A second order cartesian scheme for BGK equation

Florian Bernard (1, 2, 3) , Angelo Iollo (2, 3) , Gabriella Puppo (4)

1 Polito - Politecnico di Torino = Polytechnic of Turin
2 IMB - Institut de Mathématiques de Bordeaux
3 MC2 - Modélisation, contrôle et calcul
4 Uninsubria - Universitá degli Studi dell’Insubria = University of Insubria [Varese]

A simple second order scheme is presented for BGK equation on cartesian grids to simulate rarefied gas flows. An immersed boundary technique is then used since the mesh is body fitted. The asymptotic preserving properties of the BGK equation discretization towards Euler limit are also investigated with emphasis on the boundary conditions as the Knudsen number goes to zero. Reconstruction techniques and levelset functions are used to modify the fluxes at the nearest interface of the body and enforce the boundary conditions at second order. The same method is applied in 1D and 2D cases to demonstrate its accuracy

Mots clés: BGK model; cartesian meshes; second order

Domaines: Analyse numérique [math.NA]; Mécanique [physics]; Sciences de l'ingénieur [physics]

Florian Bernard, Angelo Iollo, Gabriella Puppo. A second order cartesian scheme for BGK equation. 2nd ECCOMAS Young Investigators Conference (YIC 2013), Sep 2013, Bordeaux, France. ⟨hal-00855885⟩