基于有限体积HWENO格式的一维溃坝流模拟

Simulation of one-dimensional dam break based on finite volume HWENO scheme

基于浅水波方程组建立一维溃坝流模型,并给出数值模拟结果.其中,空间离散采用HWENO(Hermit Weighted Es-sentially Non-Oscillatory)格式,时间离散采用四步TVD(Total Variation Diminish-ing)Runge-Kutta方法,模拟堤坝溃决时洪水演进过程.模拟结果表明:较采用WENO格式所得数值解更精确;同时,相比WENO格式的相应算法,该算法解决一维溃坝流问题能更有效地减弱振荡,对间断具有更高的分辨率.

This paper presents a new model of one-dimensional dam break flows based on shallow water equations, in which HWENO scheme is employed for spacial discretization and four steps TVD Runge-Kutta method is used for time discretization. The numerical results demonstrate that they are more accurate than those based on WENO scheme;simultaneously, the program in this paper can weaken oscillation for one-dimensional dam-break flows more effectively, and possesses higher resolution than that of WENO scheme.