A high-resolution Godunov method for compressible multi-material flow on overlapping grids

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform-pressure–velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the Jones–Wilkins–Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock–interface collision, steady interaction of a planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.