English
Related papers

Related papers: HOW-MHD: A High-Order WENO-Based Magnetohydrodynam…

200 papers

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…

High Energy Astrophysical Phenomena · Physics 2023-12-20 Vittoria Berta , Andrea Mignone , Matteo Bugli , Giancarlo Mattia

We have written and tested a new general relativistic magnetohydrodynamics (GRMHD) code, capable of evolving MHD fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled…

High Energy Astrophysical Phenomena · Physics 2010-10-27 Zachariah B. Etienne , Yuk Tung Liu , Stuart L. Shapiro

Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation…

Astrophysics · Physics 2009-11-10 Matthew D. Duez , Yuk Tung Liu , Stuart L. Shapiro , Branson C. Stephens

The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been developed to enforce this condition. In this work, we…

Numerical Analysis · Mathematics 2019-08-06 Firat Cakir , Andrew Christlieb , Yan Jiang

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…

High Energy Astrophysical Phenomena · Physics 2024-07-12 Andrea Mignone , Vittoria Berta , Marco Rossazza , Matteo Bugli , Giancarlo Mattia , Luca Del Zanna , Lorenzo Pareschi

In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…

Numerical Analysis · Mathematics 2025-05-09 Lorenzo Micalizzi , Eleuterio F. Toro

In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…

General Relativity and Quantum Cosmology · Physics 2015-05-13 Michael Dumbser , Olindo Zanotti

We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum,…

Astrophysics of Galaxies · Physics 2016-05-13 Dominik Derigs , Andrew R. Winters , Gregor J. Gassner , Stefanie Walch

Explicit numerical computations of super-fast differentially rotating disks are subject to the time-step constraint imposed by the Courant condition. When the bulk orbital velocity largely exceeds any other wave speed the time step is…

Instrumentation and Methods for Astrophysics · Physics 2015-06-05 A. Mignone , M. Flock , M. Stute , S. M. Kolb , G. Muscianisi

We present THC: a new high-order flux-vector-splitting code for Newtonian and special-relativistic hydrodynamics designed for direct numerical simulations of turbulent flows. Our code implements a variety of different reconstruction…

Instrumentation and Methods for Astrophysics · Physics 2012-10-23 David Radice , Luciano Rezzolla

The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of gamma-ray bursts, requires the solution of the…

General Relativity and Quantum Cosmology · Physics 2008-11-26 B. Giacomazzo , L. Rezzolla

Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by…

Instrumentation and Methods for Astrophysics · Physics 2019-02-08 Thomas Guillet , Rüdiger Pakmor , Volker Springel , Praveen Chandrashekar , Christian Klingenberg

A new code, named MAP, is written in Fortran language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for…

Instrumentation and Methods for Astrophysics · Physics 2012-04-27 R. L. Jiang , C. Fang , P. F. Chen

We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous Lagrange polynomials in space and explicit Runge-Kutta schemes in time. The shock-capturing…

Numerical Analysis · Mathematics 2021-12-17 Tuan Anh Dao , Murtazo Nazarov

This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…

Numerical Analysis · Mathematics 2020-03-30 Junming Duan , Huazhong Tang

We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein Toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the…

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…

Astrophysics · Physics 2009-06-23 Andrew J. Cunningham , Adam Frank , Peggy Varniere , Sorin Mitran , Thomas W. Jones

We design a conservative finite difference scheme for ideal magnetohydrodynamic simulations that attains high-order accuracy, shock-capturing, and divergence-free condition of the magnetic field. The scheme interpolates pointwise physical…

Instrumentation and Methods for Astrophysics · Physics 2019-06-05 Takashi Minoshima , Takahiro Miyoshi , Yosuke Matsumoto

The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…

Numerical Analysis · Mathematics 2020-09-29 David Frenzel , Jens Lang

Magnetohydrodynamics (MHD) couples the Navier--Stokes and Maxwell equations into a nonlinear system of partial differential equations governing stellar interiors, astrophysical jets, fusion plasmas, and space weather. Numerical advances,…

High Energy Astrophysical Phenomena · Physics 2026-05-20 E. A. Huerta