Related papers: Characteristic boundary conditions for magnetohydr…
This paper first studies the admissible state set $\mathcal G$ of relativistic magnetohydrodynamics (RMHD). It paves a way for developing physical-constraints-preserving (PCP) schemes for RMHD equations with the solutions in $\mathcal G$.…
For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global…
We present a new magnetohydrodynamic (MHD) simulation code with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements…
We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates the need for ad hoc parameters. The viscosity is…
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 develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions (BCs) that are intrinsically consistent…
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 propose and analyse a hybrid high-order (HHO) scheme for stationary incompressible magnetohydrodynamics equations. The scheme has an arbitrary order of accuracy and is applicable on generic polyhedral meshes. For sources that are small…
In this paper we propose a novel thermodynamically compatible finite volume scheme for the numerical solution of the equations of magnetohydrodynamics (MHD) in one and two space dimensions. As shown by Godunov in 1972, the MHD system can be…
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…
In an attempt to investigate the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, we have developed a new special…
In this work we introduce the concept of characteristic boundary conditions (CBCs) within the framework of Hybridizable Discontinuous Galerkin (HDG) methods, including both the Navier-Stokes characteristic boundary conditions (NSCBCs) and a…
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 present a finite-volume, genuinely 4th-order accurate numerical method for solving the equations of resistive relativistic magnetohydrodynamics (Res-RMHD) in Cartesian coordinates. In our formulation, the magnetic field is evolved in…
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical…
Magnetic fields play an important role in many astrophysical systems and a detailed understanding of their impact on the gas dynamics requires robust numerical simulations. Here we present a new method to evolve the ideal…
I consider the nonaxisymmetric linear theory of a rotating, isothermal magnetohydrodynamic (MHD) shear flow. The analysis is performed in the shearing box, a local model of a thin disk, using a decomposition in terms of shearing waves,…
In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
The global regularity for the incompressible magnetohydrodynamic equations (MHD) in three dimensions is a long standing open problem of fluid dynamics and PDE theory. The Navier-Stokes equations can be viewed as a special case of MHD with a…