基于自适应网格的急流条件下污染物输运高效高精度模拟
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摘要
为了高效准确模拟急流条件下突发水污染事件中污染物的输运规律,基于自适应网格技术构建了Godunov格式有限体积模型。模型利用自适应结构网格离散二维浅水控制方程,对水位梯度或污染物浓度梯度较大的区域进行精细网格划分,同时细化干湿边界区域网格。模型采用MUSCL-Hancock方法求解二维浅水控制方程,使模型具有时空二阶精度;利用HLLC格式近似Riemann解计算界面通量,对界面两侧的Riemann变量进行非负重构和局部底部高程修正以确保模型计算的和谐性和稳定性。算例验证表明:自适应网格技术可以自动识别水位梯度或污染物浓度梯度较大的区域以及干湿边界区域并细化该区域网格,保证模型模拟精度的基础上,提升模型模拟效率;该模型能够准确高效地模拟急流条件下污染物的输运过程,适用于突发水污染事件的评估、预警和应急管理。
A Godunov-type scheme finite volume model based on adaptive structured grid method is proposed for accurately simulating pollutant transport in sudden water pollution accidents with torrential flow conditions. In the model, two-dimensional shallow water governing equations are discretized by adaptive structured grids. The structured grids with high gradients of water level or pollutant concentration are subdivided to improve grid resolution. In addition,the grids near wet/dry fronts are also subdivided. The model has spatial-temporal second-order precision through solving shallow water governing equations by MUSCLHancock method. HLLC's approximate Riemann solution is used to compute the interface flux based on non-negative reconstruction and local modification of bed slope,it can maintain the stability and well-balanced condition of the model. The test results indicate that adaptive gird method can automatically identify and subdivide the grids with high gradients of water level or pollutant concentration as well as the girds near wet/dry fronts. It can improve model computational efficiency without compromising solution accuracy.The model can efficiently and accurately simulate pollutant transport in sudden water pollution accidents with torrential flow conditions and is applicable for assessment,early warning and emergency management of sudden water pollution accidents.
A Godunov-type scheme finite volume model based on adaptive structured grid method is proposed for accurately simulating pollutant transport in sudden water pollution accidents with torrential flow conditions. In the model, two-dimensional shallow water governing equations are discretized by adaptive structured grids. The structured grids with high gradients of water level or pollutant concentration are subdivided to improve grid resolution. In addition,the grids near wet/dry fronts are also subdivided. The model has spatial-temporal second-order precision through solving shallow water governing equations by MUSCLHancock method. HLLC's approximate Riemann solution is used to compute the interface flux based on non-negative reconstruction and local modification of bed slope,it can maintain the stability and well-balanced condition of the model. The test results indicate that adaptive gird method can automatically identify and subdivide the grids with high gradients of water level or pollutant concentration as well as the girds near wet/dry fronts. It can improve model computational efficiency without compromising solution accuracy.The model can efficiently and accurately simulate pollutant transport in sudden water pollution accidents with torrential flow conditions and is applicable for assessment,early warning and emergency management of sudden water pollution accidents.
引文
[1]陶亚,雷坤,夏建新.突发水污染事故中污染物输移主导水动力识别——以深圳湾为例[J].水科学进展,2017,28(6):888-897.
[2]徐小钰,朱记伟,李占斌,等.国内外突发性水污染事件研究综述[J].中国农村水利水电,2015(6):1-5.
[3]李林子,钱瑜,张玉超.基于EFDC和WASP模型的突发水污染事故影响的预测预警[J].长江流域资源与环境,2011,20(8):1010-1016.
[4]蒋云钟,冶运涛,王浩.基于物联网的河湖水系连通水质水量智能调控及应急处置系统研究[J].系统工程理论与实践,2014,34(7):1895-1903.
[5] ZHANG L L,LIANG Q H,WANG Y L,et al. A robust coupled model for solute transport driven by severe flow conditions[J]. Journal of Hydro-environment Research,2015,9(1):49-60.
[6]陶亚,任华堂,夏建新.河流突发污染事故下游城市应急响应时间预测——以淮河淮南段为例[J].应用基础与工程科学学报,2012,20(s1):77-86.
[7]陶亚,任华堂,夏建新.突发水污染事故不同应对措施处置效果模拟[J].应用基础与工程科学学报,2013,21(2):203-213.
[8]饶清华,曾雨,张江山,等.闽江下游突发性水污染事故时空模拟[J].环境科学学报,2011,31(3):554-559.
[9] DONG L,LIU J,DU X,et al. Simulation-based risk analysis of water pollution accidents combining multistressors and multi-receptors in a coastal watershed[J]. Ecological Indicators,2017,92:161-170.
[10]丁玲,逄勇,吴建强,等.模拟水质突跃问题的三种二阶高性能格式[J].水利学报,2004,35(9):50-55.
[11] LIANG Q H. A well-balanced and nonnegative numerical scheme for solving the integrated shallow water and sol?ute transport equations[J]. Communications in Computational Physics,2010,7(5):1049-1075.
[12]杨中华,朱政涛,槐文信,等.鄱阳湖水利调控对湖区典型丰枯水年水动力水质影响研究[J].水利学报,2018,49(2):156-167.
[13] LIANG Q H,BORTHWICK A G L. Adaptive quadtree simulation of shallow flows with wet-dry fronts over com?plex topography[J]. Computers&Fluids,2009,38(2):221-234.
[14] LIANG Q H. A simplified adaptive Cartesian grid system for solving the 2D shallow water equations[J]. Interna?tional Journal for Numerical Methods in Fluids,2012,69(2):442-458.
[15]张华杰.湖泊流场数学模型及水动力特性研究[D].武汉:华中科技大学,2014.
[16] SIBSON R. A vector identity for the Dirichlet tessellation[J]. Mathematical Proceedings of the Cambridge Philo?sophical Society,1980,87(1):151-155.
[17] LIANG Q H,BORTHWICK A G L,STELLING G. Simulation of dam-and dyke-break hydrodynamics on dy?namically adaptive quadtree grids[J]. International Journal for Numerical Methods in Fluids,2004,46(2):127-162.
[18]曹引,冶运涛,梁犁丽,等.基于结构网格的溃坝水流数值模拟[J].水科学进展,2017,28(6):868-878.
[19] KONG J,XIN P,SHEN C J,et al. A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh[J]. Environmental Modelling&Software,2013,40(1):109-127.
[20]宋利祥,杨芳,胡晓张,等.感潮河网二维水流-输运耦合数学模型[J].水科学进展,2014,25(4):550-559.
[21] SOARES F S,TESTA G. The Toce River test case:numerical results analysis[C]//Proc. of the 3rd CADAM Workshop. Milan,Italy:1999.
[22] HOU J M,LIANG Q H,SIMONS F,et al. A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment[J]. Advances in Water Resources,2013,52(2):107-131.
[2]徐小钰,朱记伟,李占斌,等.国内外突发性水污染事件研究综述[J].中国农村水利水电,2015(6):1-5.
[3]李林子,钱瑜,张玉超.基于EFDC和WASP模型的突发水污染事故影响的预测预警[J].长江流域资源与环境,2011,20(8):1010-1016.
[4]蒋云钟,冶运涛,王浩.基于物联网的河湖水系连通水质水量智能调控及应急处置系统研究[J].系统工程理论与实践,2014,34(7):1895-1903.
[5] ZHANG L L,LIANG Q H,WANG Y L,et al. A robust coupled model for solute transport driven by severe flow conditions[J]. Journal of Hydro-environment Research,2015,9(1):49-60.
[6]陶亚,任华堂,夏建新.河流突发污染事故下游城市应急响应时间预测——以淮河淮南段为例[J].应用基础与工程科学学报,2012,20(s1):77-86.
[7]陶亚,任华堂,夏建新.突发水污染事故不同应对措施处置效果模拟[J].应用基础与工程科学学报,2013,21(2):203-213.
[8]饶清华,曾雨,张江山,等.闽江下游突发性水污染事故时空模拟[J].环境科学学报,2011,31(3):554-559.
[9] DONG L,LIU J,DU X,et al. Simulation-based risk analysis of water pollution accidents combining multistressors and multi-receptors in a coastal watershed[J]. Ecological Indicators,2017,92:161-170.
[10]丁玲,逄勇,吴建强,等.模拟水质突跃问题的三种二阶高性能格式[J].水利学报,2004,35(9):50-55.
[11] LIANG Q H. A well-balanced and nonnegative numerical scheme for solving the integrated shallow water and sol?ute transport equations[J]. Communications in Computational Physics,2010,7(5):1049-1075.
[12]杨中华,朱政涛,槐文信,等.鄱阳湖水利调控对湖区典型丰枯水年水动力水质影响研究[J].水利学报,2018,49(2):156-167.
[13] LIANG Q H,BORTHWICK A G L. Adaptive quadtree simulation of shallow flows with wet-dry fronts over com?plex topography[J]. Computers&Fluids,2009,38(2):221-234.
[14] LIANG Q H. A simplified adaptive Cartesian grid system for solving the 2D shallow water equations[J]. Interna?tional Journal for Numerical Methods in Fluids,2012,69(2):442-458.
[15]张华杰.湖泊流场数学模型及水动力特性研究[D].武汉:华中科技大学,2014.
[16] SIBSON R. A vector identity for the Dirichlet tessellation[J]. Mathematical Proceedings of the Cambridge Philo?sophical Society,1980,87(1):151-155.
[17] LIANG Q H,BORTHWICK A G L,STELLING G. Simulation of dam-and dyke-break hydrodynamics on dy?namically adaptive quadtree grids[J]. International Journal for Numerical Methods in Fluids,2004,46(2):127-162.
[18]曹引,冶运涛,梁犁丽,等.基于结构网格的溃坝水流数值模拟[J].水科学进展,2017,28(6):868-878.
[19] KONG J,XIN P,SHEN C J,et al. A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh[J]. Environmental Modelling&Software,2013,40(1):109-127.
[20]宋利祥,杨芳,胡晓张,等.感潮河网二维水流-输运耦合数学模型[J].水科学进展,2014,25(4):550-559.
[21] SOARES F S,TESTA G. The Toce River test case:numerical results analysis[C]//Proc. of the 3rd CADAM Workshop. Milan,Italy:1999.
[22] HOU J M,LIANG Q H,SIMONS F,et al. A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment[J]. Advances in Water Resources,2013,52(2):107-131.
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