Date of Award

2014

Publication Type

Master Thesis

Degree Name

M.A.Sc.

Department

Mechanical, Automotive, and Materials Engineering

First Advisor

Barron, Ronald M.

Keywords

Applied sciences

Rights

info:eu-repo/semantics/openAccess

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Abstract

The traditional finite difference method has an important limitation in practical applications, which is the requirement of a structured grid. The purpose of this thesis is to improve the finite difference scheme for application on complex domains. The analysis of the Finite Difference method is carried out for 1D model problems governed by the convection-diffusion equation. The Stencil Mapping method is developed for complex domains. One of the features of this new scheme is that the value at a node can be calculated by using only the neighbouring values on the 3-point stencil. This allows finite differencing for arbitrary nodal distribution in the mesh, and is developed for 2 nd -order and 4 th -order differencing schemes. The numerical solutions for typical boundary and initial value problems are compared with exact solutions. Local truncation error is introduced as an effective parameter to assess accuracy of the scheme. An adaptive meshing procedure is also presented.

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