Application of a discontinuous Galerkin finite element method to special relativistic hydrodynamic models

被引：5

作者：

Qamar, Shamsul ^{[1
,2
]}

Yousaf, Muhammad ^{[1
]}

机构：

[1] COMSATS Inst Informat Technol, Dept Math, Islamabad, Pakistan

[2] Max Planck Inst Dynam Complex Tech Syst, D-39106 Magdeburg, Germany

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2013年 / 65卷 / 08期

关键词：

Special relativistic hydrodynamics; Conservation laws; Discontinuous solutions; Discontinuous Galerkin method; Runge-Kutta method; CONSERVATION-LAWS; GAS-DYNAMICS; SCHEMES; EQUATIONS;

D O I：

10.1016/j.camwa.2013.02.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Runge-Kutta discontinuous Galerkin (RKDG) finite element method is proposed for solving the special relativistic hydrodynamic (SRHD) equations and as a limiting case the ultra-relativistic hydrodynamic (URHD) equations. The latter model is obtained by ignoring the rest-mass energy when the internal energy of fluid particles is sufficiently large. Several test problems of SRHD and URHD models are carried out. For validation, the results of DG-method are compared with the staggered central scheme. The numerical results verify the accuracy of the proposed method qualitatively and quantitatively. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：1220 / 1232

页数：13

共 34 条

[1] Genesis:: A high-resolution code for three-dimensional relativistic hydrodynamics [J].

Aloy, MA ;

Ibáñez, JM ;

Martí, JM ;

Müller, E .

ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 1999, 122 (01) :151-166

[2]

[Anonymous], SPRINGER TEXTS APPL

[3]

[Anonymous], 1972, Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity

[4]

[Anonymous], 1997, 9765 ICASE

[5] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[6] THE RUNGE-KUTTA LOCAL PROJECTION RHO-1-DISCONTINUOUS-GALERKIN FINITE-ELEMENT METHOD FOR SCALAR CONSERVATION-LAWS [J].

COCKBURN, B ;

SHU, CW .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1991, 25 (03) :337-361

[7] Runge-Kutta discontinuous Galerkin methods for convection-dominated problems [J].

Cockburn, Bernardo ;

Shu, Chi-Wang .

Journal of Scientific Computing, 2001, 16 (03) :173-261

[8] TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .2. GENERAL FRAMEWORK [J].

COCKBURN, B ;

SHU, CW .

MATHEMATICS OF COMPUTATION, 1989, 52 (186) :411-435

[9] TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .3. ONE-DIMENSIONAL SYSTEMS [J].

COCKBURN, B ;

LIN, SY ;

SHU, CW .

JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 84 (01) :90-113

[10]

Csernai L.P., 1994, Introduction to relativistic heavy ion collisions

← 1 2 3 4 →