Multiphase Flows Simulation with the Particle Finite Element Method and its Comparison with Eulerian Alternatives

Abstract

The latest version of the Particle-Finite Element Method (PFEM), which incorporates the novel explicit integration strategy named eXplicit Integration of Velocity and Acceleration following Streamlines (X-IVAS), has proven to be fast and accurate to solve homogeneous flows, mainly thanks to the possibility of using large time-steps. In this work the extension of this strategy to solve multiphase flows is presented, where the calculation of the interface evolution is of fundamental importance.
In Eulerian formulations, one of the most used strategies to determine the interface position is the advection of an indicator function. This approach is followed, by example, in the Volume of Fluid (VoF) technique, which can add limiters as a method of guaranteeing boundedness and/or sharpness of phasefractions.
On the other hand, Lagrangian frames use typically marker particles. In the case of PFEM, the same set of particles transported for flow calculation allows to carry a marker function to determinate the interface position without any extra cost. In order to compare the accuracy of PFEM interface evolution strategy with the Eulerian one implemented in the widely used OpenFOAM®suite, several classical tests are presented.
In addition to capture the sharpen interface evolution, PFEM algorithm includes the use of an enriched finite element space to avoid spurious solutions due to the discontinuity of pressure gradients, which also requires some changes in the streamline integration strategy. The description of those improvements are also presented in this work. Finally the PFEM algorithm is tested for a number of problems involving free surface flows with different ratio between the densities and viscosities of the fluids involved. The accuracy of the results are compared with reference ones, focusing in the capability of using large time steps in contrast with Eulerian solvers, including those with implicit phase-fractions advection treatment, represented by the OpenFOAM®suite.