Three-dimensional 12-velocity Multiple-relaxation-time Lattice Boltzmann Model Of Incompressible Flows

In this work,a 12-speed multiple-relaxation-time lattice Boltzmann model(iD3Ql3 MRT model)for three-dimensional incompressible flow is proposed by using inversion method when the 13-speed multiple-relaxation-time lattice Boltzmann model(D3Q13 MRT model)proposed by d'Humieres et al.has no corresponding LBGK model.This may be the current multi-relaxation lattice Boltzmann model for three-dimensional incompressible flow with the least discrete velocity.This model has higher computational efficiency in principle than the commonly used D3Q13 model.In the part of numerical simulation,we compare the iD3Q12 MRT model with another 13-speed multiple-relaxation-time lattice Boltzmann model(He-Luo D3Q13 MRT model)proposed by d'Humieres with lower compressibility in terms of accuracy and stability.By simulating different flows,including steady Poiseuille flow driven by pressure,unsteady pulsating flow driven by periodic pressure and square cavity flow driven by top cover,the results show that the accuracy of the two models is the same and has the second-order accuracy when simulating steady Poiseuille flow.When simulating unsteady pulsating flow,the 13-speed model shows better stability,but the 12-speed model has higher accuracy in most cases.The iD3Q12 model has second-order accuracy in simulating pulsating flow at four different times of a cycle.The 13-speed model shows slightly better stability than the new 12-speed model when simulating the square cavity flow driven by the top cover at different Reynolds numbers.The thesis is arranged as follows:In the first chapter,introduce the development of lattice Boltzmann method,major compo-nents and evolution process,various lattice Boltzmann models,incompressible lattice Boltzmann model.In the second chapter,we introduce two kinds of 13-velocity multiple-relaxation-time lattice Boltzmann method,namely d'Humieres D3Q13 MRT LBE and He-Luo D3Q13 MRT LBE,iD3Q12MRT model is proposed.In the third chapter,numerical simulation and analysis of the validity,accuracy and sta-bility of the proposed iD3Q12 MRT model.In the fourth chapter,we restore the iD3Q12 model to incompressible Navier-Stokes equa-tion by Champan-Enskog expansion methodIn the last chapter,We summarize the whole paper and put forward some questions on the basis of the existing research conclusions,and look forward to the problems that can be studied in the future.