One- and two-step semi-Lagrangian integrators for ALE-FEtwo-phase flow simulations
International Journal for Numerical Methods in Fluids
ABSTRACT:
Semi-lagrangian (SL) schemes are of utmost relevance to simulate two-phase flowswhere advection dominates. The combination of SL schemes with the finite element(FE) method and arbitrary Lagrangian-Eulerian (ALE) dynamic meshes yields astrong ingredient to deal with applications in Earth sciences, environmental engineering, and oil and gas industry whose numerical background is incipient. This paper isintended to propose a second-order time multistep SL/ALE/FE scheme to track par-ticle trajectories traveling amidst single- or two-phase incompressible flows both infixed and moving mesh situations. The novel scheme is a BDF2-like implementationthat considers the mesh velocity as part of its backward-in-time integration. Trajectory departure points are searched through extrapolation and followed by a multi step interpolation corrector that works both for constant and varying time steps. A seriesof two-phase benchmark flow simulations are carried out by using the cubic elementto compare the performance of the new integrator against single-step approximationsas well as to analyze enhancements in representing the two-phase flow dynamics. Weuse the 2D axisymmetric Navier-Stokes equations as underlying model. Error analysis, convergence tests, quantitative and qualitative comparisons are presented anddiscussed to highlight the superior conservative feature of the novel scheme.