Work

Well-balanced second-order approximation of the compressible atmospheric Euler equations

Year: 2026

Type: preprint

Abstract: We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to stratified rest states, including isentropic and isothermal equilibria. The approximation is built upon discrete auxiliary states derived from a hydrostatic reconstruction of the density and potential temperature. These auxiliary states, together with an affine shift of the numerical state, provide local bounds needed for maintaining well-balancing and invariant domain preserving properties of the method. The numerical method is then verified and validated with analytic solutions, well-balancing tests, and typical benchmark problems for atmospheric flows.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2606.19764

Authors: Farris, Crystal, Maier, Matthias, Tovar, Eric J.

Institution: Texas A&M University

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, National Nuclear Security Administration, U.S. Air Force, Laboratory Directed Research and Development, Los Alamos National Laboratory

Awards: G1017065088, G1279347439, G2356915424, Desiccation of Porous Media to Limit Contaminant Migration, CAREER: Robust and High-Performance Computational Methods for Simulating Metamaterial-Based Optical Devices, G6410514744, G6563880843, G70659677, G7090116110

OpenAlex ID: W7165398329

Cites: 1

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Related to: 10