A second-order semi-Lagrangian particle finite element method for fluid flows

In this paper, 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 variable information from the particles to the background mesh, while a second-order interpolation scheme is used to transfer the accelerations from the mesh to the particles. Convergence analyses are carried out to assess the second-order convergence.