High Order Well-balanced Discontinuous Galerkin Method For Solving The Ripa Model

Ripa model has been successfully applied to canal opening,tidal flow problem and so on.Proposals for resolving this issue include finite difference,finite volume,and Discontinuous Galerkin(DG)techniques,all numerical.This paper concentrates on the Galerkin method of high order discontinuity to resolve the steady answer of both the one-dimensional Ripa model and the twodimensional Ripa model,with a focus on the Ripa water solution for the static and stable solution of the model.Equations of flux that are not zero,with the source terms offset,can be discovered.However,most numerical methods are unable to maintain a stable solution,leading to a numerical pseudo shock in the calculation process.Thus,the answer to this was found.In order to achieve the stable solution properties,we introduce an artificial variables to the special factorization of the source term,by choosing appropriate artificial variables,the equations of restructuring.The eigenvalues of the original system and their corresponding eigenvectors are not changed after artificial variables are introduced into the system.Through this unique way of decomposition,no need to build intricate numerical circulation.The arbitrary numerical flux method of Discontinuous Galerkin can provide stable solution properties.The discrete equation of the decomposed by Discontinuous Galerkin method,with part of the source term staying constant in flux discrete form,is applied again to a discrete format Ripa model of third order Runge-Kutta method of discrete time.At long last,a secure answer to the high-order Discontinuous Galerkin was attained.