Simplified method for simulation of incompressible viscous flows inspired by the lattice Boltzmann method

The lattice Boltzmann method (LBM) has gained increasing popularity in incompressible viscous flow simulations, but it uses many more variables than necessary. This defect was overcome by a recent approach that solves the actual macroscopic equations obtained through Taylor series expansion analysis of [Lu et al., J. Comp. Phys., 415, 109546 (2020)]. key is to keep some small additional terms (SATs) stabilize numerical solution weakly compressible Navier-Stokes equations. However, there are SATs complicate implementation their method. Based on analyses and numerous tests, we ultimately pinpoint two essential ingredients for stable simulations: (1) suitable density (pressure) diffusion added continuity equation; (2) proper dissipation related velocity divergence momentum Then, propose simplified not only easier implement noticeably faster original LBM. It contains much simpler involve derivatives requires no intermediate steps or variables. Besides, extended two-phase flows with uniform viscosity. Several test cases, including problems under dimensional, axisymmetric three dimensional geometries, presented demonstrate its capability. work may help pave way simplest simulation collocated grids based artificial compressibility methodology.