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We present a new algorithm for numerical magnetohydrodynamics on staggered meshes preserving $\nabla \cdot B = 0$. Our algorithm is based on the constrained transport method and supports both cell-based adaptive mesh refinement and temporal…

Space Physics · Physics 2025-12-15 Ilja Honkonen , Riku Jarvinen , David Phillips

In this work, we develop a discretisation method for the mixed formulation of the magnetostatic problem supporting arbitrary orders and polyhedral meshes. The method is based on a global discrete de Rham (DDR) sequence, obtained by patching…

Numerical Analysis · Mathematics 2020-11-12 Daniele A. Di Pietro , Jérôme Droniou

We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently large choices of the control parameter and resolution and…

Analysis of PDEs · Mathematics 2019-08-20 Animikh Biswas , Joshua Hudson , Adam Larios , Yuan Pei

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

We prove the low Mach number limit of non-isentropic ideal magnetohydrodynamic (MHD) equations with general initial data in the half-space whose boundary satisfies the perfectly conducting wall condition. By observing a special structure…

Analysis of PDEs · Mathematics 2024-12-16 Qiangchang Ju , Jiawei Wang , Junyan Zhang

We present a carefully designed, systematic study of the angular resolution dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics code. Employing a simplified neutrino heating-cooling scheme in the Prometheus…

High Energy Astrophysical Phenomena · Physics 2020-03-11 Tobias Melson , Daniel Kresse , H. -Thomas Janka

In this work we extend the non-ideal magnetohydrodynamics (MHD) solver in the moving mesh code AREPO to include the Hall effect. The core of our algorithm is based on an estimation of the magnetic field gradients by a least-square…

Instrumentation and Methods for Astrophysics · Physics 2023-09-29 Oliver Zier , Alexander C. Mayer , Volker Springel

The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…

Numerical Analysis · Mathematics 2026-02-25 Peiyao Zhao , Rui Wang , Tingting Wu , Yuesheng Xu

Compressible magnetohydrodynamic (MHD) turbulence is a common feature of astrophysical systems such as the solar atmosphere and interstellar medium. Such systems are rife with shock waves that can redistribute and dissipate energy. For an…

Plasma Physics · Physics 2025-01-22 B. Snow , A. Hillier , G. Murtas , G. J. J. Botha

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

Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…

Numerical Analysis · Mathematics 2022-10-19 Thomas Bellotti , Loïc Gouarin , Benjamin Graille , Marc Massot

This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…

Numerical Analysis · Mathematics 2026-04-06 Yizhou Liang , Ngoc Tien Tran

We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key $L^{3}$ estimate for divergence-free finite element…

Numerical Analysis · Mathematics 2019-05-03 Kaibo Hu , Weifeng Qiu , Ke Shi

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic…

Numerical Analysis · Mathematics 2023-06-14 Wei Chen , Kailiang Wu , Tao Xiong

We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equations gives a symmetric system for the vector of primitive…

Analysis of PDEs · Mathematics 2015-06-04 Heinrich Freistühler , Yuri Trakhinin

The charge exchange between the interstellar medium (ISM) and the solar wind plasma is crucial for determining the structures of the heliosphere. Since both the neutral-ion and neutral-neutral collision mean free paths are either comparable…

Space Physics · Physics 2024-03-20 Yuxi Chen , Gabor Toth , Erick Powell , Talha Arshad , Ethan Bair , Marc Kornbleuth , Merav Opher

Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for…

Computational Engineering, Finance, and Science · Computer Science 2026-04-28 Khodr Jaber , Ebenezer E. Essel , Pierre E. Sullivan

We develop a numerical scheme for solving a fully special relativistic resistive radiation magnetohydrodynamics. Our code guarantees conservations of total mass, momentum and energy. Radiation energy density and radiation flux are…

High Energy Astrophysical Phenomena · Physics 2019-08-19 Hiroyuki R. Takahashi , Ken Ohsuga

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

It has been recognized that magnetic reconnection process is of great importance in high-energy astrophysics. We develop a new two-dimensional relativistic resistive magnetohydrodynamic (R$^2$MHD) code, and carry out numerical simulations…

Astrophysics · Physics 2009-11-11 Naoyuki Watanabe , Takaaki Yokoyama