High-order well-balanced finite volume schemes for the Euler equations\n with gravitation

2018/07/11 by Luc Grosheintz, Grosheintz, Luc, Roger Käppeli +1 · 2 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1807.04074

openalex publication_date 2018/07/11 · openalex created_date 2022/08/04 · openalex updated_date 2026/08/01

Abstract

A high-order well-balanced scheme for the Euler equations with gravitation is\npresented. The scheme is able to preserve a spatially high-order accurate\ndiscrete representation of a large class of hydrostatic equilibria. It is based\non a novel local hydrostatic reconstruction, which, in combination with any\nstandard high-order accurate reconstruction procedure, achieves genuine\nhigh-order accuracy for smooth solutions close or away from equilibrium. The\nresulting scheme is very simple and can be implemented into any existing finite\nvolume code with minimal effort. Moreover, the scheme is not tied to any\nparticular form of the equation of state, which is crucial for example in\nastrophysical applications. Several numerical experiments demonstrate the\nrobustness and high-order accuracy of the scheme nearby and out of hydrostatic\nequilibrium.\n

Citations

• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
• Strong Stability-Preserving High-Order Time Discretization Methods

Cited by

• High order well-balanced and total-energy-conserving local discontinuous Galerkin methods for compressible self-gravitating Euler equations
• Well-balanced high-order method for non-conservative hyperbolic PDEs with source terms: application to one-dimensional blood flow equations with gravity

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