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In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient…

Numerical Analysis · Mathematics 2015-06-17 Andrew J. Christlieb , James A. Rossmanith , Qi Tang

We report a new finite-difference scheme for two-dimensional magnetohydrodynamics (MHD) simulations, with and without rotation, in unstructured grids with quadrilateral cells. The new scheme is implemented within the code VULCAN/2D, which…

Astrophysics · Physics 2009-11-13 Eli Livne , Luc Dessart , Adam Burrows , Casey A. Meakin

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher-order Godunov methods with the constrained…

Astrophysics · Physics 2009-11-13 James M. Stone , Thomas A. Gardiner , Peter Teuben , John F. Hawley , Jacob B. Simon

We employ the PLUTO code for computational astrophysics to assess and compare the validity of different numerical algorithms on simulations of the magneto-rotational instability in 3D accretion disks. In particular we stress on the…

Earth and Planetary Astrophysics · Physics 2015-05-13 M. Flock , N. Dzyurkevich , H. Klahr , A. Mignone

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…

Computational Physics · Physics 2018-03-23 Prabal Singh Verma , Jean-Mathieu Teissier , Oliver Henze , Wolf-Christian Müller

Hyperbolic conservation laws with stiff source terms appear in the study of a variety of physical systems. Early work showed that the use of formally second-order accurate semi-implicit methods could lead to a substantial loss of accuracy,…

Astrophysics · Physics 2008-11-26 Francesco Miniati , Phillip Colella

Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Els\"asser variables. We…

Numerical Analysis · Mathematics 2025-07-18 Zhen Yao , Catalin Trenchea , Wenlong Pei

This paper introduces a novel second-order splitting scheme for charged-particle dynamics in strong magnetic fields characterized by the maximal ordering. The proposed scheme is explicit and symmetric, which respectively ensure the…

Numerical Analysis · Mathematics 2026-04-14 Mengting Hu , Jiyong Li , Bin Wang

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…

Astrophysics of Galaxies · Physics 2015-05-28 Kazunari Iwasaki , Shu-ichiro Inutsuka

In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum and total energy…

Numerical Analysis · Mathematics 2018-12-26 Michael Dumbser , Dinshaw S. Balsara , Maurizio Tavelli , Francesco Fambri

We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces…

Computational Physics · Physics 2019-05-01 A. Mignone , G. Mattia , G. Bodo , L. Del Zanna

We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…

In this paper, we present exact divergence-free spectral method for solving the incompressible and resistive magneto-hydrodynamic (MHD) equations in two and three dimensions, as well as the efficient solution algorithm and unconditionally…

Numerical Analysis · Mathematics 2023-12-20 Lechang Qin , Huiyuan Li , Zhiguo Yang

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…

Plasma Physics · Physics 2018-11-14 A. Stanier , L. Chacón , G. Chen

We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields…

Analysis of PDEs · Mathematics 2021-06-04 Wei-Xi Li , Rui Xu

A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…

Computational Physics · Physics 2017-09-13 Haran Jackson

We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of…

High Energy Astrophysical Phenomena · Physics 2019-02-20 Kazuya Takahashi , Shoichi Yamada

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states…

Solar and Stellar Astrophysics · Physics 2024-05-29 G. Leidi , R. Andrassy , W. Barsukow , J. Higl , P. V. F. Edelmann , F. K. Röpke

We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…

Numerical Analysis · Mathematics 2022-01-07 Thad A. Gleason , Eric L. Peters , John A. Evans