A second order finite-volume scheme on cartesian grids for Euler equations

We present a simple globally second order scheme inspired by ghost cell approaches to solve compressible inviscid flows [4]. In the fluid domain, away from the boundary, we use a classical finite-volume method based on an approximate Riemann solver for the convective fluxes. At the cells located on the boundary, we solve an ad hoc Riemann problem taking into account the relevant boundary condition for the convective fluxes by an appropriate definition of the contact discontinuity speed. To avoid pressure oscillations near the solid we balance the boundary condition with an extrapolation of the fluid values, as a function of the angle between the normal to the solid and the normal to the cell. Our objective is to device a method that can easily be implemented in existing codes and that is suitable for massive parallelization