Numerical simulation of viscous flows using an incompressible lattice Boltzmann method on non-uniform grids

Majority of the existing lattice Boltzmann equation (LBE) models can be viewed as compressible schemes. However, the compressibility effect might cause some undesired errors in numerical simulations of incompressible fluid flows. In this work, for the first time, an incompressible model in conjunction with the explicit Taylor series expansion and least square based lattice Boltzmann method (TLLBM) is used to simulate two-dimensional incompressible viscous flows. TLLBM is based on the standard LBM with an introduction of the Taylor series expansion and the least squares approach. The final equation is an explicit form and essentially has no restriction on mesh structure and lattice model. Since the Taylor series expansion is only employed in the spatial direction, the time accuracy of this method remains the same as of the standard LBM. To validate the method, a lid driven cavity flow at different Reynolds numbers was considered. Numerical results obtained by this method agree very well with available data in the literature.