Combined Numerical Schemes

被引：6

作者：

Bragin, M. D. ^{[1
,2
]}

Kovyrkina, O. A. ^{[3
]}

Ladonkina, M. E. ^{[1
]}

Ostapenko, V. V. ^{[3
]}

Tishkin, V. F. ^{[1
]}

Khandeeva, N. A. ^{[3
]}

机构：

[1] Russian Acad Sci, Keldysh Inst Appl Math, Fed Res Ctr, Moscow 125047, Russia

[2] Natl Res Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow, Russia

[3] Russian Acad Sci, Lavrentyev Inst Hydrodynam, Siberian Branch, Novosibirsk 630090, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2022年 / 62卷 / 11期

基金：

中国国家自然科学基金; 俄罗斯基础研究基金会; 俄罗斯科学基金会;

关键词：

hyperbolic systems of conservation laws; shock waves; high-order accurate shock-capturing methods; combined schemes; DISCONTINUOUS GALERKIN METHOD; FINITE-DIFFERENCE SCHEMES; SCALAR CONSERVATION LAW; HIGHER-ORDER ACCURACY; CABARET SCHEME; BICOMPACT SCHEMES; EFFICIENT IMPLEMENTATION; MONOTONICITY; APPROXIMATION; SYSTEMS;

D O I：

10.1134/S0965542522100025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A survey of works concerning high-order accurate numerical methods designed for shock-capturing computations of discontinuous solutions to hyperbolic systems of conservation laws is presented. The basic problems arising in the theory of such methods are formulated, and approaches to their solution are proposed. Primary attention is given to fundamentally new shock-capturing methods (known as combined schemes) that monotonically localize shock fronts, while preserving high accuracy in shock influence areas. Test computations are presented that demonstrate the significant advantages of combined schemes over standard NFC ones when applied to computing discontinuous solutions with shock waves.

引用

页码：1743 / 1781

页数：39

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