VOF/Navier-Stokes implementation on 3D unstructured staggered meshes. Application to the Richtmyer-Meshkov instability

Abstract

The numerical simulation of interfacial and free surface flows is a vast and interesting topic in the areas of engineering and fundamental physics, such as the study of liquid-gas interfaces, formation of droplets, bubbles and sprays, combustion problems with liquid and gas reagents, study of wave motion and others. One of the most powerful and robust methods for interface tracking on fixed grids is the Volume-of-Fluid (VOF). This method tracks the interface between different fluids by evolving the volume fraction scalar field, ratio of fluid to total volume, in time. First, the interface geometry is reconstructed from local volume fraction data. Then, the interface reconstruction and the solution of the Navier-Stokes equations are used to solve the volume fraction advection equation. The objective of this work is to implement a fast, accurate and parallelizable VOF/Navier-Stokes model well suited to 3D unstructured staggered meshes. The interface will be reconstructed by a PLIC method and the advection step will be computed by the means of an unsplit-advection volume tracking algorithm. On the other hand, the Navier- Stokes equations will be solved using an unstructured staggered formulation. The VOF/Navier-Stokes implementation will be tested by comparing the solution of the Richtmyer-Meshkov instability (RMI) to experimental results. The Richtmyer-Meshkov instability occurs at a nearly planar interface separating two fluids that are impulsively accelerated in the direction normal to the interface. This impulsive acceleration can be the result of an impulsive body force or a passing shock wave.