Study On The Theory And Application In Hydraulic Computation Of The Lattice Boltzmann Method

Lattice Boltzmann (LB) method was developed into a flow-field simulating scheme in the middle of 1980s. Compared with traditional numerical methods such as the FEM, FDM, etc, the LB method has several important features, including: simplicity in algorithm, easily programming, direct calculation of pressure from a state equation and amenability to simulate all kinds of flow field with complex boundaries, it also has much advantage in the respect of parallel computation because of its regional evolution. In recent years, plentiful and substantial fruits achieved by the LB method in simulations of hydraulics, multiphase flows, flows in porous media and heat transfer as well as magnetohydrodynamics, have revealed a broad perspective of application of this method, it will become a powerful competitor to the conventional approaches. In order to absorb the recent achievement in theory and application of the LB method, explore new ways in hydraulic computation to promote the development of practice, some work is carried out in this thesis, as following:Advances in the theory research and application, deductive process of the D2Q9 model and some other commonly used models of the LB method are summarized.Based on the hydrodynamic and general boundary conditions, a new joint boundary condition is presented, it integrates advantage of the two conditions above and obtains very good results in dealing with all kinds of boundaries of flow fields. This boundary condition becomes more applicable after treatment of being modularized.Aiming at the defect of low computational efficiency in the uniform-mesh LB method, a new double-mesh Lattice Boltzmann method is put forth and three numerical examples, two-dimensional Poiseulle flow, backward-facing step flow and flow in channel with a rectangular slot, are simulated, proving this method can obviously enhance the computational efficiency.In addition, according to the character of flow field in complex region, a new decomposition-couple algorithm of the Lattice Boltzmann method is put forward, itmakes good use of character of the LB method to implement data exchanges between divided regions, sufficiently utilizes the computational resource to increase computational efficiency. Then, fork pipelines with "T", "+" and "X" geometries are simulated, depicting the character and merits of this algorithm, as well as its perspective in application.Through the research in this thesis, following conclusion can be drew: on the condition of nearly incompressible limit, the N-S equations can be recovered by the LB method's models with 2-order numerical precision; computational efficiency in simulating flow fields can be improved effectively by perfection of the LB method's theory; development of parallel computation can contribute to the simulation of large-scale flow field with complex geometry. In the future, some issues need to be investigated further, which include: enforcement of the stability, raising Reynolds number of the flow field being simulated, treatment of curve boundaries as well as further development of application.