A simple second-order cartesian scheme for compressible flows

A simple second order scheme for compressible inviscid flows on cartesian meshes is presented. An appropriate Rieman solver is used to impose the impermeability condition. The level set function defines the immersed body and provides some useful geometrical data to increase the scheme accuracy. A modification of the convective fluxes computation for the cells near the solid ensures the boundary condition at second order accuracy. The same procedure is performed in each direction independently. An application to the simulation of a Ringleb flow is presented to demonstrate the accuracy of the method