艾丛芳,金生.求解具有复杂地形二维浅水方程的修正HLL格式[J].,2009,(6):926-931 |
求解具有复杂地形二维浅水方程的修正HLL格式 |
Solution of 2D shallow water equations with complicated geometry using modified HLL scheme |
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DOI:10.7511/dllgxb200906026 |
中文关键词: 浅水方程 HLL格式 有限体积 |
英文关键词: shallow water equation HLL scheme finite volume |
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中文摘要: |
采用非结构网格的有限体积方法,对具有复杂地形的二维浅水方程进行数值模拟.采用HLL近似Riemann解计算界面数值通量,基于三角形网格,底坡源项采用简单的斜底模型离散,保证了地形的离散精度,摩阻源项采用全隐方式求解以保证格式的稳定性.采用多维重构及多维限制器的方法获得空间二阶精度的格式,时间离散采用三阶Runge-Kutta法以获得高阶时间精度.为保证格式的和谐性,对经典的HLL格式计算的数值通量中的静水压力项进行了修正.数值计算的结果验证此格式具有良好的高精度捕捉间断的能力,可以应用到地形复杂的二维浅水问题计算中去. |
英文摘要: |
A numerical model based on the unstructured grid finite volume method is developed for two-dimensional shallow water equation with complicated geometry. The HLL approximate Riemann solver is used for the computation of numerical flux functions. Based on triangular grid, the bed slope source terms are computed since three vertices of a triangle lie on the same plane. The friction source terms are treated in a fully implicit way to alleviate stabilities of the scheme. To achieve high-order spatial accuracy and prevent nonphysical oscillations, the multidimensional reconstruction technique and multidimensional limiter are employed. The time discretization is made by the third-order Runge-Kutta method to accomplish high-order temporal accuracy. To balance the pressure and bed slope terms, the hydrostatic pressure term in the momentum equation is corrected. The good quality of the results verifies that the scheme has good capability of shock capturing, and can be applied to real flows with complex boundary. |
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