一种用于间断装配的流场结构辨识算法
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摘要
使用激波装配法时,初始激波是否准确将会对计算过程产生影响。为了确定初始激波的位置,提出了一种新的流场结构辨识算法。该算法以捕捉法计算得到的流场作为系统观测数据,根据密度、压力等参数从该数据中获取激波和接触间断等流动特征周围的网格节点作为离散点集。通过将该离散点集分割成若干子区域,在各子区域内进行分片拟合,最终将离散点集拟合成连续光滑的实体模型,并将此作为初始激波面。在二维方法的基础上,通过引入单位球模型成功将该辨识算法拓展到三维应用。结果表明,采用该方法获得的间断曲面(激波和接触间断)与捕捉法流场中的间断分布吻合较好,作为初始间断面用于装配法可快速得到收敛解。该方法解决了应用激波装配法时确定初始间断面的难题。此外,该方法还可用于网格自适应方法。选择不同流动参数,可以获得相应流场特征结构的空间曲面,在此曲面的基础上可进行网格局部加密或重剖分。该流场结构辨识算法用于网格自适应具有网格尺度自由设置的优势。
A new surface extraction method named source-rays method is proposed to locate and shape initial shock wave surface for shock-fitting algorithms.In this method,the flow field data acquired by the shock-capturing schemes are used as the observed data,and the grid nodes with the features such as shock waves and contact discontinuities are obtained as a discrete point set according to the parameters of density,pressure and others.The discrete point set is finally assembled into a continuous smooth surface by being segmented into several subsets for fragment fitting.Based on the two-dimensional method,this identification algorithm is extended to threedimensional application by introducing a unit sphere model.The discrete points are fitted to a series of triangular patches with determined connection relationship by a unit sphere,and a smooth continuous surface can be assembled.The results show that the feature surface(shock wave and contact discontinuity)obtained by the source-rays method coincides with the discontinuous distribution in the flow field calculated by the shock-capturing schemes.By using the extracted feature surface as the initial shock wave surface,the convergence solution can be quickly obtained in shock-fitting algorithm.In addition,this method can also be used in the adaptive mesh refinement procedure.According to different flow parameters,the spatial surfaces of the corresponding flow field structures can be obtained.Based on these surfaces,the mesh grid can be locally refined.This flow field feature surface extraction method has the advantage of grid scale set arbitrarily for mesh adaptation procedure.
A new surface extraction method named source-rays method is proposed to locate and shape initial shock wave surface for shock-fitting algorithms.In this method,the flow field data acquired by the shock-capturing schemes are used as the observed data,and the grid nodes with the features such as shock waves and contact discontinuities are obtained as a discrete point set according to the parameters of density,pressure and others.The discrete point set is finally assembled into a continuous smooth surface by being segmented into several subsets for fragment fitting.Based on the two-dimensional method,this identification algorithm is extended to threedimensional application by introducing a unit sphere model.The discrete points are fitted to a series of triangular patches with determined connection relationship by a unit sphere,and a smooth continuous surface can be assembled.The results show that the feature surface(shock wave and contact discontinuity)obtained by the source-rays method coincides with the discontinuous distribution in the flow field calculated by the shock-capturing schemes.By using the extracted feature surface as the initial shock wave surface,the convergence solution can be quickly obtained in shock-fitting algorithm.In addition,this method can also be used in the adaptive mesh refinement procedure.According to different flow parameters,the spatial surfaces of the corresponding flow field structures can be obtained.Based on these surfaces,the mesh grid can be locally refined.This flow field feature surface extraction method has the advantage of grid scale set arbitrarily for mesh adaptation procedure.
引文
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[2] LAX P,WENDROFF B.Systems of conservation laws[J].Communications on Pure and Applied mathematics,1960,13(2):217-237.
[3]张涵信,沈孟育.计算流体力学—差分格式原理和应用[M].北京:国防工业出版社,2003.ZHANG H X,SHEN M Y.Computational fluid dynamicstheory and application of difference scheme[M].Beijing:National Defense Industry Press,2003.(in Chinese)
[4] VON NEUMANN J,RICHTMYER R D.A method for the numerical calculation of hydrodynamic shocks[J].Journal of Applied Physics,1950,21(3):232-237.
[5] KUNDU P K.Fluid mechanics[M].San Diego:Academic Press,1990.
[6]赵学瑞,廖其奠.黏性流体力学[M].北京:机械工业出版社,1983.ZHAO X R,LIAO Q D.Viscous fluid mechanics[M].Beijing:China Machine Press,1983.(in Chinese)
[7]吴其芬,陈伟芳,等.稀薄气体动力学[M].湖南长沙:国防科技大学出版社,2004.WU Q F,CHEN W F.Rarefied gas dynamics[M].Changsha:National University of Defense Technology Press,2004.(in Chinese)
[8] ABBETT M,MORETTI G.A time-dependent computational method for blunt body flows[J].AIAA Journal,1966,4(12):2136-2141.
[9] MORETTI G.Thirty-six years of shock fitting[J].Computers&Fluids,2002,31(4):719-723.
[10]张德良.计算流体力学教程[M].北京:高等教育出版社,2010.ZHANG D L.A Course in Computational Fluid Dynamics[M].Beijing:Higher Education Press,2010.(in Chinese)
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[12]RAWAT P S,ZHONG X L.On high-order shock-fitting and front-tracking schemes for numerical simulation of shockdisturbance interactions[J].Journal of Computational Physics,2010,229(19):6744-6780.
[13]PRAKASH A,PARSONS N,WANG X,et al.High-order shock-fitting methods for direct numerical simulation of hypersonic flow withchemical and thermal nonequilibrium[J].Journal of Computational Physics,2011,230(23):8474-8507.
[14]PACIORRI R,BONFIGLIOLI A.A shock-fitting technique for 2D unstructured grids[J].Computers&Fluids,2009,38(3):715-726.
[15]PACIORRI R,BONFIGLIOLI A.Shock interaction computations on unstructured,two-dimensional grids using a shock-fitting technique[J].Journal of Computational Physics,2011,230(8):3155-3177.
[16]BONFIGLIOLI A,GROTTADAUREA M,PACIORRI R,et al.An unstructured,three-dimensional,shock-fitting solver for hypersonic flows[J].Computers&Fluids,2013,73:162-174.
[17]刘君,邹东阳,徐春光.基于非结构动网格的非定常激波装配法[J].空气动力学学报,2015,33(1):10-16.LIU J,ZOU D Y,XU C G.An unsteady shock-fitting technique based on unstructured moving grids[J].Acta Aerodynamica Sinica,2015,33(1):10-16.(in Chinese)
[18]刘君,徐春光,白晓征.有限体积方法和非结构动网格[M].北京:科学出版社,2016.LIU J,XU C G,BAI X Z.Finite volume methods and unstructured dynamic meshes[M].Beijing:Science Press,2016.(in Chinese)
[19]ZOU D,XU C,DONG H,et al.A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes[J].Journal of Computational Physics,2017,345:866-882.
[20]刘君,邹东阳,董海波.动态间断装配法模拟斜激波壁面反射[J].航空学报,2016,37(3):836-846.LIU J,ZOU D Y,DONG H B.A moving discontinuity fitting technique to simulate shock waves impinged on a straight wall[J].Acta Aeronautica et Astronautica Sinica,2016,37(3):836-846.(in Chinese)
[21]刘君,邹东阳,董海波.基于非结构变形网格的间断装配法原理[J].气体物理,2017,(1):13-20.LIU J,ZOU D Y,DONG H B.Principle of new discontinuity fitting technique based on unstructured moving grid[J].Physics of Gases,2017,(1):13-20.(in Chinese)
[22] WU Z N,XU Y Z,WANG W B,et al.Review of shock wave detection method in CFD post-processing[J].Chinese Journal of Aeronautics,2013,26(3):501-513.
[23]PAGENDARM H G,SEITZ B.An algorithm for detection and visualization of discontinuities in scientific data fields applied to flow data with shock waves[J].Scientific Visualization:Advanced Software Techniques,1993:161-177.
[24]LOVELY D,HAIMES R.Shock detection from computational fluid dynamics results[C]//14th Computational Fluid Dynamics Conference.1999:3285.
[25]KANAMORI M,SUZUKI K.Shock wave detection in twodimensional flow based on the theory of characteristics from CFD data[J].Journal of Computational Physics,2011,230(8):3085-3092.
[26]KANAMORI M,SUZUKI K.Shock wave detection based on the theory of characteristics for CFD results[C]//20th AIAA Computational Fluid Dynamics Conference.Honolulu,Hawaii,2011.
[2] LAX P,WENDROFF B.Systems of conservation laws[J].Communications on Pure and Applied mathematics,1960,13(2):217-237.
[3]张涵信,沈孟育.计算流体力学—差分格式原理和应用[M].北京:国防工业出版社,2003.ZHANG H X,SHEN M Y.Computational fluid dynamicstheory and application of difference scheme[M].Beijing:National Defense Industry Press,2003.(in Chinese)
[4] VON NEUMANN J,RICHTMYER R D.A method for the numerical calculation of hydrodynamic shocks[J].Journal of Applied Physics,1950,21(3):232-237.
[5] KUNDU P K.Fluid mechanics[M].San Diego:Academic Press,1990.
[6]赵学瑞,廖其奠.黏性流体力学[M].北京:机械工业出版社,1983.ZHAO X R,LIAO Q D.Viscous fluid mechanics[M].Beijing:China Machine Press,1983.(in Chinese)
[7]吴其芬,陈伟芳,等.稀薄气体动力学[M].湖南长沙:国防科技大学出版社,2004.WU Q F,CHEN W F.Rarefied gas dynamics[M].Changsha:National University of Defense Technology Press,2004.(in Chinese)
[8] ABBETT M,MORETTI G.A time-dependent computational method for blunt body flows[J].AIAA Journal,1966,4(12):2136-2141.
[9] MORETTI G.Thirty-six years of shock fitting[J].Computers&Fluids,2002,31(4):719-723.
[10]张德良.计算流体力学教程[M].北京:高等教育出版社,2010.ZHANG D L.A Course in Computational Fluid Dynamics[M].Beijing:Higher Education Press,2010.(in Chinese)
[11]RICHTMYER R D,MORTON K W.Difference methods for initial-value problems[M].Interscience Publisher,New York,1967.
[12]RAWAT P S,ZHONG X L.On high-order shock-fitting and front-tracking schemes for numerical simulation of shockdisturbance interactions[J].Journal of Computational Physics,2010,229(19):6744-6780.
[13]PRAKASH A,PARSONS N,WANG X,et al.High-order shock-fitting methods for direct numerical simulation of hypersonic flow withchemical and thermal nonequilibrium[J].Journal of Computational Physics,2011,230(23):8474-8507.
[14]PACIORRI R,BONFIGLIOLI A.A shock-fitting technique for 2D unstructured grids[J].Computers&Fluids,2009,38(3):715-726.
[15]PACIORRI R,BONFIGLIOLI A.Shock interaction computations on unstructured,two-dimensional grids using a shock-fitting technique[J].Journal of Computational Physics,2011,230(8):3155-3177.
[16]BONFIGLIOLI A,GROTTADAUREA M,PACIORRI R,et al.An unstructured,three-dimensional,shock-fitting solver for hypersonic flows[J].Computers&Fluids,2013,73:162-174.
[17]刘君,邹东阳,徐春光.基于非结构动网格的非定常激波装配法[J].空气动力学学报,2015,33(1):10-16.LIU J,ZOU D Y,XU C G.An unsteady shock-fitting technique based on unstructured moving grids[J].Acta Aerodynamica Sinica,2015,33(1):10-16.(in Chinese)
[18]刘君,徐春光,白晓征.有限体积方法和非结构动网格[M].北京:科学出版社,2016.LIU J,XU C G,BAI X Z.Finite volume methods and unstructured dynamic meshes[M].Beijing:Science Press,2016.(in Chinese)
[19]ZOU D,XU C,DONG H,et al.A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes[J].Journal of Computational Physics,2017,345:866-882.
[20]刘君,邹东阳,董海波.动态间断装配法模拟斜激波壁面反射[J].航空学报,2016,37(3):836-846.LIU J,ZOU D Y,DONG H B.A moving discontinuity fitting technique to simulate shock waves impinged on a straight wall[J].Acta Aeronautica et Astronautica Sinica,2016,37(3):836-846.(in Chinese)
[21]刘君,邹东阳,董海波.基于非结构变形网格的间断装配法原理[J].气体物理,2017,(1):13-20.LIU J,ZOU D Y,DONG H B.Principle of new discontinuity fitting technique based on unstructured moving grid[J].Physics of Gases,2017,(1):13-20.(in Chinese)
[22] WU Z N,XU Y Z,WANG W B,et al.Review of shock wave detection method in CFD post-processing[J].Chinese Journal of Aeronautics,2013,26(3):501-513.
[23]PAGENDARM H G,SEITZ B.An algorithm for detection and visualization of discontinuities in scientific data fields applied to flow data with shock waves[J].Scientific Visualization:Advanced Software Techniques,1993:161-177.
[24]LOVELY D,HAIMES R.Shock detection from computational fluid dynamics results[C]//14th Computational Fluid Dynamics Conference.1999:3285.
[25]KANAMORI M,SUZUKI K.Shock wave detection in twodimensional flow based on the theory of characteristics from CFD data[J].Journal of Computational Physics,2011,230(8):3085-3092.
[26]KANAMORI M,SUZUKI K.Shock wave detection based on the theory of characteristics for CFD results[C]//20th AIAA Computational Fluid Dynamics Conference.Honolulu,Hawaii,2011.