The simplified and highly stable lattice Boltzmann method (SHSLBM) was proposed as an alternative approach to construct solution schemes within the lattice Boltzmann framework. Comparing with the conventional lattice Boltzmann method (LBM), the SHSLBM shows advantages in memory cost and boundary treatment: it can directly evolve the macroscopic variables and implement physical boundary conditions. The numerical stability is another intriguing characteristic of the SHSLBM, which allows acquisition of converged solutions in extreme flow conditions.
This talk will recall the path of developing the SHSLBM and report the ongoing studies carried out by the speaker’s group in understanding and applying this method. The essential idea of the SHSLBM is to reconstruct solutions to the macroscopic equations recovered by the lattice Boltzmann equation tailored for specific fluid problem. The validity of the various schemes established with this idea will be showcased in abundant benchmark examples of isothermal flows, thermal flows, multiphase flows, axisymmetric flows, acoustic problems, etc. In the meantime, since the construction of the SHSLBM scheme is associated with the lattice velocity model, the dependency study will be presented, with specific attentions paid to the efficiency, the stability, and the memory cost. Finally, to pave the way to industrial applications, efforts have been made in the employment of the SHSLBM on the multi-resolution mesh and the unstructured mesh, which will also be included in this talk.

Lattice Boltzmann method; Stability; Lattice velocity model