基于非结构网格的近海海域污染物迁移三维数值模拟并行算法
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摘要
针对浅水环境下的污染物迁移问题,提出了一种基于非结构网格的全隐格式可扩展并行算法。首先,对计算区域进行非结构网格建模;然后,对污染物迁移方程时间方向采用二阶向后差分隐式格式、空间方向采用有限元方法进行离散,并使用基于区域分解的NKS并行算法对离散系统进行求解。最后,使用该算法对珠江前航道和珠江出海口的污染物扩散过程进行了测试模拟,在"天河二号"超级计算机上,最高使用2 400个处理器核时获得了64%的并行效率。测试结果表明NKS算法能有效地用于复杂区域大规模问题的数值模拟。
An unstructural-grid-based fully implicit scalable algorithm was proposed for the problem of contaminant transport in shallow water environment. Firstly, the computational domain was meshed with unstructured tetrahedral elements, and then the second-order backward differentiation formula in time direction and the finite element method in space were applied to discretize the contaminant transport equations. The NKS(Newton-Krylov-Schwarz) parallel algorithm based on domain decomposition was used to solve the discrete system. Finally, the contaminant transport process of the Pearl River front channel and the Pearl River estuary were simulated, and a parallel efficiency of 64% was achieved for 2 400 processor cores on the "Tianhe 2" supercomputer. The experimental results show that the NKS algorithm can be effectively used for numerical simulation of large-scale problems in complex regions.
An unstructural-grid-based fully implicit scalable algorithm was proposed for the problem of contaminant transport in shallow water environment. Firstly, the computational domain was meshed with unstructured tetrahedral elements, and then the second-order backward differentiation formula in time direction and the finite element method in space were applied to discretize the contaminant transport equations. The NKS(Newton-Krylov-Schwarz) parallel algorithm based on domain decomposition was used to solve the discrete system. Finally, the contaminant transport process of the Pearl River front channel and the Pearl River estuary were simulated, and a parallel efficiency of 64% was achieved for 2 400 processor cores on the "Tianhe 2" supercomputer. The experimental results show that the NKS algorithm can be effectively used for numerical simulation of large-scale problems in complex regions.
引文
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[4] 堵盘军,胡克林,孔亚珍,等.ECOMSED模式在杭州湾海域流场模拟中的应用[J].海洋学报,2007,29(1):7-16.
[5] WANG Y,YANG Y,CHEN X,et al.The moving confluence route technology with WAD scheme for 3D hydrodynamic simulation in high altitude inland waters [J].Journal of Hydrology,2018,559:411-427.
[6] 华祖林,刘晓东,褚克坚,等.基于边界拟合下的水流与污染物质输运数值模拟[M].北京:科学出版社,2013:8-62.
[7] 袁益让,芮洪兴,梁栋.环境科学数值模拟的理论和实际应用,信息与计算科学从书[M].北京:科学出版社,2012:30-68.
[8] COCKBURN B,SHU C W.Runge-Kutta discontinuous Galerkin methods for convection-dominated problems [J].Journal of Scientific Computing,2001,16(3):173-261.
[9] LONG X,YUAN Y.Multistep characteristic method for incompressible flow in porous media [J].Applied Mathematics and Computation,2009,214(1):259-270.
[10] BROOKS A N,HUGHES T J.Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations [J].Computer Methods in Applied Mechanics and Engineering,1982,32(1/2/3):199-259.
[11] CAI X-C,SARKIS M.A restricted additive Schwarz preconditioner for general sparse linear systems [J].SIAM Journal on Scientific Computing,1999,21(2):792-797.
[12] CHEN R,CAI X-C.Parallel one-shot Lagrange-Newton-Krylov- Schwarz algorithms for shape optimization of steady incompressible flows [J].SIAM Journal on Scientific Computing,2012,34(5):B584-B605.
[13] DENG X,CAI X-C,ZOU J.A parallel space-time domain decomposition method for unsteady source inversion problems [J].arXiv Preprint,2015,2015:arXiv.1508.06064.
[14] YANG H,PRUDENCIO E E,CAI X-C.Fully implicit Lagrange- Newton-Krylov-Schwarz algorithms for boundary control of unsteady incompressible flows [J].International Journal for Numerical Methods in Engineering,2012,91(6):644-665.
[15] LARGE W G,POND S.Open ocean momentum flux measurements in moderate to strong winds [J].Journal of Physical Oceanography,1981,11(3):324-336.
[16] FRANCA L P,FREY S L.Stabilized finite element methods:II.The incompressible Navier-Stokes equations [J].Computer Methods in Applied Mechanics and Engineering,1992,99(2/3):209-233.
[17] EISENSTAT S C,WALKER H F.Globally convergent inexact Newton methods [J].SIAM Journal on Optimization,1994,4(2):393-422.
[18] EISENSTAT S C,WALKER H F.Choosing the forcing terms in an inexact Newton method [J].SIAM Journal on Scientific Computing,1996,17(1):16-32.
[19] LIAO Z-J,CHEN R,YAN Z,et al.A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes [J].International Journal for Numerical Methods in Fluids,2019,89(9):343-361.