Solution of the advection equation using finite difference schemes and the method of characteristics
Numerical models are important engineering tools when considering the prediction of pollution transport in a body of water. Such a prediction is achieved by the solution of the advection-diffusion equation. At present, there exist many numerical techniques which can be used to solve the advection-diffusion equation. The major difficulty when considering undertaking such a simulation, is what method should be used to calculate the advection term. It is now accepted that the appropriate method to follow would involve, splitting up this water quality equation into two separate terms, advection and diffusion. By using this process, each term can be solved individually and the numerical difficulties associated with each term, treated separately. This work discusses the various numerical modelling techniques which can be used to solve the advection term. Two-dimensional finite difference schemes, including QUICKEST, are compared with multi-point method of characteristics techniques. These are analysed in terms of solving advection for various distributions of concentration. The adaptation of these schemes to allow for the use of Courant numbers exceeding unity is also explored. The ultimate aim is to develop a numerical scheme which can be implemented in an industrial model.