Analysis and reconstruction of the revised formulations of the simplified and highly stable lattice Boltzmann method

Abstract

The present study aims to find the reason for the good numerical stability of the revised formulations of the simplified and highly stable lattice Boltzmann method (RSHSLBM) at high Reynolds number and reconstruct RSHSLBM in the macroscopic scale to overcome the limitation of uniform mesh. To this end, the macroscopic equations of RSHSLBM (MEs-RSHSLBM) with actual numerical dissipative terms are derived by approximating its actual computational process. By directly solving MEs-RSHSLBM with the least squares-based finite difference method, the limitation of uniform mesh can be easily overcome. Numerical investigations prove that those numerical dissipative terms help achieve good numerical stability at high Reynolds numbers of RSHSLBM. By retaining those numerical dissipative terms, the discretized MEs-RSHSLBM can recover the numerical stability and accuracy of RSHSLBM very well. Besides, the discretized MEs-RSHSLBM can be easily implemented on non-uniform meshes and achieve significantly higher computational efficiency.