Compact integrated radial basis function modelling of particulate suspensions

The present Ph.D. thesis is concerned with the development of computational procedures based on Cartesian grids, point collocation, immersed boundary method, and compact integrated radial basis functions (CIRBF), for the simulation of heat transfer and steady/unsteady viscous flows in complex geometries, and their applications for the prediction of macroscopic rheological properties of particulate suspensions. The thesis consists of three main parts. In the first part, integrated radial basis function approximations are developed into compact local form to achieve sparse system matrices and high levels of accuracy together. These stencils are employed for the discretisation of the Navier-Stokes equation in the pressurevelocity formulation. The use of alternating direction implicit (ADI) algorithms to enhance the computational efficiency is also explored. In the second part, compact local IRBF stencils are extended for the simulation of flows in multiply-connected domains, where the direct forcing-immersed boundary (DFIB) method is adopted to handle such complex geometries efficiently. In the third part, the DFIB-CIRBF method is applied for the investigation of suspensions of rigid particles in a Newtonian liquid, and the prediction of their bulk viscosity and stresses. The proposed computational procedures are verified successfully with several test problems in Computational Fluid Dynamics and Computational Rheology. Accurate results are achieved using relatively coarse grids.