External and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method

The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several approaches have been developed to remove this drawback of standard LBM. One of these methods is the Taylor series expansion and least squares-based LBM (TLLBM). This method is based on the standard LBM combined with the Taylor series expansion and the least squares approach. The prominent feature of the TLLBM is the fact that the final equation is an explicit form and in essence has no limitation on the mesh structure and lattice model. In the present work, the TLLBM with D2Q9 lattice model is used to simulate 2-D steady incompressible viscous flows (both internal and external) on non-uniform meshes. Four test cases are studied: (i) flow past a circular cylinder with a non-uniform O-type mesh; (ii) flow in a rectangular lid driven cavity with a non-uniform H-type mesh; and (iii) flow over a backward- facing step. It was found that this model could give very accurate results for both the internal and external flows.