  In this paper we propose a new diffuse interface model for the numerical
simulation of inviscid compressible flows around fixed and moving solid bodies
of arbitrary shape. The solids are assumed to be moving rigid bodies, without
any elastic properties. The model is a simplified case of the seven-equation
Baer-Nunziato model of compressible multi-phase flows, and results in a
nonlinear hyperbolic system with non-conservative products. The geometry of the
solid bodies is simply specified via a scalar field that represents the volume
fraction of the fluid present in each control volume. This allows the
discretization of arbitrarily complex geometries on simple uniform or adaptive
Cartesian meshes. Inside the solid bodies, the fluid volume fraction is zero,
while it is unitary in the fluid phase. We prove that at the material
interface, i.e. where the volume fraction jumps from unity to zero, the normal
component of the fluid velocity assumes the value of the normal component of
the solid velocity. This result can be directly derived from the governing
equations, either via Riemann invariants or from the generalized Rankine
Hugoniot conditions according to the theory of Dal Maso, Le Floch and Murat,
which justifies the use of a path-conservative approach for treating the
nonconservative products. The governing equations of our new model are solved
on uniform Cartesian grids via a high order path-conservative ADER
discontinuous Galerkin (DG) method with a posteriori sub-cell finite volume
(FV) limiter. Since the numerical method is of the shock capturing type, the
fluid-solid boundary is never explicitly tracked by the numerical method,
neither via interface reconstruction, nor via mesh motion. The effectiveness of
the proposed approach is tested on a set of numerical test problems, including
1D Riemann problems as well as supersonic flows over fixed and moving rigid
bodies.
