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This is a Quantitative Study study.

October 3, 2025Open Access

Structure-Preserving High-Order Methods for the Compressible Euler Equations in Potential Temperature Formulation for Atmospheric Flows

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Numerical methods ensure entropy and total energy conservation in atmospheric flows using potential temperature.

The proposed methods ensure conservation of entropy and total energy in atmospheric flows, enhancing numerical stability.
Three numerical fluxes are developed to support structure-preserving properties in the compressible Euler equations.
Well-balanced schemes are established for different background states, facilitating robust simulations on curvilinear meshes.
Validation demonstrates the effectiveness of the potential temperature formulation against traditional methods in atmospheric scenarios.

Artiano et al. (2025) studied this question.

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