A Simplified Lattice Boltzmann Method Without Evolution of Distribution Function (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, a simplified lattice Boltzmann method (SLBM) without evolutionof the distribution function is developed for simulating incompressible viscousflows. This method is developed from the application of fractional step techniqueto the macroscopic Navier-Stokes (N-S) equations recovered from lattice Boltzmannequation by using Chapman-Enskog expansion analysis. In SLBM, the equilibriumdistribution function is calculated from the macroscopic variables, while thenon-equilibrium distribution function is simply evaluated from the difference of twoequilibrium distribution functions. Therefore, SLBM tracks the evolution of the macroscopicvariables rather than the distribution function. As a result, lower virtual memoriesare required and physical boundary conditions could be directly implemented.Through numerical test at high Reynolds number, the method shows very nice performancein numerical stability. An accuracy test for the 2D Taylor-Green flow showsthat SLBM has the second-order accuracy in space. More benchmark tests, includingthe Couette flow, the Poiseuille flow as well as the 2D lid-driven cavity flow, are conductedto further validate the present method; and the simulation results are in goodagreement with available data in literatures.