Comparing the Semi-Lagrangian Integration of Trajectories in Mixed Finite Element Spaces Through One- and Two-Level Time-Stepping Schemes

Abstract

Numerical simulations comparing the accuracy of trajectory integrators are presented in this paper through a qualitative error analysis. The core methodology presents one- and two-level schemes to be applied for incompressible flow problems discretised by the Taylor-Hood’s MINI element. Emphasis is given to a time-stepping algorithm which seeks intermediary values of the advected quantity to capture precisely the trajectory of particles. Analises are organized regarding numerical tests that bring up the overall differences associated to each of the semi-lagrangian integrators. Comparisons take into account the advection of a scalar concentrate over a two-dimensional domain when submitted to a rotating velocity field, thereby highlighting the advantages of the sub-step integrator for simulating flows that experience, mainly, swirling or curved motions.