Related papers: Numerical Magnetohydrodynamics in Astrophysics: Al…
Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The…
We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the…
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct…
The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…
We study the Rayleigh-Taylor problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows, with zero resistivity, surface tension (or without surface tenstion) and special initial magnetic field, evolving with a free…
Following the previous work of Ferretti and Yang on the role of magnetic fields in the theory of conformal turbulence, we show that non-unitary minimal model solutions to 2-dimensional magnetohydrodynamics (MHD) obtained by dimensional…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh refinement code for ideal magnetohydrodynamics. The code provides several high resolution, shock capturing schemes which are constructed to maintain…
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…
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…
We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
We study 1+1 dimensional relativistic non-resistive magnetohydrodynamics (MHD) with longitudinal boost invariance and shear stress tensor. Several analytical solutions that describe the fluid temperature evolution under the equation of…
We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic…
The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the…
The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful insights on many astrophysical problems. We describe a pseudo-spectral MHD code suitable for the study of incompressible turbulence. We review our recent works on…
We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because…
We extend recently-developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray…
Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of…
Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed…