Entropy-stable schemes in the low-Mach-number regime: Flux-preconditioning, entropy breakdowns, and entropy transfers

Entropy-Stable (ES) schemes, specifically those built from [Tadmor \textit{Math. Comput.} 49 (1987) 91], have been gaining interest over the past decade, especially in context of under-resolved simulations compressible turbulent flows using high-order methods. These schemes are attractive because they can provide stability a global and nonlinear sense (consistency with thermodynamics). However, fully realizing potential ES requires better grasp their local behavior. Entropy-stability itself does not imply good behavior [Gouasmi \textit{et al.} \textit{J. Sci. Comp.} 78 (2019) 971, Gouasmi \textit{Comput. Methd. Appl. M.} 363 (2020) 112912]. In this spirit, we studied problems where \textit{global is core issue}. present work, consider accuracy degradation issues typically encountered by upwind-type low-Mach-number regime [Turkel \textit{Annu. Rev. Fluid Mech.} 31 (1999) 285] treatment \textit{Flux-Preconditioning} Comput. Phys.} 72 277, Miczek \textit{A \& A} 576 (2015) A50]. suffer same Flux-Preconditioning improve without interfering entropy-stability. This first demonstrated analytically: similarity congruence transforms were able to establish conditions for preconditioned flux be ES, introduce variants Miczek's Turkel's fluxes. then numerically through first-order two simple test representative incompressible acoustic limits, Gresho Vortex right-moving wave. The results overall consistent previous studies [...]