. International Journal of Hydrogen Energy,2009,34(9):3647-3652.
[13] I.K. Kapdan, F. Kargi. Bio-hydrogen production from waste materials [J]. Enzyme andMicrobial Technology,2006,38(5):569-582.
[14] J.O. Kim, Y.H. Kim, J.Y. Ryu, B.K. Song, I.H. Kim, S.H. Yeom. Immobilization methods forcontinuous hydrogen gas production biofilm formation versus granulation [J]. ProcessBiochemistry,2005,40(3-4):1331-1337.
[15] Q. Liao, Y.J. Wang, Y.Z. Wang, X. Zhu, X. Tian, J. Li. Formation and hydrogen production ofphotosynthetic bacterial biofilm under various illumination conditions [J]. BioresourceTechnology,2010,101(14):5315-5324.
[16] C.N. Lin, S.Y. Wu, J.S. Chang. Fermentative hydrogen production with a draft tube fluidizedbed reactor containing silicone-gel-immobilized anaerobic sludge [J]. International Journal ofHydrogen Energy,2006,31(15):2200-2210.
[17] X. Tian, Q. Liao, W. Liu, Y.Z. Wang, X. Zhu, J. Li, H. Wang. Photo-hydrogen production rate ofa PVA-boric acid gel granule containing immobilized photosynthetic bacteria cells [J].International Journal of Hydrogen Energy,2009,34(11):4708-4717.
[18] C.M. Lee, P.C. Chen, C.C. Wang, Y.C. Tung. Photohydrogen production using purple nonsulfurbacteria with hydrogen fermentation reactor effluent [J]. International Journal of HydrogenEnergy,2002,27(11–12):1309-1313.
[19] Y.J. Wang, Q. Liao, Y.Z. Wang, X. Zhu, J. Li. Effects of flow rate and substrate concentrationon the formation and H2production of photosynthetic bacterial biofilms [J]. BioresourceTechnology,2011,102(13):6902-6908.
[20] G. Kars, U. Gündüz. Towards a super H2producer: Improvements in photofermentativebiohydrogen production by genetic manipulations [J]. International Journal of Hydrogen Energy,2010,35(13):6646-6656.
[21] Z.P. Zhang, K.Y. Show, J.H. Tay, D.T. Liang, D.J. Lee. Biohydrogen production with anaerobicfluidized bed reactors--A comparison of biofilm-based and granule-based systems [J].International Journal of Hydrogen Energy,2008,33(5):1559-1564.
[22] C. Zhang, X. Zhu, Q. Liao, Y.Z. Wang, J. Li, Y.D. Ding, H. Wang. Performance of agroove-type photobioreactor for hydrogen production by immobilized photosynthetic bacteria[J]. International Journal of Hydrogen Energy,2010,35(11):5284-5292.
[23] Y.Z. Wang, Q. Liao, X. Zhu, X. Tian, C. Zhang. Characteristics of hydrogen production andsubstrate consumption of Rhodopseudomonas palustris CQK01in an immobilized-cellphotobioreactor [J]. Bioresource Technology,2010,101(11):4034-4041.
[24] X. Tian, Q. Liao, X. Zhu, Y.Z. Wang, P. Zhang, J. Li, H. Wang. Characteristics of a biofilmphotobioreactor as applied to photo-hydrogen production [J]. Bioresource Technology,2010,101(3):977-983.
[25] Y.Y. Yan. Recent advances in computational simulation of macro-, meso-, and micro-scalebiomimetics related fluid flow problems [J]. Journal of Bionic Engineering,2007,4(2):97-107.
[26] I. Banerjee, J.M. Modak, K. Bandopadhyay, D. Das, B.R. Maiti. Mathematical model forevaluation of mass transfer limitations in phenol biodegradation by immobilized Pseudomonasputida [J]. Journal of Biotechnology,2001,87(3):211-223.
[27] A.Y. Dursun, O. Tepe. Internal mass transfer effect on biodegradation of phenol by Ca-alginateimmobilized Ralstonia eutropha [J]. Journal of Hazardous Materials,2005,126(1-3):105-111.
[28] T.Y. Hsien, Y.H. Lin. Biodegradation of phenolic wastewater in a fixed biofilm reactor [J].Biochemical Engineering Journal,2005,27(2):95-103.
[29] Q. Liao, D.M. Liu, D.D. Ye, X. Zhu, D.J. Lee. Mathematical modeling of two-phase flow andtransport in an immobilized-cell photobioreactor [J]. International Journal of Hydrogen Energy,2011,36(21):13939-13948.
[30] Y.H. Lin, J.Y. Leu, C.R. Lan, P.H.P. Lin, F.L. Chang. Kinetics of inorganic carbon utilization bymicroalgal biofilm in a flat plate photoreactor [J]. Chemosphere,2003,53(7):779-787.
[31] O. Tepe, A.Y. Dursun. Combined effects of external mass transfer and biodegradation rates onremoval of phenol by immobilized Ralstonia eutropha in a packed bed reactor [J]. Journal ofHazardous Materials,2008,151(1):9-16.
[32] J. Obeid, J.P. Magnin, J.M. Flaus, O. Adrot, J.C. Willison, R. Zlatev. Modelling of hydrogenproduction in batch cultures of the photosynthetic bacterium Rhodobacter capsulatus [J].International Journal of Hydrogen Energy,2009,34(1):180-185.
[33] X. Wang, J. Ding, N.Q. Ren, B.F. Liu, W.Q. Guo. CFD simulation of an expanded granularsludge bed (EGSB) reactor for biohydrogen production [J]. International Journal of HydrogenEnergy,2009,34(24):9686-9695.
[34] D. Das, P.K. Badri, N. Kumar, P. Bhattacharya. Simulation and modeling of continuous H2production process by Enterobacter cloacae IIT-BT08using different bioreactor configuration[J]. Enzyme and Microbial Technology,2002,31(6):867-875.
[35] G. Spigno, M. Zilli, C. Nicolella. Mathematical modelling and simulation of phenol degradationin biofilters [J]. Biochemical Engineering Journal,2004,19(3):267-275.
[36] Q. Liao, Y.J. Wang, Y.Z. Wang, R. Chen, X. Zhu, Y.K. Pu, D.J. Lee. Two-dimensionmathematical modeling of photosynthetic bacterial biofilm growth and formation [J].International Journal of Hydrogen Energy,2012,37(20):15607-15615.
[37] Y. Pomeau.20Years of Lattice Dynamics: A Personal View [J]. International Journal of ModernPhysics C,2007,18(4):437.
[38] S. Succi. The lattice Boltzmann equation For Fluid Dynamics and Beyond [M]. Oxford: OxfordUniversity Press,2001.
[39]郭照立，郑楚光.格子Boltzmann方法的原理及应用[M].北京;科学出版社.2008.
[40]郭照立，郑楚光，李青，王能超.流体动力学的格子Boltzmann方法[M].武汉;湖北科学技术出版社.2002.
[41]何雅玲，王勇，李庆.格子Boltzmann方法的理论及应用[M].北京;科学出版社.2008.
[42] J. Hardy, O. De Pazzis, Y. Pomeau. Molecular dynamics of a classical lattice gas: Transportproperties and time correlation functions [J]. Physical Review A,1976,13(5):1949-1961.
[43] J. Hardy, Y. Pomeau, O. De Pazzis. Time evolution of a two-dimensional model system. I.Invariant states and time correlation functions [J]. Journal of Mathematical Physics,1973,14(12):1746-1759.
[44] U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet. Lattice gashydrodynamics in two and three dimensions [J]. Complex Systems,1987,1(4):649-707.
[45] U. Frisch, B. Hasslacher, Y. Pomeau. Lattice-gas automata for the Navier-Stokes equation [J].Physical Review Letters,1986,56(14):1505-1508.
[46] G.R. McNamara, G. Zanetti. Use of the Boltzmann equation to simulate lattice-gas automata [J].Physical Review Letters,1988,61(20):2332-2335.
[47]F.J. Higuera, J. Jimenez. Boltzmann approach to lattice gas simulations [J]. Europhysics Letters,2007,9(7):663-668.
[48] F.J. Higuera, S. Succi, R. Benzi. Lattice gas dynamics with enhanced collisions [J]. EurophysicsLetters,2007,9(4):345-349.
[49] S. Chen, H. Chen, D. Martnez, W. Matthaeus. Lattice Boltzmann model for simulation ofmagnetohydrodynamics [J]. Physical Review Letters,1991,67(27):3776-3779.
[50] Y.H. Qian, D. d'Humieres, P. Lallemand. Lattice BGK models for Navier-Stokes equation [J].Europhysics Letters,1992,17(6):479.
[51] P.L. Bhatnagar, E.P. Gross, M. Krook. A model for collision processes in gases. I. Smallamplitude processes in charged and neutral one-component systems [J]. Physical Review A,1954,94(3):511-525.
[52] C. Chang, C.H. Liu, C.A. Lin. Boundary conditions for lattice Boltzmann simulations withcomplex geometry flows [J]. Computers&Mathematics with Applications,2009,58(5):940-949.
[53] R.R. Nourgaliev, T.N. Dinh, T.G. Theofanous, D. Joseph. The lattice Boltzmann equationmethod: theoretical interpretation, numerics and implications [J]. International Journal ofMultiphase Flow,2003,29(1):117-169.
[54] D. Raabe. Overview of the lattice Boltzmann method for nano-and microscale fluid dynamicsin materials science and engineering [J]. Modelling and Simulation in Materials Science andEngineering,2004,12(6): R13.
[55] M.C. Sukop, D.T. Thorne. Lattice Boltzmann modeling: An introduction for geoscientists andengineers [M]. Springer Verlag,2006.
[56] L. Amaya Bower, T. Lee. Numerical simulation of single bubble rising in vertical and inclinedsquare channel using lattice Boltzmann method [J]. Chemical Engineering Science,2011,66(5):935-952.
[57] H.X. Bai, P. Yu, S.H. Winoto, H.T. Low. Lattice Boltzmann method for flows in porous andhomogenous fluid domains coupled at the interface by stress jump [J]. International Journal forNumerical Methods in Fluids,2009,60(6):691-708.
[58] L. Biferale, P. Perlekar, M. Sbragaglia, F. Toschi. Convection in multiphase fluid flows usinglattice Boltzmann methods [J]. Physical Review Letters,2012,108(10):104502.
[59] Z. Chai, Z. Guo, B. Shi. Study of electro-osmotic flows in microchannels packed with variableporosity media via lattice Boltzmann method [J]. Journal of Applied Physics,2007,101(10):104913-104913-8.
[60] Z. Dong, W. Li, Y. Song. A numerical investigation of bubble growth on and departure from asuperheated wall by lattice Boltzmann method [J]. International Journal of Heat and MassTransfer,2010,53(21-22):4908-4916.
[61] M.M. Dupin, I. Halliday, C.M. Care. A multi-component lattice Boltzmann scheme: towards themesoscale simulation of blood flow [J]. Medical Engineering&Physics,2006,28(1):13-18.
[62] M.M. Dupin, I. Halliday, C.M. Care, L. Alboul, L.L. Munn. Modeling the flow of densesuspensions of deformable particles in three dimensions [J]. Physical Review E,2007,75(6):066707.
[63] Z. Guo, T.S. Zhao. A lattice Boltzmann model for convection heat transfer in porous media [J].Numerical Heat Transfer, Part B,2005,47(2):157-177.
[64] Z.L. Guo, T.S. Zhao. Lattice Boltzmann model for incompressible flows through porous media[J]. Physical Review E,2002,66(3):036304.
[65] A. H lzer, M. Sommerfeld. Lattice Boltzmann simulations to determine drag, lift and torqueacting on non-spherical particles [J]. Computers&Fluids,2009,38(3):572-589.
[66] X.Y. Kang, Q. Liao, X. Zhu, Y.X. Yang. Non-equilibrium extrapolation method in the latticeBoltzmann simulations of flows with curved boundaries (non-equilibrium extrapolation ofLBM)[J]. Applied Thermal Engineering,2010,30(13):1790-1796.
[67] F. Khan, F. Enzmann, M. Kersten, A. Wiegmann, K. Steiner.3D simulation of the permeabilitytensor in a soil aggregate on basis of nanotomographic imaging and LBE solver [J]. Journal ofSoils and Sediments,2012,12(1):86-96.
[68] N. Verma, D. Mewes, A. Luke. Lattice Boltzmann study of velocity, temperature, andconcentration in micro-reactors [J]. International Journal of Heat and Mass Transfer,2010,53(15):3175-3185.
[69] Y.X. Yang, Q. Liao, X. Zhu, H. Wang, R. Wu, D.J. Lee. Lattice Boltzmann simulation ofsubstrate flow past a cylinder with PSB biofilm for bio-hydrogen production [J]. InternationalJournal of Hydrogen Energy,2011,36(21):14031-14040.
[70] T. Zeiser, P. Lammers, E. Klemm, Y.W. Li, J. Bernsdorf, G. Brenner. CFD-calculation of flow,dispersion and reaction in a catalyst filled tube by the lattice Boltzmann method [J]. ChemicalEngineering Science,2001,56(4):1697-1704.
[71] B. Chopard, P.O. Luthi. Lattice Boltzmann computations and applications to physics [J].Theoretical Computer Science,1999,217(1):115-130.
[72] S. Chen, G.D. Doolen. Lattice Boltzmann method for fluid flows [J]. Annual Review of FluidMechanics,1998,30(1):329-364.
[73] O. Filippova, D. H nel. Grid refinement for lattice-BGK models [J]. Journal of ComputationalPhysics,1998,147(1):219-228.
[74] R.W. Mei, D.Z. Yu, W. Shyy, L.S. Luo. Force evaluation in the lattice Boltzmann methodinvolving curved geometry [J]. Physical Review E,2002,65(4):041203.
[75] Y. Xu, Y. Liu, Y. Xia, F. Wu. Lattice-Boltzmann simulation of two-dimensional flow over twovibrating side-by-side circular cylinders [J]. Physical Review E,2008,78(4):046314.
[76] A. Mussa, P. Asinari, L.S. Luo. Lattice Boltzmann simulations of2D laminar flows past twotandem cylinders [J]. Journal of Computational Physics,2009,228(4):983-999.
[77] X.W. Shan. Simulation of Rayleigh-Benard convection using a lattice Boltzmann method [J].Physical Review E,1997,55(3):2780.
[78] G.W. Yan, Y.S. Chen, S.X. Hu. Simple lattice Boltzmann model for simulating flows with shockwave [J]. Physical Review E,1999,59(1):454-459.
[79] Y. Liu, J. Cui, Y.X. Jiang, W.Z. Li. A numerical study on heat transfer performance ofmicrochannels with different surface microstructures [J]. Applied Thermal Engineering,2011,31(5):921-931.
[80] Y.Y. Yan, Y.Q. Zu. Numerical simulation of heat transfer and fluid flow past a rotatingisothermal cylinder-A LBM approach [J]. International Journal of Heat and Mass Transfer,2008,51(9-10):2519-2536.
[81] M. Wang, J.K. Wang, N. Pan, S.Y. Chen. Mesoscopic predictions of the effective thermalconductivity for microscale random porous media [J]. Physical Review E,2007,75(3):036702.
[82] E.G. FlekkZy. Lattice Bhatnagar-Gross-Krook models for miscible fluids [J]. Physical ReviewE,1993,47(6):4247.
[83] N. Jeong, D.H. Choi, C.L. Lin. Estimation of thermal and mass diffusivity in a porous mediumof complex structure using a lattice Boltzmann method [J]. International Journal of Heat andMass Transfer,2008,51(15):3913-3923.
[84] Q. Li, K. Zhao, Y.M. Xuan. Simulation of flow and heat transfer with evaporation in a porouswick of a CPL evaporator on pore scale by lattice Boltzmann method [J]. International Journalof Heat and Mass Transfer,2011,54(13-14):2890-2901.
[85] S. Bekri, P.M. Adler. Dispersion in multiphase flow through porous media [J]. InternationalJournal of Multiphase Flow,2002,28(4):665-697.
[86] S.H. Kim, H. Pitsch, I.D. Boyd. Lattice Boltzmann modeling of multicomponent diffusion innarrow channels [J]. Physical Review E,2009,79(1):016702.
[87] J. Onishi, Y. Chen, H. Ohashi. Dynamic simulation of multi-component viscoelastic fluidsusing the lattice Boltzmann method [J]. Physica A: Statistical Mechanics and its Applications,2006,362(1):84-92.
[88] X. Shan, H. Chen. Lattice Boltzmann model for simulating flows with multiple phases andcomponents [J]. Physical Review E,1993,47(3):1815.
[89] X. Shan, G. Doolen. Diffusion in a multicomponent lattice Boltzmann equation model [J].Physical Review E,1996,54(4):3614.
[90] Z.L. Yang, T.N. Dinh, R.R. Nourgaliev, B.R. Sehgal. Numerical investigation of bubble growthand detachment by the lattice-Boltzmann method [J]. International Journal of Heat and MassTransfer,2001,44(1):195-206.
[91] J.G. Zhou. A lattice Boltzmann method for solute transport [J]. International Journal forNumerical Methods in Fluids,2009,61(8):848-863.
[92] X. He, S. Chen, R. Zhang. A lattice Boltzmann scheme for incompressible multiphase flow andits application in simulation of Rayleigh-Taylor instability [J]. Journal of ComputationalPhysics,1999,152(2):642-663.
[93] X. Shan, G. Doolen. Multicomponent lattice-Boltzmann model with interparticle interaction [J].Journal of Statistical Physics,1995,81(1):379-393.
[94] Y. Gao, X. Zhang, P. Rama, Y. Liu, R. Chen, H. Ostadi, K. Jiang. Calculating the AnisotropicPermeability of Porous Media Using the Lattice Boltzmann Method and X-ray ComputedTomography [J]. Transport in Porous Media,2012,92(2):457-472
[95] N. Verma, D. Mewes. Lattice Boltzmann methods for simulation of micro and macrotransportin a packed bed of porous adsorbents under non-isothermal condition [J]. Computers&Mathematics with Applications,2009,58(5):1003-1014.
[96] X. Wang, B. Chen, J. Wu. A semianalytical solution of periodical electro-osmosis in arectangular microchannel [J]. Physics of Fluids,2007,19(12):127101.
[97] A. Gabrielli, S. Succi, E. Kaxiras. A lattice Boltzmann study of reactive microflows [J].Computer Physics Communications,2002,147(1-2):516-521.
[98] Z.W. Tian, C. Zou, H.J. Liu, Z.L. Guo, Z.H. Liu, C.G. Zheng. Lattice Boltzmann scheme forsimulating thermal micro-flow [J]. Physica A: Statistical Mechanics and its Applications,2007,385(1):59-68.
[99] M. Spasov, D. Rempfer, P. Mokhasi. Simulation of a turbulent channel flow with an entropicLattice Boltzmann method [J]. International Journal for Numerical Methods in Fluids,2009,60(11):1241-1258.
[100] D.Z. Yu, S.S. Girimaji. Multi-block Lattice Boltzmann method: Extension to3D andvalidation in turbulence [J]. Physica A: Statistical Mechanics and its Applications,2006,362(1):118-124.
[101] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman. Mechanisms of heat flow insuspensions of nano-sized particles (nanofluids)[J]. International Journal of Heat and MassTransfer,2002,45(4):855-863.
[102] R.M. MacMeccan, J.R. Clausen, G.P. Neitzel, C.K. Aidun. Simulating deformable particlesuspensions using a coupled lattice-Boltzmann and finite-element method [J]. Journal of FluidMechanics,2009,618(1):13-39.
[103] Z.G. Feng, E.E. Michaelides. Interparticle forces and lift on a particle attached to a solidboundary in suspension flow [J]. Physics of Fluids,2002,14(1):49-60.
[104] A.J.C. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmannequation. Part1. Theoretical foundation [J]. Journal of Fluid Mechanics,1994,271(1):285-309.
[105] A.J.C. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmannequation. Part2. Numerical results [J]. Journal of Fluid Mechanics,1994,271(1):311-339.
[106] S. Chen, S.P. Dawson, G.D. Doolen, D.R. Janecky, A. Lawniczak. Lattice methods andtheir applications to reacting systems [J]. Computers&Chemical Engineering,1995,19(6):617-646.
[107] H. Yu, L.S. Luo, S. Girimaji. Scalar mixing and chemical reaction simulations using latticeBoltzmann method [J]. International Journal of Computational Engineering Science,2002,3(1):73-87.
[108] X.M. Yu, B.C. Shi. A lattice Boltzmann model for reaction dynamical systems with timedelay [J]. Applied Mathematics and Computation,2006,181(2):958-965.
[109] A. Nabovati, E.W. Llewellin, A. Sousa. A general model for the permeability of fibrousporous media based on fluid flow simulations using the lattice Boltzmann method [J].Composites: Part A,2009,40(6):860-869.
[110] D. Gao, Z. Chen. Lattice Boltzmann simulation of natural convection dominated meltingin a rectangular cavity filled with porous media [J]. International Journal of Thermal Sciences,2011,50(4):493-501.
[111] H. Shokouhmand, F. Jam, M.R. Salimpour. The effect of porous insert position on theenhanced heat transfer in partially filled channels [J]. International Communications in Heatand Mass Transfer,2011,38(8):1162-1167.
[112] N. Verma, K. Salem, D. Mewes. Simulation of micro-and macro-transport in a packed bedof porous adsorbents by lattice Boltzmann methods [J]. Chemical Engineering Science,2007,62(14):3685-3698.
[113] M. Raúl. Numerical simulations of surface reaction in porous media with latticeBoltzmann [J]. Chemical Engineering Science,2012,69(1):628-643.
[114] S.P. Sullivan, L.F. Gladden, M.L. Johns.3D chemical reactor LB simulations [J].Mathematics and Computers in Simulation,2006,72(2-6):206-211.
[115] S.P. Sullivan, F.M. Sani, M.L. Johns, L.F. Gladden. Simulation of packed bed reactorsusing lattice Boltzmann methods [J]. Chemical Engineering Science,2005,60(12):3405-3418.
[116] K. Yamamoto, N. Takada, M. Misawa. Combustion simulation with Lattice Boltzmannmethod in a three-dimensional porous structure [J]. Proceedings of the Combustion Institute,2005,30(1):1509-1515.
[117] M. Selzer, M. Jainta, B. Nestler. A Lattice Boltzmann model to simulate the growth ofdendritic and eutectic microstructures under the influence of fluid flow [J]. Physica StatusSolidi B2009,246(6):1197-1205.
[118] D.A. von der Schulenburg, T.R.R. Pintelon, C. Picioreanu, M.C.M. Van Loosdrecht, M.L.Johns. Three‐dimensional simulations of biofilm growth in porous media [J]. AIChE Journal,2009,55(2):494-504.
[119] D. Alemani, F. Pappalardo, M. Pennisi, S. Motta, V. Brusic. Combining cellular automataand lattice Boltzmann method to model multiscale avascular tumor growth coupled withnutrient diffusion and immune competition [J]. Journal of Immunological Methods,2012,376(1-2):55-68.
[120] Q. Kang, D. Zhang, S. Chen. Unified lattice Boltzmann method for flow in multiscaleporous media [J]. Physical Review E,2002,66(5):056307.
[121] S. Succi, O. Filippova, G. Smith, E. Kaxiras. Applying the lattice Boltzmann equation tomultiscale fluid problems [J]. Computing in Science&Engineering,2001,3(6):26-37.
[122] M.A. Van der Hoef, M. van Sint Annaland, J.A.M. Kuipers. Computational fluid dynamicsfor dense gas-solid fluidized beds: a multi-scale modeling strategy [J]. Chemical EngineeringScience,2004,59(22):5157-5165.
[123] Y. Wang, J.G. Brasseur, G.G. Banco, A.G. Webb, A.C. Ailiani, T. Neuberger. A multiscalelattice Boltzmann model of macro-to micro-scale transport, with applications to gut function [J].Philosophical Transactions of the Royal Society A,2010,368(1921):2863-2880.
[124] T.D. Scheibe, A.M. Tartakovsky, D.M. Tartakovsky, G.D. Redden, P. Meakin, B.J. Palmer,K.L. Schuchardt. Hybrid numerical methods for multiscale simulations of subsurfacebiogeochemical processes [J]. Journal of Physics: Conference Series,2008,125(1):012054.
[125] W.C. Sun, J.E. Andrade, J.W. Rudnicki. Multiscale method for characterization of porousmicrostructures and their impact on macroscopic effective permeability [J]. InternationalJournal for Numerical Methods in Engineering,2011,88(12):1260-1279.
[126] X. He, L.S. Luo. A priori derivation of the lattice Boltzmann equation [J]. Physical ReviewE,1997,55(6):6333-6336.
[127] X. He, L.S. Luo. Theory of the lattice Boltzmann method: From the Boltzmann equation tothe lattice Boltzmann equation [J]. Physical Review E,1997,56(6):6811.
[128] Z.L. Guo, B.C. Shi, N.C. Wang. Lattice BGK model for incompressible Navier-Stokesequation [J]. Journal of Computational Physics,2000,165(1):288-306.
[129] S. Chen, D. Martinez, R. Mei. On boundary conditions in lattice Boltzmann methods [J].Physics of Fluids,1996,8(9):2527-2536.
[130] Z.L. Guo, C.G. Zheng, B.C. Shi. An extrapolation method for boundary conditions inlattice Boltzmann method [J]. Physics of Fluids,2002,14(6):2007.
[131] X. He, Q. Zou, L.S. Luo, M. Dembo. Analytic solutions of simple flows and analysis ofnonslip boundary conditions for the lattice Boltzmann BGK model [J]. Journal of StatisticalPhysics,1997,87(1):115-136.
[132] X.Y. He, G. Doolen. Lattice Boltzmann method on curvilinear coordinates system: flowaround a circular cylinder [J]. Journal of Computational Physics,1997,134(2):306-315.
[133] P.H. Kao, R.J. Yang. An investigation into curved and moving boundary treatments in thelattice Boltzmann method [J]. Journal of Computational Physics,2008,227(11):5671-5690.
[134] R. Mei, L.S. Luo, W. Shyy. An accurate curved boundary treatment in the latticeBoltzmann method [J]. Journal of Computational Physics,1999,155(2):307-330.
[135] G.H. Tang, W.Q. Tao, Y.L. He. Thermal boundary condition for the thermal latticeBoltzmann equation [J]. Physical Review E,2005,72(1):016703.
[136] Q. Zou, X. He. On pressure and velocity boundary conditions for the lattice BoltzmannBGK model [J]. Physics of Fluids,1997,9(6):1591-1598.
[137] D.P. Ziegler. Boundary conditions for lattice Boltzmann simulations [J]. Journal ofStatistical Physics,1993,71(5):1171-1177.
[138] D.R. Noble, S. Chen, J.G. Georgiadis, R.O. Buckius. A consistent hydrodynamic boundarycondition for the lattice Boltzmann method [J]. Physics of Fluids,1995,7(1):203-209.
[139] D.R. Noble, J.G. Georgiadis, R.O. Buckius. Direct assessment of lattice Boltzmannhydrodynamics and boundary conditions for recirculating flows [J]. Journal of StatisticalPhysics,1995,81(1):17-33.
[140]杨艳霞,廖强,朱恂,王宏,丁玉栋.绕流具有光合生化反应管束的格子Boltzmann模拟[J].化工学报,2012,63(8):2383-2391.
[141] M. Sch fer, S. Turek, F. Durst, E. Krause, R. Rannacher. Benchmark computations oflaminar flow around a cylinder [J]. Notes on numerical fluid mechanics,1996,52(547-566.
[142]刘大猛.含生化反应的固定化细胞光生物制氢反应器内的多相传输模型[D],2010.
[143] A. Dupuis, B. Chopard. Theory and applications of an alternative lattice Boltzmann gridrefinement algorithm [J]. Physical Review E,2003,67(6):066707.
[144] C.L. Lin, Y.G. Lai. Lattice Boltzmann method on composite grids [J]. Physical Review E,2000,62(2):2219.
[145] D.Z. Yu, R.W. Mei, W. Shyy. A multi‐block lattice Boltzmann method for viscous fluidflows [J]. International Journal for Numerical Methods in Fluids,2002,39(2):99-120.
[146] H. Farhat, W. Choi, J.S. Lee. Migrating multi-block lattice Boltzmann model forimmiscible mixtures:3D algorithm development and validation [J]. Computers&Fluids,2010,39(8):1284-1295.
[147] M. Pilotti. Generation of realistic porous media by grains sedimentation [J]. Transport inPorous Media,1998,33(3):257-278.
[148] R.S. Maier, D.M. Kroll, R.S. Bernard, S.E. Howington, J.F. Peters, H.T. Davis. Pore-scalesimulation of dispersion [J]. Physics of Fluids,2000,12(8):2065.
[149] M. Madadi, M. Sahimi. Lattice Boltzmann simulation of fluid flow in fracture networkswith rough, self-affine surfaces [J]. Physical Review E,2003,67(2):026309.
[150] H. Zhang, X. Ge, H. Ye. Randomly mixed model for predicting the effective thermalconductivity of moist porous media [J]. Journal of Physics D: Applied Physics,2005,39(1):220-226.
[151]王永忠.固定化光合细菌光生物制氢反应器传输与产氢特性[D];重庆大学,2008.
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