Solute transport simulations are important in water pollution events.This paper introduces a finite volume Godunovtype model for solving a 4×4 matrix form of the hyperbolic conservation laws consisting of 2D shal...Solute transport simulations are important in water pollution events.This paper introduces a finite volume Godunovtype model for solving a 4×4 matrix form of the hyperbolic conservation laws consisting of 2D shallow water equations and transport equations.The model adopts the Harten-Lax-van Leer-contact(HLLC)-approximate Riemann solution to calculate the cell interface fluxes.It can deal well with the changes in the dry and wet interfaces in an actual complex terrain,and it has a strong shock-wave capturing ability.Using monotonic upstream-centred scheme for conservation laws(MUSCL)linear reconstruction with finite slope and the Runge-Kutta time integration method can achieve second-order accuracy.At the same time,the introduction of graphics processing unit(GPU)-accelerated computing technology greatly increases the computing speed.The model is validated against multiple benchmarks,and the results are in good agreement with analytical solutions and other published numerical predictions.The third test case uses the GPU and central processing unit(CPU)calculation models which take 3.865 s and 13.865 s,respectively,indicating that the GPU calculation model can increase the calculation speed by 3.6 times.In the fourth test case,comparing the numerical model calculated by GPU with the traditional numerical model calculated by CPU,the calculation efficiencies of the numerical model calculated by GPU under different resolution grids are 9.8–44.6 times higher than those by CPU.Therefore,it has better potential than previous models for large-scale simulation of solute transport in water pollution incidents.It can provide a reliable theoretical basis and strong data support in the rapid assessment and early warning of water pollution accidents.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.52009104 and 52079106)the Shaanxi Provincial Department of Water Resources Project(No.2017slkj-14)the Shaanxi Provincial Department of Science and Technology Project(No.2017JQ3043),China。
文摘Solute transport simulations are important in water pollution events.This paper introduces a finite volume Godunovtype model for solving a 4×4 matrix form of the hyperbolic conservation laws consisting of 2D shallow water equations and transport equations.The model adopts the Harten-Lax-van Leer-contact(HLLC)-approximate Riemann solution to calculate the cell interface fluxes.It can deal well with the changes in the dry and wet interfaces in an actual complex terrain,and it has a strong shock-wave capturing ability.Using monotonic upstream-centred scheme for conservation laws(MUSCL)linear reconstruction with finite slope and the Runge-Kutta time integration method can achieve second-order accuracy.At the same time,the introduction of graphics processing unit(GPU)-accelerated computing technology greatly increases the computing speed.The model is validated against multiple benchmarks,and the results are in good agreement with analytical solutions and other published numerical predictions.The third test case uses the GPU and central processing unit(CPU)calculation models which take 3.865 s and 13.865 s,respectively,indicating that the GPU calculation model can increase the calculation speed by 3.6 times.In the fourth test case,comparing the numerical model calculated by GPU with the traditional numerical model calculated by CPU,the calculation efficiencies of the numerical model calculated by GPU under different resolution grids are 9.8–44.6 times higher than those by CPU.Therefore,it has better potential than previous models for large-scale simulation of solute transport in water pollution incidents.It can provide a reliable theoretical basis and strong data support in the rapid assessment and early warning of water pollution accidents.
