A pressure-based treatment for the direct numerical simulation of compressible multi-phase flow using multiple pressure variables

• A pressure-based scheme for compressible two-phase flows is presented.
• We use multiple pressure variables for the compressible–incompressible transition.
• The material interface is resolved and tracked by the level set method.
• The approach is free of spurious oscillations in the vicinity of the material interface.
• The scheme is able to simulate the propagation of pressure waves in gases and liquids.

In this paper we present a pressure-based numerical scheme for the direct numerical simulation of compressible two-phase flows using the stiffened gas equation of state. While for many technical applications, two-phase flows can be treated as incompressible, this assumption fails in cases with high pressure and temperature as they can be found in rocket combustion chambers, for example. Our interest is in the development of a pressure-based method that aims at the extension of an incompressible two-phase code to the compressible regime. The development builds upon an asymptotic pressure decomposition using multiple pressure variables and has originally been designed for single-phase flows. Its adaptation to compressible two-phase flows is presented. This includes the possibility to resolve and track the interface as well as the description of the two phases by different equations of state. It is shown that the pressure-based scheme does not necessitate a cumbersome interface treatment in order to avoid spurious oscillations in the vicinity of the material interface. We do not yet take into account phase changes whose approximation requires a careful thermodynamic consistent procedure. Numerical examples are shown ranging from the one-dimensional transport of a multi-material contact discontinuity to the three-dimensional simulation of shock-droplet interactions. The scheme proves to be able to accurately simulate the propagation of pressure waves in gaseous and liquid phases.