Adaptive scheme based on entropy production: robustness through severe test cases for hyperbolic conservation laws

Mehmet Ersoy (1) , Frederic Golay (1) , Lyudmyla Yushchenko (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

In this paper, we study the robustness of the 1D adaptive numerical scheme based on numerical density of entropy production for hyperbolic conservation. In particular, we focus on vacuum states or low densities states or both in presence of strong shocks solutions to the one-dimensional gas dynamics equations for ideal gas. To this purpose, it is numerically shown that the adaptive numerical scheme is well-designed to capture accurately these type of solutions as the pressure vanishes. The efficiency of the scheme is investigated through several test cases for first and second order scheme with a MUSCL reconstruction. We focus in particular on several numerical experiments to test the ability to conserve the entropy in the adaptive framework, to capture strong discontinuities (both shocks and contact dis- continuities) as well as strong rarefactions. We also perform some numerical test case for solutions which are close to the vacuum or vanishes.

Mots clés: strong rarefaction; strong shock; strong contact discontinuities; low density; local time stepping; numerical density of entropy production; hyperbolic system; finite volume scheme; local mesh refinement; vacuum state

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Mehmet Ersoy, Frederic Golay, Lyudmyla Yushchenko. Adaptive scheme based on entropy production: robustness through severe test cases for hyperbolic conservation laws. [Research Report] Imath. 2013. ⟨hal-00918773⟩