A Saulyev Explicit Scheme for an One-Dimensional Advection-Diffusion-Reaction Equation in an Opened Uniform Flow Stream

Pawarisa Samalerk, Nopparat Pochai

Abstract

The one-dimensional advection-diffusion-reaction equation is a mathematical model describing the transport and diffusion problems such as pollutants and suspended matter in a river or channel. If the velocity field is non-uniform the model cannot be theoretically manipulated, there for numerical techniques are required. The object of this research is to propose a simple advection-diffusion-reaction numerical simulation by using the Saulyev schemes. The proposed numerical technique uses an unconditionally stable method. It is the large or small of time step and/or grid size can be employed in the techniques. Among examples are calculated for three $\theta$ values. The case of $\theta = 0$ gives a smooth solution compare to the another values. Increasing the mass decay rate affects the maximum concentration level. The numerical experiments show that the calculated results are reasonable approximations.