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

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Guanlan Huang, Yulong Xing, Tao Xiong

Numerical Analysis · Submitted 30 Nov 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2211.16673 (version 1)
Pith IDT6FSC6TO, Pith's permanent record of this paper and its review
CitationGuanlan Huang, Tao Xiong, Yulong Xing. "High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity." arXiv:2211.16673 (2022). https://pith.science/paper/T6FSC6TO
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arXiv listing abstract v1. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 1.00 0.94 0.26 asserted 1.00
s1 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. method 0.99 0.88 0.05 asserted 1.00
s2 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. method 0.99 0.84 0.05 asserted 0.99
s3 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. contribution 0.66 0.95 0.60 asserted 1.00
s4 Extensive numerical experiments were provided to validate these properties. result 0.46 0.92 0.13 asserted 0.98

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.97.

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Original 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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