Finite volume method for a diffusion-advection equation

• Main Author: Goh, Brandon B Edison Adi
• Other Authors: Ang Whye-Teong
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Engineering
• Online Access: https://hdl.handle.net/10356/176344
• Institution: Nanyang Technological University

Computational fluid dynamics (CFD) is an emerging tool to simulate fluid motions and will continue to be increasingly more prominent with greater computational power. Coupled with the principles of the finite volume method to solve the diffusion-advection equation, a well-defined computer program can provide numerical solutions to a governing equation following the variables and constraints in a mathematical problem. This paper implemented a computer program in MATLAB to instantaneously solve a discretised one-dimensional diffusion-advection equation under both steady state and transient conditions. The numerical solutions were calculated from the user input values with a set of algorithms and were represented in both graphical and text results. Implementing a graphical user interface within the computer program minimised user input errors and visually compared the exact and numerical solutions, enabling the visualisation of the accuracy of the numerical solution. The computer program also featured multiple calculations with many linear equations and was tested against mathematical problems to conclude the successful implementation.