Time Integration for Numerical Solution of Advection-Diffusion Contaminant Transport

A semi-analytical time integration (SATI) is proposed for numerical solution of the advection-diffusion contaminant transport equation. Compared with traditional finite difference method, SATI is stable, accurate and is not affected by the time step sizes, The computation costs for a single time step using SATI can be more expensive than using the finite difference method. However, the total computation cost may not be as expensive as that in finite difference methods since an accurate solution can be achieved by SATI using larger time step sizes and without any restrictions. Two examples from the literature are provided to demonstrate the effectiveness of SATI for ID and 2D applications.