Validation of a Dynamically Adaptive Lattice Boltzmann Method for 2D Thermal Convection Simulations

Abstract

Utilizing the Boussinesq approximation, a double-population thermal lattice Boltzmann method (LBM) for forced and natural convection in two space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement procedure tailored for LBM is applied to enable computationally efficient simulations of high Rayleigh number configurations which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The effectiveness of the overall approach is demonstrated for the 2D natural convection benchmark of a cavity with differentially heated walls at Rayleigh numbers from 103 up to 108.