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The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate…

Instrumentation and Methods for Astrophysics · Physics 2011-04-28 Knut Waagan , Christoph Federrath , Christian Klingenberg

We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The…

High Energy Astrophysical Phenomena · Physics 2015-06-04 Jinho Kim , Hee Il Kim , Matthew William Choptuik , Hyung Mok Lee

Fully adaptive computations of the resistive magnetohydrodynamic (MHD) equations are presented in two and three space dimensions using a finite volume discretization on locally refined dyadic grids. Divergence cleaning is used to control…

Numerical Analysis · Mathematics 2021-02-24 Anna Karina Fontes Gomes , Margarete Oliveira Domingues , Odim Mendes , Kai Schneider

We present a set of simulations of relativistic jets from accretion disk initial setup with a new code in Fortran 90 to get numerical solutions of a system of General Relativistic Magnetohydrodynamics (GRMHD) partial differential equations…

High Energy Astrophysical Phenomena · Physics 2016-02-08 R. O. Garcia , S. R. Oliveira

Accretion of magnetized gas on compact astrophysical objects such as black holes has been successfully modeled using general relativistic magnetohydrodynamic (GRMHD) simulations. These simulations have largely been performed in the Kerr…

High Energy Astrophysical Phenomena · Physics 2024-03-07 Prashant Kocherlakota , Ramesh Narayan , Koushik Chatterjee , Alejandro Cruz-Osorio , Yosuke Mizuno

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…

High Energy Astrophysical Phenomena · Physics 2023-01-11 Kenta Kiuchi , Loren E. Held , Yuichiro Sekiguchi , Masaru Shibata

We present a method for general relativistic smoothed particle hydrodynamics (GRSPH), based on an entropy-conservative form of the general relativistic hydrodynamic equations for a perfect fluid. We aim to replace approximate treatments of…

Instrumentation and Methods for Astrophysics · Physics 2019-01-25 David Liptai , Daniel J. Price

This work presents the first numerical investigation of using Voigt regularization as a method for obtaining magnetohydrodynamic (MHD) equilibria without the assumption of nested magnetic flux surfaces. Voigt regularization modifies the MHD…

Plasma Physics · Physics 2025-06-16 Yi-Min Huang , Justin Kin Jun Hew , Andrew Brown , Amitava Bhattacharjee

A robust second order, shock-capturing numerical scheme for multi-dimensional special relativistic magnetohydrodynamics on computational domains with adaptive mesh refinement is presented. The base solver is a total variation diminishing…

Astrophysics · Physics 2009-11-13 B. van der Holst , R. Keppens , Z. Meliani

We present our new general relativistic Monte Carlo (MC)-based neutrino radiation hydrodynamics code designed to solve axisymmetric systems with several improvements. The main improvements are as follows: (i) the development of an extended…

High Energy Astrophysical Phenomena · Physics 2024-12-02 Kyohei Kawaguchi , Sho Fujibayashi , Masaru Shibata

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme using the Geometric Density average force expression (GDSPH). GDSPH has recently been shown to reduce the leading order errors and…

Instrumentation and Methods for Astrophysics · Physics 2020-07-31 Robert Wissing , Sijing Shen

We present a novel approach to study the global structure of steady, axisymmetric, advective, geometrically thin, magnetohydrodynamic (MHD) accretion flow around black holes in full general relativity (GR). Considering ideal MHD conditions…

High Energy Astrophysical Phenomena · Physics 2022-10-05 Samik Mitra , Debaprasad Maity , Indu Kalpa Dihingia , Santabrata Das

On the basis of simple principles we derive and investigate the equations of relativistic plasma magnetohydrodynamics (MHD) in an arbitrary gravitational field. An exact solution describing the motion of magnetoactive plasma against the…

General Relativity and Quantum Cosmology · Physics 2011-01-06 Yu. G. Ignatyev

The equations of 2D incompressible dissipationless extended magnetohydrodynamics (XMHD) extend the equations of incompressible Hall MHD (HMHD) by retaining finite-electron inertia. These XMHD equations couple the fluid velocity ${\bf V} =…

Plasma Physics · Physics 2025-08-26 Alain J. Brizard

Motivated by a recent paper by the Potsdam numerical relativity group, we have constructed a new numerical code for hydrodynamic simulation of axisymmetric systems in full general relativity. In this code, we solve the Einstein field…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Masaru Shibata

Relativistic macroscopic plasma dynamics can be described by general-relativistic magnetohydrodynamics. In many high-energy astrophysical settings, such as the interior dynamics of magnetized stars, the ideal GRMHD approximation, in which…

High Energy Astrophysical Phenomena · Physics 2025-10-23 Sara Azizi , Swapnil Shankar , Philipp Mösta , Roland Haas , Erik Schnetter

We present a new numerical code, ECHO, based on an Eulerian Conservative High Order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a…

Astrophysics · Physics 2009-11-13 L. Del Zanna , O. Zanotti , N. Bucciantini , P. Londrillo

General relativistic magnetohydrodynamic (GRMHD) simulations represent a fundamental tool to probe various underlying mechanisms at play during binary neutron star (BNS) and neutron star (NS) - black hole (BH) mergers. Contemporary…

High Energy Astrophysical Phenomena · Physics 2022-05-27 Jay V. Kalinani , Riccardo Ciolfi , Wolfgang Kastaun , Bruno Giacomazzo , Federico Cipolletta , Lorenzo Ennoggi

We present results of models of the physical space and parameters of the accretion disk of Sagittarius A*, as well as simulations of its emergent spectrum. This begins with HARM, a 2D general relativistic magneto-hydrodynamic (GRMHD) model,…

High Energy Astrophysical Phenomena · Physics 2011-04-18 Guy Hilburn , Edison Liang , Siming Liu , Hui Li

We investigate relativistic low angular momentum accretion of inviscid perfect fluid onto a Schwarzschild black hole. The simulations are performed with a general-relativistic, high-resolution (second-order), shock-capturing, hydrodynamical…

General Relativity and Quantum Cosmology · Physics 2018-03-13 Patryk Mach , Michał Piróg , José A. Font