求解Ripa模型的保持稳定解的高阶间断Galerkin法

High-order Discontinuous Galerkin Methodfor Maintaining the Stable Solution of Ripa Model

本文针对一维Ripa模型设计了一种保持稳定解的高阶间断Galerkin方法。首先引入一个辅助变量对源项进行特殊分解,然后通过间断Galerkin法离散分解后的方程,其中分解后的一部分源项与通量保持相同的离散方式。对辅助变量选取合适的值,本文严格证明了该方法能够精确地保持稳定解。最后,通过几个数值算例验证了该方法的高阶精度和保持稳定解的性质。

In this paper,a high-order discontinuous Galerkin method is designed to maintain the stable solution of Ripa model.This method first decomposes the source term by introducing an auxiliary variable,and then discretizes the new equation by the discontinuous Galerkin method,in which one part of the decomposed source term is discretized in the same way as the flux term.It is rigorously proved that this method can maintain the stable solution accurately by choosing a suitable value for the auxiliary variable.Finally,several numerical examples are selected to verify the high-order accuracy and well-balanced property of the method.