A Study Of Unsteady Heat Conduction Computation On Unstructured Grid

It is one of the basic problems to study the heat conduction equation (the diffusion equation) using numerical method on unstructured grids. It has been widely used in a lot of areas, because of the two main advantages of the unstructured grids, viz., the ease of grid generation for complex, realistic geometries, and the ability to dynamically adapt the grid to local features of interest.The procedure of solving unsteady heat conduction problems on unstructured grids was investigated in this thesis. It included the discretization method of governing equation, the treatment of boundary conditions and source terms. Commercial software was used to generate unstructured meshes. The diffusion term was discretized by cell-based finite volume method, and the second order accuracy. The unsteady term was discretized by explicit scheme, Crank-Nicolson scheme and implicit scheme in two dimension problems. And implicit scheme was used in three dimension problems. The feature of the schemes was studied.Computational program was made using VISUAL FORTRAN, and the codes were divided into different modules according to different purposes. The eleven examples of two groups were presented to validate the correction, integrity and universality of the program. The numerical solutions of six examples in the first group were compared with the analytic solutions, and there are five examples in the second groups, and the results were analyzed and compared with the numerical solutions computed on structured grids or the results shown in the reference. All of these prove that the method and the program are correct and perfect.It will supply useful numerical codes as reference for engineering and designing.