基于三角形网格求解二维浅水方程的改进的HLL方法

Application of improved HLL scheme for 2D shallow water equations with triangular meshes

该文采用HLL格式,在三角形网格下采用有限体积离散建立了求解二维浅水方程的数值模型。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,并证明了修正后的HLL格式具备和谐性。算例证明本文提出的方法是和谐性的并具有良好的间断捕捉能力与稳定性。

Based on the HLL＇s approximate Riemann solver with triangular meshes, a numerical model is developed for the unsteady, two-dimensional, shallow water flow with an unever bottom. In order to balance the pressure terms with the bottom slope term for arbitrary geometry with triangular mesh, the classic HLL scheme is improved. It is confirmed by an algebraic manipulation that the improved HLL scheme is well balance. The good quality of the results is illustrated by means of several examples including shallow water flow test cases.