Solving incompressible fluid flows on unstructured meshes with the lattice boltzmann flux solver

Abstract

An application of the recently developed lattice Boltzmann flux solver (LBFS) is proposed to solve incompressible flows using unstructured meshes with high aspect ratio triangular cells. The capability to solve turbulent flows is also introduced by coupling the method with a turbulence model, for which the viscosity transport equation is solved on the same mesh. The proposed computational approach is validated for the classical lid-driven cavity flow, the flow over a circular cylinder, and the turbulent flow around a NACA0012 airfoil. Overall, the results obtained agree well with reference data, and demonstrate the validity of using the LBFS on directionally refined meshes, providing the advantage of limiting the number of vertices required in boundary layer regions of the fluid flow. An alternate flux construction method derived from a lattice Boltzmann boundary condition model based on equilibrium distribution streaming is also presented.