Conservative limiting method for high-order bicompact schemes as applied to systems of hyperbolic equations

被引：11

作者：

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

Rogov, Boris V. ^{[1
,2
]}

机构：

[1] Keldysh Inst Appl Math, 4 Miusskaya Sq, Moscow 125047, Russia

[2] Moscow Inst Phys & Technol, 9 Inst Skiy Per, Dolgoprudnyi 141701, Moscow Region, Russia

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 151卷

基金：

俄罗斯科学基金会;

关键词：

Bicompact schemes; Conservative schemes; Monotonicity preserving schemes; Hyperbolic equations; Discontinuous solutions; EFFICIENT IMPLEMENTATION; ACCURATE; 4TH-ORDER;

D O I：

10.1016/j.apnum.2020.01.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, a new limiting method for bicompact schemes is proposed that preserves them conservative. The method is based upon a finite-element treatment of the bicompact approximation. An analogy between collocation finite-element schemes and bicompact schemes is established. The proposed method is tested on one-dimensional gas dynamics problems that include the Sedov problem, the "peak test" Riemann problem, the Shu-Osher problem, and the "blast wave" problem. Additionally, the method is tested as applied to a two-dimensional problem for the quasilinear Hopf equation. It is shown on these examples that bicompact schemes with conservative limiting are significantly more accurate than hybrid bicompact schemes. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：229 / 245

页数：17

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