Keywords: atmospheric modelling, atmospheric processes, convection?diffusion equations, upstream-type discretisation, efficient numerical methods, environmental modelling
On efficient numerical solution of one-dimensional convection?diffusion equations in modelling atmospheric processes
A new approach is proposed to the numerical solution of one-dimensional convection?diffusion equations that arise in modelling atmospheric processes and air pollution modelling. The technique is based on upstream-type difference approximations for first-order derivatives and non-standard difference approximations for second-order derivatives of convection?diffusion equations. This approach leads to the significant qualitative improvements in the numerical solutions behaviour. The relative contribution of convection and diffusion is directly incorporated into the corresponding numerical scheme in such a way that large spatial grids can be taken without affecting solution stability. The method is compared with the contemporary computational schemes for solving problems with severe internal and boundary gradients and is shown to be stable and computationally efficient. The results of a numerical experiment are given.