Research On Incompressible Multi-relaxation-time Lattice Boltzmann Method And Its Application

Whatever computation of combusion or gas-partile flow, there is a basic research field - fluid mechanics. Lattice Boltzmann method (LBM) is a newly developed computational fluid numerical method, which is originated from lattice gas cellular automata (LGCA) at the end of 1980's last centrury. LBM simulates the fluid movement at the microscopic particle level that is absolutely different from the conventional numerical methods. Single particle distribution satisfying classic Boltzmann equation is described by LBM. The so-called LB equation is a special discrete form of continuum Boltzmann equation in discrete particle velocity, discrete spatial and temporal spaces. By using the Chapman-Enskog multi-scale analysis technique and the conservations of physical variables, the LB equation can be recovered to the fluid dynamical equation at macroscopic level with the low Knudsen number and low Mach number assumptions. As a result, we can obtain the macroscopic fluid movement through calculating the particle distribution numerically.LB method is a high performance computing method with notable advantages, such as fully parallelism, easy implementation and simple codes. Until now, it has been widely applied in computational fluid dynamics and has become one of the most important tools for nonlinear science and complex system.However, there still exist some disadvantages in LBM, such as the treatment of the force term and multi-relaxation-time LB model. The applications of LBM have achieved great success in multiphase flow, porous flow, suspending particle flow, magnetohydrodynamics, etc. But less research on the microgravity fluid is found. On the other hand, although the code of LBM is simple, the computation may be increased dramatically as the more complex problem and the needed better numerical accuracy. It is important to do some optimization in order to apply the LBM in the engineering. Therefore, we make some valuable relevant research work to remedy the gap.Firstly, a novel scheme of the lattice BGK (LBGK) model with a force term has been proposed. Unlike the existing models, an appropriate term was added in the evolutionary equation. Through the Chapman-Enskog (C-E) procedure the Navier-Stokes (N-S) equations with a force term can be recovered with the kinetic viscosity. Three discrete methods of the added term have been discussed in detail. It can be proved that some existing models are the special cases of the model. Numerical simulation results show that the scheme is of second numerical accuracy and better stability.Second, two-dimensional nine-velocity and eight-velocity lattice Boltzmann models with multi-relaxation-time are proposed for incompressible flows, in which the equilibria in the momentum space are derived from an earlier incompressible lattice Boltzmann model with single relaxation time by Guo. Via the Gram-Schimidt orthogonalization procedure the eight-by-eight transformation matrix can be constructed which satisfies the general form by Ginzburg. Through the Chapman-Enskog expansion, the incompressible Navier-Stokes equations are recovered from the two models which eliminate the compressible effect in the existed models. The results of numerical tests exhibits much better numerical stability than the single relaxation time model. These two models afford a new method for incompressible flow.In the third part, we constructed a two distribution function LBGK model for the thermocapillary flow in microgravity. The boundary conditions for the ther-malcapillary flow are treated using the non-equilibrium extrapolation scheme. The model is validated by simulating the thermocapillary flow in a two-dimensional square cavity with a single free surface and differentially heated side walls. It is feasible to apply the LBM to the microgravity fluid dynamics.Finally, We take the classical problem-cavity flow as an example and optimize the kernel codes of the LBM. The optimization include two aspects: time and space. The efficiency of the optimized code increased much more. In the parallel frame, the efficiency also increased if the kernel code is taken the optimized code.In conclusion, this thesis proposes two incompressible LB models which improve numerical stablity of LBGK model, and a general scheme for force term proved. Furthermore the thermocapillary flow in microgravity has been considered and this work has made many valuable efforts to accelerate the applications of LBM. At last, the high performance algorithm can broaden the applications of LBM in our subject.