An asymptotic preserving multidimensional ALE method for a system of two compressible flows coupled with friction

We present a multidimensional asymptotic preserving scheme for the approximation of a mixture of compressible flows. Fluids are modelled by two Euler systems of equations coupled with a friction term. The asymptotic preserving property is mandatory for this kind of model, to derive a scheme that behaves well in all regimes (i.e. whatever the friction parameter value is). The method we propose is defined in ALE coordinates, using a Lagrange plus remap approach. This imposes a multidimensional definition and analysis of the scheme. •Compressible gas dynamics.•Multidimensional bi-fluid model.•Multidimensional Asymptotic preserving scheme.•Indirect ALE approach (each fluid is associated to its own mesh).