Consistent time-step optimization in the lattice Boltzmann method

Owing to its efficiency and aptitude for a massive parallelization, the lattice Boltzmann method generally outperforms conventional solvers in terms of execution time weakly-compressible flows. However, authorized time-step (being inversely proportional speed sound) becomes prohibitively small incompressible limit, so that performance advantage over continuum-based vanishes. A remedy increase is provided by artificially tailoring sound throughout simulation, as reach fixed target Mach number much larger than actual one. While achieving considerable speed-ups certain flow configurations, such adaptive time-stepping comes with flaw continuities mass density pressure cannot be fulfilled conjointly when varied. Therefore, trade-off needed. By leaving unchanged, conservation preserved but presents discontinuity momentum equation. In contrast, power-law rescaling allows us ensure continuity term equation (per unit mass) leaves locally discontinuous. This algorithm, which requires operation density, will called “adaptive correction” article. Interestingly, we found this second preferable. case thermal plume, whose movement governed balance buoyancy drag forces, correction (to force) has beneficial impact on resolved velocity field. pulsatile channel (Womersley's flow) driven an external body force, no difference was observed between two versions time-stepping. On other hand, if established inlet outlet conditions, results obtained continuous force agree better analytical solution. Finally, using entrance flow, it shown compulsory Poiseuille develop. The expected compressibility error due remains negligible, convergence rate not notably affected compared simulation constant step.