An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

被引：2

作者：

Chen, Li ^{[1
]}

Li, Ruo ^{[1
,2
,3
]}

Yang, Feng ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing, Peoples R China

[2] Peking Univ, HEDPS, Beijing, Peoples R China

[3] Peking Univ, CAPT, LMAM, Beijing, Peoples R China

来源：

CSIAM TRANSACTIONS ON APPLIED MATHEMATICS | 2020年 / 1卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Quadratic reconstruction; finite volume method; local maximum principle; scalar conservation law; unstructured mesh; ESSENTIALLY NONOSCILLATORY SCHEMES; LINEAR RECONSTRUCTION; UNSTRUCTURED MESHES; ADAPTIVE STENCILS; SLOPE LIMITERS;

D O I：

10.4208/csiam-am.2020-0017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and applicable on flexible grids. We show that the finite volume schemes with the new reconstruction satisfy a local maximum principle with properly setup on time steplength. Numerical examples are presented to show that the proposed scheme attains a third-order accuracy for smooth solutions in both 2D and 3D cases. It is indicated by numerical results that the local maximum principle is helpful to prevent overshoots in numerical solutions.

引用

页码：491 / 517

页数：27

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