相关论文: A comparison of approximate non-linear Riemann sol…
We present a five-wave Riemann solver for the equations of ideal relativistic magnetohydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for…
We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the…
An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The HLLC solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper (Mignone &…
We propose a new Harten-Lax-van Leer discontinuities (HLLD) approximate Riemann solver to improve the stability of shocks and the accuracy of low-speed flows in multidimensional magnetohydrodynamic (MHD) simulations. Stringent benchmark…
We implement advanced Riemann solvers HLLC and HLLD \cite{Mignone:2005ft,MUB:2009} together with an advanced constrained transport scheme \cite{Gardiner:2007nc} in a numerical-relativity neutrino-radiation magnetohydrodynamics code. We…
Approximate Riemann solvers are widely used for solving hyperbolic conservation laws, including those of magnetohydrodynamics (MHD). However, due to the nonlinearity and complexity of MHD, obtaining accurate and robust numerical solutions…
We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and…
In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid…
With the advance of supercomputers we can now afford simulations with very large ranges of scales. In astrophysical applications, e.g. simulating Solar, stellar and planetary atmospheres, interstellar medium, etc; physical quantities, like…
We are interested in the numerical solution of large systems of hyperbolic conservation laws or systems in which the characteristic decomposition is expensive to compute. Solving such equations using finite volumes or Discontinuous Galerkin…
A new approximate Riemann solver for the equations of magnetohydrodynamics (MHD) with an isothermal equation of state is presented. The proposed method of solution draws on the recent work of Miyoshi and Kusano, in the context of adiabatic…
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization…
It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of…
In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions.…
The Harten-Lax-van Leer with contact (HLLC) scheme is known to be plagued by various forms of numerical shock instabilities. In this paper, we propose a new framework for developing shock stable, contact and shear preserving approximate…
A new Riemann solver is presented for the ideal magnetohydrodynamics (MHD) equations with the so-called Boris correction. The Boris correction is applied to reduce wave speeds, avoiding an extremely small timestep in MHD simulations. The…
The Riemann problem, and the associated generalized Riemann problem, are increasingly seen as the important building blocks for modern higher order Godunov-type schemes. In the past, building a generalized Riemann problem solver was seen as…
This paper presents an application of the recent relativistic HLLC approximate Riemann solver by Mignone & Bodo to magnetized flows with vanishing normal component of the magnetic field. The numerical scheme is validated in two dimensions…
This work presents a review of high-order hybridisable discontinuous Galerkin (HDG) methods in the context of compressible flows. Moreover, an original unified framework for the derivation of Riemann solvers in hybridised formulations is…
We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic…