Solving Direct and Inverse Problems of Convection Diffusion Equation

The pollution is a big issue in estuarine and coastal engineering, inducing a huge impact on the environment. It would be helpful for engineering practice to analyze the emission and the dynamic motion of the pollution. The subject of this thesis is to solve the convection diffusion equation without knowing the source term by the boundary integral element method (BIEM) and the collocation method which are both meshless methods to recover 1D pollution source and concentration problem. Firstly, BIEM is applied to solve the inverse source problem. Secondly, BIEM as well as the collocation method are applied to solve the direct concentration problem. Other than Fourier series and polynomial basis, we tried to use the exponential functions and mode shapes as the basis of trial solution as well. Furthermore, we tried the fractional order exponential functions as the basis to see if the accuracy can be increased. The supplementary techniques such as multi-scale method, conjugate gradient method (CGM) and orthogonality of trigonometric functions are also used in this thesis.