Development of a multiblock solver utilizing the lattice Boltzmann and traditional finite difference methods for fluid flow problems

This dissertation develops the lattice Boltzmann method (LBM) as a strong alternative to traditional numerical methods for solving incompressible fluid flow problems. The LBM outperforms traditional methods on a standalone basis for certain problem cases while for other cases it can be coupled with the traditional methods using domain decomposition. This brings about a composite numerical scheme which associates the efficient numerical attributes of each individual method in the composite scheme with a particular region in the flow domain. Coupled lattice Boltzmann-traditional finite difference procedures are developed and evaluated for CPU time reduction and accuracy of standard test cases. The standard test cases are numerical solutions of the two-dimensional unsteady and steady convection-diffusion equations and two-dimensional steady laminar incompressible flows represented by the backward-facing step flow problem and the flow problem around a cylinder. Multiblock Cartesian grids and hybrid Cartesian-cylindrical grid systems are employed with the composite numerical scheme. A cache-optimized lattice Boltzmann technique is developed to utilize the full computational strength of the LBM. The LBM is an explicit time-marching method and therefore has a time step size limitation. The time step size is limited by the grid spacing and the Mach number. A lattice Boltzmann simulation necessarily requires a low Mach number since it relates to the incompressible Navier-Stokes equations in the low Mach number limit. For steady state problems, the smaller time step results in slow convergence. To improve the time step limitation imposed by the grid spacing, an improved LBM that adopts a new numerical discretization for the advection term has been developed and the results were computed for a convection-diffusion equation and compared with the original LBM. The performance of traditional finite difference methods based on the alternating direction implicit scheme for the convection-diffusion equation and the vorticity-stream function method for the laminar incompressible flow problems is evaluated against the composite numerical scheme. The composite numerical scheme is shown to take lesser CPU time for solving the given benchmark problems