All Speed Multi-phase Flow Solvers

A new second order primitive preconditioner technique (an all speed method) for solving all speed single/multi-phase flow is presented. With this technique, one can compute both compressible and incompressible flows with Mach-uniform accuracy and efficiency (i.e., accuracy and efficiency of the method are independent of Mach numbers). The new primitive preconditioner (all speed/Mach uniform) technique can handle both strong and weak shocks, providing highly resolved shock solutions together with correct shock speeds. In addition, the new technique performs very well at the zero Mach limit. In the case of multi-phase flow, the new primitive preconditioner technique enables one to accurately treat phase boundaries in which there is a large impedance mismatch. When solving multi-dimensional all speed multi-phase flows, we introduce adaptive solution techniques which exploit the advantages of Mach-uniform methods. We compute a variety of problems from low (low speed) to high Mach number (high speed) flows including multi-phase flow tests, i.e, computing the growth and collapse of adiabatic bubbles for study of underwater explosions.