Development of a Cell-Centred Finite Difference Numerical Methodology on Triangulated Domains

摘要

A cell-centred finite difference (CCFD) method for unstructured mesh topology is proposed and applied to model partial differential equations (PDEs) governing fluid flow and solid mechanics phenomena. The numerical method implements a finite difference approximation at cell centroids by taking differencing points along orthogonal Cartesian axes localized within each cell. The predominant advantage of this method is that it can be applied to arbitrary mesh topologies, including structured, unstructured and hybrid meshes. Either a direct or iterative approach is used to solve the system of equations developed by the proposed method. The numerical method is designed to solve a variety of physical phenomena governed by PDEs, such as electrostatic potential in electromagnetic fields, stress and strain in structural mechanics and wave phenomena in physics. The focus of the thesis research is to investigate the application of this methodology in heat transfer and fluid mechanics problems. This new finite difference methodology is applied to typical u22benchmarku22 problems in such fields, covering the representative in different types of PDEs with initial and boundary conditions. Solutions obtained are compared to exact solutions if available from analytical methods or to the results from other reliable numerical simulations.