Related papers: Relativistic Magnetohydrodynamics: Renormalized ei…
In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is…
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…
In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and…
Smoothed Particle Hydrodynamics is reformulated in terms of the convolution of the original hydrodynamics equations, and the new evolution equations for the particles are derived. The same evolution equation of motion is also derived 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 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…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
A numerical method for the quasi-neutral two-fluid (QNTF) plasma model is described. The basic equations are ion and electron fluid equations and the Maxwell equations without displacement current. The neglect of displacement current is…
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…
In this paper, we develop a new method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov method is applied to SPH instead of artificial dissipation terms. In the…
A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general,…
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two…
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…
This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property…
We consider two Large Eddy Simulation (LES) models for the approximation of large scales of the equations of Magnetohydrodynamics (MHD in the sequel). We study two $\alpha$-models, which are obtained adapting to the MHD the approach by…
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic…
We analyze the cosmic-ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
We introduce CAFE, a new independent code designed to solve the equations of Relativistic ideal Magnetohydrodynamics (RMHD) in 3D. We present the standard tests for a RMHD code and for the Relativistic Hydrodynamics (RHD) regime since we…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…