Related papers: A Fourth-Order Finite Volume Scheme for Resistive …
In this work, a simple fourth-order accurate finite volume semi-discrete scheme is introduced to solve astrophysical magnetohydrodynamics (MHD) problems on Cartesian meshes. Hydrodynamic quantities like density, momentum and energy are…
We present a novel implementation of a genuinely $4^{\rm th}$-order accurate finite volume scheme for multidimensional classical and special relativistic magnetohydrodynamics (MHD) based on the constrained transport (CT) formalism. The…
We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation…
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer…
We have written and tested a new general relativistic magnetohydrodynamics (GRMHD) code, capable of evolving MHD fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled…
A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…
We develop a numerical scheme for solving a fully special relativistic resistive radiation magnetohydrodynamics. Our code guarantees conservations of total mass, momentum and energy. Radiation energy density and radiation flux are…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric…
Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using…
We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from nonrelativistic to relativistic (shock, contact discontinuity, and Alfv\'en wave).…
We construct a relativistic resistive magneto-hydrodynamic (RRMHD) numerical simulation code for high-energy heavy-ion collisions. We split the system of differential equations into two parts, a non-stiff and a stiff part. For the non-stiff…
A third order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against several numerical tests. The simple and efficient central scheme described in Paper…
The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO…
We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Rung-Kutta…
We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the…
In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum and total energy…
Relativistic macroscopic plasma dynamics can be described by general-relativistic magnetohydrodynamics. In many high-energy astrophysical settings, such as the interior dynamics of magnetized stars, the ideal GRMHD approximation, in which…
The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts…