The present talk tries to summarize the work performed by Lluis Jofre-Cruanyes during his PhD.The research aims at developing a basis for the numerical simulation of multiphase flows of immiscible fluids. The formulation is based on a finite-volume approach and is suitable for three-dimensional (3-D) unstructured meshes, as well for Cartesian grids. The software implemented is part of an in-house high performance computing platform able to simulate multiphysics problems. This platform is based on object-oriented programming, using C++ language, and parallelization is accomplished via MPI. Hence, rather than focusing on the study of the physics associated to these flows, most of the work is focused on the numerical discretization of the equations that govern
The work can be separated into two large blocks. The first part consists in developing numerical models able to embed fluid interfaces on static grids. This is accomplished by proposing a Volume-of-Fluid (VOF) method, and its parallelization strategy, for capturing interfaces on 3-D Cartesian and unstructured meshes. The method reconstructs interfaces as first- and second-order piecewise planar approximations (PLIC), and
advects volumes in a single unsplit Lagrangian-Eulerian (LE) geometrical algorithm based on constructing flux polyhedrons by tracing back the Lagrangian trajectories of the cell-vertex velocities.
The second part focuses on the development of a finite volume based discretization of the Navier-Stokes equations for multiphase immiscible flow on 3-D unstructured meshes that properly preserves mass, momentum and kinetic energy. In order to gain experience, the single-phase flow case is first studied to later extend it to the case of multiphase immiscible flow. Two main mesh discretizations have been analyzed: collocated and staggered schemes. Aside from accuracy, the focus has been placed on their capacity to discretely conserve kinetic energy, specially when solving turbulent flows.
Finally, the Richtmyer-Meshkov (RM) instability of two incompressible immiscible liquids has been numerically simulated. Rather than being a detailed study of the physical phenomena of RM instabilities, the tests performed are a general assessment of the numerical methods developed.