THE LATTICE BOLTZMANN METHOD FOR FLOWS WITH SLIP AND NO-SLIP BOUNDARIES

Abstract

This thesis assesses and extends a modern method to study the physics of simple and complex flows by using the lattice Boltzmann method (LBM). With the moment-based boundary conditions, different problems with no-slip and slip boundaries are simulated. The moment method is based on the specification of the appropriate hydrodynamic moments of LBM. Throughout this thesis, distinct collision operators of D2Q9 LBM are presented and examined; the models include the Bhatnager-Gross-Krook (BGK), multiple relaxation time (MRT) and a special case of the last model which is two relaxation times (TRT-LBM). Simple numerical simulations are given and the LBM proved its accuracy when it is compared with other numerical methods. The accuracy of the LBM with the no-slip and slip moment-based boundary conditions is examined numerically by studying the dipole wall collision flow. The two relaxation times lattice Boltzmann model is used to simulate this flow and the results are compared with other numerical methods. Our implementation shows excellent agreement with other numerical results. The vorticity generation on the wall shows interesting behaviour after the dipole collides with no-slip wall. The angle of the incidence effects the behaviour of the dipole after the wall collision, the dissipation of the energy and the growth of the enstrophy. Throughout this thesis the impact of the slip length and Reynolds number on the dipole wall collision is studied. By applying the Navier-slip condition with moment boundary conditions the behaviour of the flow changes and the dissipation of the energy is affected by slip length and the peaks of the enstrophy decreases with higher slip lengths. The dissipation of the energy and its relation to the enstrophy over dipole wall collision are also investigated for different types of boundaries and angles. The theoretical and the numerical investigation shows that the presence of the wall modifies this relation. Moreover, the dissipation of the energy in the absence and the existence of the viscosity effect are studied. Finally, an analysis is done of the stress field of the LBM by using the same boundary conditions for simple flow.