基于非结构网格求解二维浅水方程的高精度有限体积方法

采用HLL格式,在三角形非结构网格下采用有限体积离散,建立了求解二维浅水方程的高精度的数值模型.本文采用多维重构和多维限制器的方法来获得高精度的空间格式以及防止非物理振荡的产生,时间离散采用三阶Runge-Kutta法以获得高阶的时间精度.基于三角形网格,底坡源项采用简单的斜底模型离散,为保证计算格式的和谐性,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.算例证明本文提出的方法的和谐性并具有高精度的间断捕捉能力和稳定性.

Solution of the 2D shallow water equations using the high-resolution finite-volume method on unstructured meshes

Based on the HLL's approximate Riemann solver,a high-resolution model is developed for unsteady,two-dimensional,shallow water flow with triangular mesh.In order to achieve high-order spatial accuracy and to prevent nonphysical oscillations,the multi-dimensional reconstruction technique and the multi-dimensional limiter are employed in this study.A third-order Runge-Kutta method is used for the time integration of semi-discrete equations.In order to establish a well-balanced scheme for arbitrary geometry with triangular mesh,the classic HLL scheme is improved.The good quality of the results is illustrated by means of several examples including shallow water flow test cases.