A Lattice Boltzmann method in generalized curvilinear coordinat

Abstract

A second-order central time-explicit method is implemented to solve the Lattice Boltzmann Equation in generalized curvilinear coordinates in order to simulate fluid flows with non-uniform grids and curved boundaries. Several test cases are used for verification, including the Taylor-Green vortex in two-dimensions, the square lid-driven cavity and the 2D circular cylinder. The Taylor-Green vortex is a classical benchmark test that is compared with the analytical solution using a non-uniform grid. The 2D lid-driven cavity is solved for moderate Reynolds numbers, where a clustering function is employed to stretch the mesh and increase the resolution in the cavity corners. The boundary conditions for these two test-cases are relatively straightforward to implement since there are no curved walls. Therefore, the 2D circular cylinder is used to demonstrate the capacity of the present method to perform steady and unsteady simulations with curved boundaries. Our results have been compared with the literature available, and the outcomes of this method are consistent with other results, confirming the feasibility of the implemented scheme. In addition, the present method has been compared to our own standard Cartesian lattice Boltzmann solver with adaptive mesh refinement for the 2D circular cylinder problem.