A family of HLL-type solvers for the generalized Riemann problem

被引:19
|
作者
Goetz, Claus R. [1 ]
Balsara, Dinshaw S. [2 ]
Dumbser, Michael [3 ]
机构
[1] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany
[2] Univ Notre Dame, Dept Phys, 333h Nieuwland Sci Hall, Notre Dame, IN 46556 USA
[3] Dept Civil Environm & Mech Engn, Via Mesiano 77, I-38123 Trento, Italy
基金
欧洲研究理事会; 美国国家科学基金会;
关键词
Generalized Riemann problems; Hyperbolic conservation laws; High order finite volume methods; COMPRESSIBLE FLUID-FLOWS; HIGH-ORDER; ASYMPTOTIC-EXPANSION; CONSERVATION-LAWS; EQUATIONS; SCHEMES; SYSTEMS;
D O I
10.1016/j.compfluid.2017.10.028
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The generalized Riemann problem (GRP) is the initial value problem for a conservation law with piece-wise smooth, but discontinuous initial data. We provide a new method for solving the GRP approximately, that can be used as a building block for high order finite volume or discontinuous Galerkin methods. Our new GRP solvers use the approximate states and wave speeds obtained through a HLL-type Riemann solver and use this information to build an approximation of the state in the GRP of any order. What is new about this approach compared to most previous solvers is that we no longer need to solve a classical Riemann problem exactly. We give a detailed explanation of this strategy for HLL and HLLC solvers for the Euler equations, as well as for the HLLD solver for MHD equations. We demonstrate the performance of the solvers from this new family of GRP solvers for a broad range of test problems. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:201 / 212
页数:12
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