Well-balanced methods for Computational Astrophysics
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Date
2022-09
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Report
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yes
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Abstract
We review well-balanced methods for the faithful approximation of solutions of systems of hyperbolic balance laws that are of interest to computational astrophysics. Well-balanced methods are specialized numerical techniques that guarantee the accurate resolution of non-trivial steady-state solutions, that balance laws prominently feature, and perturbations thereof. We discuss versatile frameworks and techniques for generic systems of balance laws for finite volume and finite difference methods. The principal emphasis of the presentation is on the algorithms and their implementation. Subsequently, we specialize in hydrodynamics' Euler equations to exemplify the techniques and give an overview of the available well-balanced methods in the literature, including the classic hydrostatic equilibrium and steady adiabatic flows. The performance of the schemes is evaluated on a selection of test problems.
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published
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Volume
2022-40
Pages / Article No.
Publisher
Seminar for Applied Mathematics, ETH Zurich
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Subject
Numerical methods; Hydrodynamics; Source terms; Well-balanced schemes
Organisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
Notes
Funding
169631 - Structure preserving numerical methods for astrophysics (SNF)
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