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arXiv · 2211.16673

High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity

Guanlan Huang·Yulong Xing·Tao Xiong
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Abstract

In this paper, we propose a high order semi-implicit well-balanced finite difference scheme for all Mach Euler equations with a gravitational source term. To obtain the asymptotic preserving property, we start from the conservative form of full compressible Euler equations and add the evolution equation of the perturbation of potential temperature. The resulting system is then split into a (non-stiff) nonlinear low dynamic material wave to be treated explicitly, and (stiff) fast acoustic and gravity waves to be treated implicitly. With the aid of explicit time evolution for the perturbation of potential temperature, we design a novel well-balanced finite difference WENO scheme for the conservative variables, which can be proven to be both asymptotic preserving and asymptotically accurate in the incompressible limit. Extensive numerical experiments were provided to validate these properties.

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Guanlan Huang, Yulong Xing, Tao Xiong. 2022-11-30. High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity. https://arxiv.org/abs/2211.16673

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