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arXiv · 2602.01938

A Flux-Correction Form of the Third-Order Edge-Based Scheme for a General Numerical Flux Function

Hiroaki Nishikawa
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Abstract

In this short note, we present a flux-correction form of the third-order edge-based scheme for the Euler equations that enables the direct use of a general flux function. The core idea is to replace, without loss of accuracy, the arithmetic average of the flux extrapolations by a general numerical flux evaluated at the edge midpoint, together with a correction term. We show that the proposed flux-correction form preserves third-order accuracy, provided that the general numerical flux is evaluated with the left and right states that are computed exactly for a quadratic function, which can be achieved effectively by the U-MUSCL scheme with {\kappa} = 1/2. Numerical results are presented to verify third-order accuracy with the HLLC and LDFSS flux functions on irregular tetrahedral grids.

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Hiroaki Nishikawa. 2026-02-02. A Flux-Correction Form of the Third-Order Edge-Based Scheme for a General Numerical Flux Function. https://arxiv.org/abs/2602.01938

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