Related papers: Numerical Magnetohydrodynamics in Astrophysics: Al…
We present a second-order upwind numerical scheme for equations of relativistic hydrodynamics with a source term. A new non-linear Riemann solver is constructed. Solution of a Riemann problem on a cells boundary is based on exact relations…
We present a new code designed to solve the equations of classical ideal magneto-hydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centers on the analysis of solar phenomena within…
In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been…
A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-oscillatory (WENO) scheme. It computes a high-order numerical…
We present a new numerical code which solves the general relativistic magneto-hydrodynamics (GRMHD) equations coupled to the Einstein equations for the evolution of a dynamical spacetime within the conformally-flat approximation. This code…
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 propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented…
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven…
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…
We prove the non-uniqueness of weak solutions to 3D magnetohydrodynamic (MHD for short) equations. The constructed weak solutions do not conserve the magnetic helicity and can be close to any given smooth, divergence-free and mean-free…
We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic…
Numerical methods to improve the treatment of magnetic fields in smoothed field magnetohydrodynamics (SPMHD) are developed and tested. Chapter 2 is a review of SPMHD. In Chapter 3, a mixed hyperbolic/parabolic scheme is developed which…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in $C([0,T];L^2(\mathbb{T}^3))$ for any initial data in $H^{\bar{\beta}}(\mathbb{T}^3)$~($\bar{\beta}>0$), by exhibiting that the total energy…
A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging…
Magnetohydrodynamics is an important tool to study the dynamics of plasma Space Physics. In this context, we introduce a three-dimensional magnetohydrodynamic solver with divergence-cleaning in the adaptive multiresolution CARMEN code. The…
The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with finite electrical conductivity describe the motion of viscous electrically conducting fluids in a magnetic field. In this paper, we find twelve families of…
In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the convective and coupling terms, we propose…