Journal ArticleDOI
Hyperbolic divergence cleaning for the MHD equations
Andreas Dedner,Friedemann Kemm,Dietmar Kröner,Claus-Dieter Munz,T. Schnitzer,Matthias Wesenberg +5 more
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TLDR
A new approach to the stabilization of numerical schemes in magnetohydrodynamic processes in which the divergence errors are transported to the domain boundaries with the maximal admissible speed and are damped at the same time is developed.About:
This article is published in Journal of Computational Physics.The article was published on 2002-01-20. It has received 1194 citations till now. The article focuses on the topics: Divergence (statistics) & Continuity equation.read more
Citations
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Athena: a new code for astrophysical mhd
TL;DR: Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods.
Journal ArticleDOI
Adaptive numerical algorithms in space weather modeling
Gabor Toth,Bart van der Holst,Igor V. Sokolov,D. L. De Zeeuw,Tamas I. Gombosi,Fang Fang,Ward B. Manchester,Xing Meng,Dalal Najib,Kenneth G. Powell,Quentin F. Stout,Alex Glocer,Yingjuan Ma,Merav Opher +13 more
TL;DR: The framework and the adaptive algorithms enable physics-based space weather modeling and even short-term forecasting and the algorithms of BATL, the Block-Adaptive Tree Library, are described and its efficiency and scaling properties for various problems are described.
Journal ArticleDOI
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Takahiro Miyoshi,Kanya Kusano +1 more
TL;DR: In this paper, a multi-state Harten-Lax-van Leer (HLL) approximate Riemann solver for the ideal magnetohydrodynamic (MHD) equations is developed based on the assumption that the normal velocity is constant over the riemann fan.
Journal ArticleDOI
Smoothed particle hydrodynamics and magnetohydrodynamics
TL;DR: A basic grounding in the fundamentals of SPH is given, showing how the equations of motion and energy can be self-consistently derived from the density estimate, and how to interpret these equations using the basic SPH interpolation formulae is shown.
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A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
TL;DR: A conservative least-squares polynomial reconstruction operator is applied to the discontinuous Galerkin method, which yields space–time polynomials for the vector of conserved variables and for the physical fluxes and source terms that can be used in a natural way to construct very efficient fully-discrete and quadrature-free one-step schemes.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.
Journal ArticleDOI
ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I - The hydrodynamic algorithms and tests. II - The magnetohydrodynamic algorithms and tests
James M. Stone,Michael L. Norman +1 more
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Regular Article: A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics
TL;DR: In this article, the authors present a computational scheme for compressible magnetohydrodynamics (MHD) based on the same elements that make up many modern compressible gas dynamics codes: high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and solution-adaptive refinement and coarsening.
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Simulation of magnetohydrodynamic flows: A Constrained transport method
Charles R. Evans,John F. Hawley +1 more
TL;DR: In this paper, a nouvelle technique numerique, appelee methode du transport contraint, is presented, for etudier l'evolution de l'equation d'induction en fonction du flux magnetique.
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Simulation of magnetohydrodynamic flows: A Constrained transport method
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