Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws
作者机构：College of Mathematics and StatisticsFujian Normal UniversityFuzhou350117FujianChina School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific ComputingXiamen UniversityXiamen361005FujianChina
出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)
年 卷 期：2024年第6卷第1期
页 面：605-624页
核心收录：
基 金：supported by the NSFC grant 12101128 supported by the NSFC grant 12071392.
主 题：Finite volume Dimension by dimension HWENO Hyperbolic conservation laws
摘 要：In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.
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