Parallel Multiphase Navier-Stokes Solver

Abstract

We study and implement methods to solve the variable density Navier-Stokes equations. More specifically, we study the transport equation with the level set method and the momentum equation using two methods: the projection method and the artificial compressibility method. This is done with the aim of numerically simulating multiphase fluid flow in gravity oil-water-gas separator vessels. The result of the implementation is the parallel Aspen software framework based on the massively parallel deal.II .

For the transport equation, we briefly discuss the theory behind it and several techniques to stabilize it, especially the graph laplacian artificial viscosity with higher order elements. Also, we introduce the level set method to model the multiphase flow and study ways to maintain a sharp surface in between phases.

For the momentum equation, we give an overview of the two methods and discuss a new projection method with variable time stepping that is second order in time. Then we discuss the new third order in time artificial compressiblity method and present variable density version of it. We also provide a stability proof for the discrete implicit variable density artificial compressibility method.

For all the methods we introduce, we conduct numerical experiments for verification, convergence rates, as well as realistic models.