A comparison of semi-Lagrangian vortex method and lattice Boltzmann method for incompressible flows. (30th June 2021) - Mimeau, Chloé; Marié, Simon; Mortazavi, Iraj
Highlights: Algorithmic and numerical comparison of a semi-Lagrangian vortex method (VM) to a lattice Boltzmann method (LBM). Extensive study of the diffusive and dispersive behavior of both methods. Three benchmarks of various three-dimensional flows : advection of a simple vortex, Taylor–Green vortex, the stiff test case of flow past a cube. VM provides a higher accuracy and a lower numerical dissipation than LBM for simulations performed on medium and coarse grids. LBM shows a better accuracy for fine grid resolutions and a higher order of convergence than VM. Abstract: The semi-Lagrangian Vortex method (VM) and the Lattice Boltzmann method (LBM) are used to investigate flows simulations in the incompressible regime. In this study, a proven version of each method is used and compared on different three dimensional benchmarks in terms of numerical accuracy, convergence, numerical diffusion and dissipation. The first comparisons are made on a convected vortex to study and compare the numerical dissipation of LBM and VM. Then the Taylor–Green vortex is investigated to compare the dissipation rate of the kinetic energy of each method. It is shown that both methods converge to the same solution but in a different way. The VM performs better than the LBM for the lowest resolution whereas LBM appears to be more accurate for the growing resolutions. These results are confirmed on 3D simulations with wall boundaries for the stiff test case of the wake behind a 3D cube at R e = 290 and R e = 570 .