Related papers: A new thermodynamically compatible finite volume s…
In this work we present a novel second order accurate well balanced (WB) finite volume (FV) scheme for the solution of the general relativistic magnetohydrodynamics (GRMHD) equations and the first order CCZ4 formulation (FO-CCZ4) of the…
We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference method on an Eulerian grid, called the Total Variation Diminishing…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
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…
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 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…
The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning…
This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and finite volume methods which provably preserve the positivity of density and pressure for the ideal MHD on general meshes. Unified auxiliary theories are…
We are interested in the discretisation of a drift-diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear…
We present a structure-preserving and thermodynamically consistent numerical scheme for classical magnetohydrodynamics, incorporating viscosity, magnetic resistivity, heat transfer, and thermoelectric effect. The governing equations are…
We present a new computational method for smoothly matching general relativistic ideal magnetohydrodynamics (MHD) to its force-free limit. The method is based on a flux-conservative formalism for MHD and its force-free limit, and a vector…
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form. The approach is based on the definition of compatible…
A well-balanced second order finite volume central scheme for the magnetohydrodynamic (MHD) equations with gravitational source term is developed in this paper. The scheme is an unstaggered central scheme that evolves the numerical solution…
We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented…
A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…
We present the first conservative finite volume numerical scheme for the causal, stable relativistic Navier-Stokes equations developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). BDNK theory has arisen very recently as a promising…
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 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…
Based on a rigorous thermodynamic framework, this work develops a two-fluid magnetohydrodynamic model grounded in the Helmholtz free energy formalism. The model maintains full thermodynamic consistency by simultaneously satisfying energy…
Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such…