AHigh-OrderWell-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model

作     者：Jiaojiao Li Gang Li Shouguo Qian Jinmei Gao Qiang Niu 

作者机构：School of Mathematics and StatisticsQingdao UniversityQingdaoShandong 266071China Department of Mathematical SciencesXi’an Jiaotong-Liverpool UniversitySuzhouJiangsu 215123China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2020年第12卷第6期

页      面：1416-1437页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：support of the Natural Science Foundation of China through Grants No.11771228 The author Qiang Niu is supported by the XJTLU research enhancement fund with No.REF-18-01-04 and the Key Programme Special Fund(KSF)in XJTLU with Nos.KSF-E-32,KSF-E-21 and KSF-P-02 

主　　题：Ripa model lake at rest steady state source term discontinuous Galerkin method,well-balancing property hydrostatic reconstruction. 

摘      要：In this work,we present a high-order discontinuous Galerkin method for the shallow water equations incorporating horizontal temperature gradients(also known as the Ripa model),which exactly maintains the lake at rest steady ***,we propose original numerical fluxes defined on the basis of the hydrostatic reconstruction idea and a simple source term *** novel approach allows us to achieve the well-balancing of the discontinuous Galerkin method without ***,the proposed method retains genuinely high-order accuracy for smooth solutions and it shows good resolution for discontinuous solutions at the same *** numerical analysis as well as extensive numerical results all verify the good performances of the proposed method.