High order ADER schemes for multiphase flows and a simple diffuse interface approach for compressible flows around solid bodies

In this second part of the talk I will briefly introduce the families of available techniques to deal with multiphase flows. Then, I will focus on a diffuse interface model for the simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape.

The employed model is a nonlinear system of hyperbolic conservation laws with non-conservative products, obtained as a simplified case of the Baer-Nunziato model. The geometry of the solid is simply specified via a scalar field that represents the volume fraction of the fluid present in each control volume and allows the discretization of arbitrarily complex geometries on Cartesian meshes. Moreover, it is possible to prove that at the material interface the normal component of the fluid velocity assumes the value of the normal component of the solid velocity.

The numerical solution is computed via a high order path-conservative ADER discontinuous Galerkin method with a posteriori sub-cell finite volume limiter and tested on a set of different benchmarks, including 1D Riemann problems as well as supersonic flows over fixed and moving rigid bodies.