Theory And Applications Of Lattice Boltzmann Method In Computational Fluid Dynamics

A new force suddenly rises, the computational fluid dynamics, as the organic union of classic fluid mechanics, numerical computation methods and computer science, develops to become the efficient means of both science research and engineering design. The interaction among theoretical analysis, experimental research and numerical simulation promotes both the theoretic renovation and engineering applications of fluid mechanics. In this background, the lattice Boltzmann method comes forth and progresses rapidly as an attractive numerical computation method.Aiming at the key issues of lattice Boltzmann method applications in engineering design, the main work, based on the extensive inquisition and pursuing the evolution and status in quo, is presented as following:Firstly, the intrinsic relationship between lattice Boltzmann method and other traditional numerical methods is interpreted through the Chapman-Enskog expansion and multi-scale analytic technique. And the essential idea and foundation of lattice Boltzmann model are set forth.According to the mathematic modeling principle of physical problem, the error of lattice Boltzmann model is analyzed in Chapter 3. The nonlinear deviation term from the Navier-Stokes equation is given, and the main model coefficients, such as speed of sound, viscosity and so on, are verified by numerical computation, the results show that the lattice Boltzmann method has second order precision in space and in time which satisfy the engineering application, whereas, the compressible effect can't be neglected along with Mach number increasing, and must be reduced or eliminated.Chapter 4 proposes an incompressible lattice BGK model, in which the velocity and pressure instead of the mass density that is a constant are the independent dynamic variables. And the incompressible Navier-Stokes equations are exactly derived from this incompressible LBGK model, thus the compressible effect due to the density fluctuation is theoretically eliminated. The results of steady or unsteady flow show that the incompressible lattice BGK model is validate in reducing the compressibility error. And then, the cavity flow is simulated, and the streamline and pressure contour at different Reynoldsnumber are plotted, the stream function and location of vortex centers are agree well with the previous results, which indicate the incompressible lattice BGK model is reliable.Numerical stability, the other issue of the lattice Boltzmann method, is discussed in Chapter 5. Corresponding to the uniform and shear background flow, the stability of d2q7 d2q9 and d3ql5 model is analyzed through the Von Neumann linear stability theory, both the conclusion about the mass distribution parameters, the wave number, the relaxation timeand the uniform velocity, and the linear stability criterion N R0.58 are instructive tonumerical simulation of flow.Chapter 6 presents the lattice Boltzmann algorithm on body-fitted coordinates system, which not only avoids the restriction of uniform regular mesh, but also enhances the stability. After the coordinate transformation, the discrete velocity Boltzmann equation is solved directly in computational domain to preserve the geometry of body. The results comparison of cylindrical couette flow at different size meshes, different lattice BGK models and different algorithms shows that, not only the precision of the incompressible lattice BGK model is satisfactory, but also the curvilinear coordinate algorithm is efficient. Therefore, the circular cylinder flow is simulated. And the results of the wake length, separation angle, and drag or pressure coefficient for low Reynolds number are excellent agreement with previous experimental and numerical results. Furthermore, the streamlines for Reynolds numbers up to 9500 display the evolution with time of flow, and capture the possible flow pattern at different times.Finally, the whole paper is summarized and the further research interests are put forward in Chapter 7.