Improvement of Numerical Instability of Lattice Boltzmann Methods Using Various Techniques

In this work, different alternatives for increasing numerical stability of Lattice Boltzmann (LB) models have been preliminary studied. The Entropic Lattice Boltzmann (ELB) method, the Fractional Volumetric Lattice Boltzmann (FV-LB) scheme, the Multi- Relaxation-Time Lattice Boltzmann (MRT-LB) method, and a combination of the two last methods, i.e. FVMRT- LB model, are presented for the simulation of a 2- D cavity driven flow. The FV-MRT-LB model is a new approach that is presented in this work and its results are compared with the results obtained by other methods. Results show that these methods, i.e. MRT-LB, ELB, FV-LB, FV-MRT-LB methods, achieve stability enhancements over the single-relaxation-time lattice Boltzmann scheme and that the MRT results are more stable and slightly more accurate in comparison with those of ELB, FV-LB and FV-MRT-LB models, especially at higher Reynolds numbers.

Keywords:

lattice Boltzmann method , SRT-LB model , MRT-LB method , ELB model , FV-LB scheme