Author
Matthias Wesenberg
Bio: Matthias Wesenberg is an academic researcher from University of Freiburg. The author has contributed to research in topics: Finite volume method & Conservation law. The author has an hindex of 6, co-authored 12 publications receiving 1160 citations.
Papers
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TL;DR: 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.
1,194 citations
TL;DR: In this article, a method of deriving artificial nonreflecting boundary conditions for systems of conservation laws is discussed, based on the ideal compressible magnetohydrodynamics (MHD), which are solved in a gravitationally stratified atmosphere.
33 citations
TL;DR: An efficient parallel code for the approximate solution of initial boundary value problems for hyperbolic balance laws is introduced, applied to the equations of compressible magnetohydrodynamics (MHD).
Abstract: An efficient parallel code for the approximate solution of initial boundary value problems for hyperbolic balance laws is introduced. The method combines three modern numerical techniques: locally-adaptive upwind finite-volume methods on unstructured grids, parallelization based on non-overlapping domain decomposition, and dynamic load balancing. Key ingredient is a hierarchical mesh in three space dimensions.
The proposed method is applied to the equations of compressible magnetohydrodynamics (MHD). Results for several testproblems with computable exact solution and for a realistic astrophysical simulation are shown.
28 citations
01 Jan 2003
TL;DR: A number of approaches for reducing the divergence errors in magnetohydrodynamic simulations are presented, derived from a general framework, which for example also includes the Hodge projection scheme.
Abstract: In this paper we present a number of approaches for reducing the divergence errors in magnetohydrodynamic simulations. The methods are derived from a general framework, which for example also includes the Hodge projection scheme. The corrections can be easily added to an existing scheme as is demonstrated for a finite-volume scheme. Numerical results in 2d and 3d confirm the advantages of our approach.
11 citations
01 Jan 2001
TL;DR: In this article, the Euler equations of gas dynamics have been extended to cope with a more general EOS and two general approaches for this extension have been proposed, which can also be applied to MHD.
Abstract: In recent years many numerical schemes — mainly based on approximate Riemann solvers — for the equations of ideal magnetohydrodynamics (MHD) have been developed; their robustness and efficiency have been shown in many examples. But since the underlying equation of state (EOS) of an ideal gas is far from reality in many applications (e.g. solar physics), these numerical schemes have to be extended to cope with a more general EOS. For the Euler equations of gas dynamics two general approaches for this extension have recently been proposed. We will show that they can also be applied to MHD. Furthermore we will validate the resulting schemes and will discuss some important aspects of their behaviour.
9 citations
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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.
Abstract: 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 transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume averages for mass, momentum, and energy, and face-centered area averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally split time advance, and (3) the extension to MHD of two different dimensionally unsplit integration methods. Implementation of the algorithm in both C and FORTRAN95 is detailed, including strategies for parallelization using domain decomposition. 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. The source code is freely available for download on the web.
1,096 citations
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.
693 citations
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.
668 citations
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.
611 citations
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.
555 citations