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In this paper we propose a new diffuse interface model for the numericalsimulation of inviscid compressible flows around fixed and moving solid bodiesof arbitrary shape. The solids are assumed to be moving rigid bodies, withoutany elastic properties. The model is a simplified case of the seven-equationBaer-Nunziato model of compressible multi-phase flows, and results in anonlinear hyperbolic system with non-conservative products. The geometry of thesolid bodies is simply specified via a scalar field that represents the volumefraction of the fluid present in each control volume. This allows thediscretization of arbitrarily complex geometries on simple uniform or adaptiveCartesian meshes. Inside the solid bodies, the fluid volume fraction is zero,while it is unitary in the fluid phase. We prove that at the materialinterface, i.e. where the volume fraction jumps from unity to zero, the normalcomponent of the fluid velocity assumes the value of the normal component ofthe solid velocity. This result can be directly derived from the governingequations, either via Riemann invariants or from the generalized RankineHugoniot conditions according to the theory of Dal Maso, Le Floch and Murat,which justifies the use of a path-conservative approach for treating thenonconservative products. The governing equations of our new model are solvedon uniform Cartesian grids via a high order path-conservative ADERdiscontinuous Galerkin (DG) method with a posteriori sub-cell finite volume(FV) limiter. Since the numerical method is of the shock capturing type, thefluid-solid boundary is never explicitly tracked by the numerical method,neither via interface reconstruction, nor via mesh motion. The effectiveness ofthe proposed approach is tested on a set of numerical test problems, including1D Riemann problems as well as supersonic flows over fixed and moving rigidbodies.

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model