In this thesis a 2D Lattice Boltzmann model has been developed to simulate non- Newtonian fluid flows over geometries with curved boundaries. The accuracy of numerical results are investigated for several problems. The non- Newtonian nature of the flow is implemented using the power-law model. The simulations are performed for a range of power-law model parameter values representing shear thinning and shear thickening fluids. Four test cases are considered in this research. First a non- Newtonian flow in a simple channel is simulated. In this case, predicted numerical results are compared with those of the analytic solution. in the second case, a Lattice Boltzmann simulation is performed for a non- Newtonian flow over a circular cylinder. Curved boundaries are treated in the Lattice Boltzmann model with an interpolation over solid surfaces which is an improved modification of a previous. The resulting dates such as the drag coefficients and centerline velocities are compared with those of existing date in the literature. As third test case, a non- Newtonian flow over a moving cylinder is studied. This study is conducted within two reference coordinates, a moving and a stationary coordinate with respect to the cylinder. Numerical results are compared against each other for these two situations. For a last test case, a non- Newtonian flow over two side-by-side cylinders is conducted. Numerical results for all these test cases show very good agreement with those of analytical existing results, which indicate the ability and accuracy of the Lattice Boltzmann for non- Newtonian flow simulations over geometries with curved boundaries. Key words: Lattice Boltzmann, Non-Newtonian Fluid flow, power-law model, curved boundaries, interpolation method
