DEVELOPMENT OF SIMPLIFIED AND HIGHLY STABLE LATTICE BOLTZMANN METHOD AND ITS APPLICATIONS

Abstract

A simplified and highly stable lattice Boltzmann method (SHSLBM) is developed in this thesis for simulation of incompressible viscous flows. SHSLBM is derived by reconstructing solutions to the macroscopic equations recovered from lattice Boltzmann equation (LBE) through Chapman-Enskog (C-E) expansion analysis and resolved in a predictor-corrector scheme. It essentially tracks the evolution of macroscopic variables rather than the distribution functions, which reduces the cost in virtual memory and facilitates direct implementation of physical boundary conditions. Additionally, through von Neumann stability analysis, it is shown that the scheme outperforms existing LBE models at high Reynolds/Rayleigh numbers. Extensions and applications of SHSLBM are carried out in this thesis to enhance and demonstrate its adaptability in various problems and the potential for engineering applications. And a highly accurate simplified lattice Boltzmann method (HSLBM) is finally developed within the same framework to offer stable and accurate solutions on coarser meshes.