A second-order semi-Lagrangian particle FEM (SL-PFEM) method for the incompressible Navier-Stokes equations

Abstract

The Semi-Lagrangian Particle Finite Element Method (SL-PFEM) is a numerical method tailored for solving the fluid dynamics equations. Despite of its excellent numerical properties, such as a minimum numerical erosion in the convective transport and that it exhibits great stability, it has not yet received much attention in the scientific literature. In this presentation, a second order SL-PFEM scheme for solving the incompressible Navier-Stokes equations is presented. This scheme is based on the second order velocity Verlet algorithm, which uses an explicit integration for the particle’s trajectory and an implicit integration for the velocity. The algorithm is completed with a predictor-multicorrector scheme for the integration of the velocity correction using the Finite Element Method. A second order projector based on least squares is used to transfer the intrinsic variables information from the particles onto the background mesh, while a second order interpolation scheme is used to transfer the pressure gradient and viscous accelerations from the mesh to the particles. This presentation was made on 11th February 2020 at the Repsol Technology Lab.

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