A simple second order cartesian scheme for compressible Euler flows

Yannick Gorsse (1, 2) , Angelo Iollo (1, 2) , Haysam Telib (3) , Lisl Weynans (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 MC2 - Modélisation, contrôle et calcul
3 DIASP - Dipartimento di Ingegneria Aeronautica e Spaziale [Torino]

We present a finite-volume scheme for compressible Euler flows where the grid is cartesian and it does not fit to the body. The scheme, based on the definition of an ad hoc Riemann problem at solid boundaries, is simple to implement and it is formally second order accurate. Error convergence rates with respect to several exact test cases are investigated and examples of flow solutions in one, two and three dimensions are presented.

Mots clés: immersed boundary; compressible; cartesian; second order scheme

Domaines: Analyse numérique [math.NA]

Yannick Gorsse, Angelo Iollo, Haysam Telib, Lisl Weynans. A simple second order cartesian scheme for compressible Euler flows. 2012. ⟨hal-00701277⟩