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arXiv · 2608.02862

Selection criteria for the compressible Euler equations: numerical study

Megala Anandan·Bahulayan Chalil Aravind·Mária Lukáčová-Medvid'ová·S. V. Raghurama Rao·Kedar Shridhar Wagh·Changsheng Yu·Jiahui Zhang
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Abstract

We numerically investigate selection criteria for dissipative weak solutions of the compressible Euler equations. Using the Kelvin-Helmholtz problem as a benchmark, we compare four standard numerical schemes - the viscous finite volume (VFV) method, the discrete velocity Boltzmann finite volume (DVBFV) method, the Runge-Kutta discontinuous Galerkin (RKDG) method, and the discontinuous Galerkin spectral element method (DGSEM), and demonstrate that each may converge to a different dissipative weak solution. We evaluate these solutions with respect to several selection criteria based on entropy production, total energy, and energy defect, and examine the sensitivity of selection functionals to the numerical diffusion inherent in each scheme.

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Megala Anandan, Bahulayan Chalil Aravind, Mária Lukáčová-Medvid'ová, S. V. Raghurama Rao, Kedar Shridhar Wagh, Changsheng Yu, Jiahui Zhang. 2026-08-03. Selection criteria for the compressible Euler equations: numerical study. https://arxiv.org/abs/2608.02862

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