Abordagem level-set para simulação de fluidos bifasicos baseada no método de elementos finitos

Abstract

In this work, we present a level set approach for the simulation of two-phase immiscible newtonian fluids. The model consists on the incompressible Navier-Stokes equations, coupled with an advection equation for the level set function. The so-called Continuum Surface Force approach (CSF) is used to model the effect of surface tension. The level set method is used to capture the interface between the fluids. Here, the level set function is advected and reinitialized at each timestep. The spatial discretization is based on an unstructured Finite Element mesh that uses adaptive mesh refinement for higher accuracy. Refinement levels are set to be high on regions near the interface and low away from it. For the discretization of velocity and pressure fields, standard (LBB stable) finite element spaces are taken in consideration. Discretization of the time derivative is given by backward differentiation resulting in an implicit approximation. The finite element algorithm is implemented using the libmesh library.