Parallel multiphase flow software for solving the Navier‐Stokes equations

Abstract

A code based on finite element method was built and applied on the variable density incompressible Navier-Stokes equations for accurately simulating immiscible two phase flows. The algorithm simulates the interface between the two liquid phases with high accuracy; it utilizes both the level-set method with a third order strong stability property Runge-Kutta (SSPRK) time integrator and a secondorder projection method for the momentum equation. The solver developed is based on deal.II, an open source framework code. Numerical assessments on the transport and momentum equations are presented to verify the code accuracy. Nonconforming manufactured solutions are shown to produce the expected convergence rate of the used numerical schemes. Simulation of classical Rayleigh- Taylor instability was carried out and shown to match those in the published work