@unpublished{WildeKr{\"a}merReithetal.2019, author = {Wilde, Dominik and Kr{\"a}mer, Andreas and Reith, Dirk and Foysi, Holger}, title = {Semi-Lagrangian lattice Boltzmann method for compressible flows}, doi = {10.48550/arXiv.1910.13918}, institution = {Fachbereich Ingenieurwissenschaften und Kommunikation}, year = {2019}, abstract = {This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.}, language = {en} }