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The aim of this thesis is to study the Lattice Boltzmann method for fluid dynamics by using moment based boundary condition to implement no-slip and partial slip boundary conditions in two and three dimensions. The main topics are the theory of the Lattice Boltzmann method, an examination of boundary conditions and the application of the Lattice Boltzmann method to a variety of fluid flows. We developed and successfully implemented combinations of no-slip, Navier-slip, pressure boundaries and inlet conditions in two and three dimensions using moment-based boundary conditions including careful treatments of conditions along edges and at corners. A useful advantage of the use of moment based boundary conditions is that it allows for Navier-slip conditions to be implemented exactly i.e. without the use of arbitrary coefficients required in some other methods. The first application of the method is pulsatile fluid flow with no-slip and Navierslip boundary conditions in two and three dimensions. The results are in good agreement with exact solutions and some interesting results related to non-convergence of acoustic scaling for the two dimensions are found. The next application is three-dimensional laminar flow in a square duct driven by a body force. The results agree well with the analytical solution. Next, a study is presented of the rarefaction and compressibility effect on laminar flow between two parallel plates and in a three-dimensional micro-duct which are driven by differential pressures at the inlet and outlet. The results are again compatible with those found in the literature. Finally, we investigate the developing three-dimensional laminar flow in the entrance region of a rectangular channel. Results demonstrate some interesting Reynolds number dependence and are found to be in line with the literature for high Reynolds number. |
