A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics

Miyoshi, Tetsuya; Kusano, K.

doi:10.1016/j.jcp.2005.02.017

Cited by 668 publications

(575 citation statements)

References 30 publications

(117 reference statements)

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“…The simplest f m flux is Lax-Friedrichs flux but our MAP code also implemented approximate Riemann solvers like HLLC [27], HLLD [28] and Roe solver [29,30]. Since the formulae of these Riemann solvers are too complicated to be given here, thus we only list the Lax-Friedrichs flux as…”

Section: Lf Schemementioning

confidence: 99%

A new MHD code with adaptive mesh refinement and parallelization for astrophysics

Jiang

Fang

Chen

2012

Computer Physics Communications

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A new code, named MAP, is written in FORTRAN language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax-Fridrichs scheme (LF) and weighted essentially non-oscillatory (WENO) scheme. All of them are second order, twostep, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the MAP code. The details of the AMR and MPI algorithms are described in the paper.

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Section: Lf Schemementioning

confidence: 99%

A new MHD code with adaptive mesh refinement and parallelization for astrophysics

Jiang

Fang

Chen

2012

Computer Physics Communications

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“…For example, Roe's Riemann solvers are developed by Brio and Wu [1], Dai and Woodward [6], Zachary and Collelaz [7], Roe and Balsara [2] and Cargo and Gallice [8]. HLL (Harten-Lax-van Leer)-type schemes are developed by Janhunen [9], Honkkila and Janhunen [10], Gurski [11], Li [12], Miyoshi and Kusano [13] and Balsara et al [14]. Flux vector splitting methods are developed by MacCormack [15] and Jiang and Wu [4].…”

Section: Introductionmentioning

confidence: 99%

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Shen

Zha

Huerta

2012

Journal of Computational Physics

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a b s t r a c tAn E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

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“…No stability analysis is known in their case, and indeed instabilities can occur in practice. Miyoshi and Kusano proposed in [11] an approximate Riemann solver with 5 waves, that also accurately resolves Alfven contact waves. Even if no analysis of stability is provided, it is stable in practice.…”

Section: 1mentioning

confidence: 99%

“…For comparison purposes we consider the Roe solver of [1], the HLL solver, and the 5-wave solver of [11], denoted by MK5. As signal speeds for HLL and MK5 we used the speeds for the 3-wave solver from Section 3.…”

Section: Numerical Testsmentioning

confidence: 99%

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A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework

Bouchut

Klingenberg

Waagan³

2007

Numer. Math.

132

125

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Abstract. In the first part of this work ([5]), we introduced an approximate Riemann solver for one-dimensional ideal MHD derived from a relaxation system. We gave sufficient conditions for the solver to satisfy discrete entropy inequalities, and to preserve positivity of density and internal energy. In this paper we consider the practical implementation, and derive explicit wave speed estimates satisfying the stability conditions of [5]. We present a 3-wave solver that well resolves fast waves and material contacts, and a 5-wave solver that accurately resolves the cases when two eigenvalues coincide. A full 7-wave solver, which is highly accurate on all types of waves, will be described in a follow-up paper. We test the solvers on one-dimensional shock tube data and smooth shear waves.

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A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics

Cited by 668 publications

References 30 publications

A new MHD code with adaptive mesh refinement and parallelization for astrophysics

A new MHD code with adaptive mesh refinement and parallelization for astrophysics

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework

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