A new approach is proposed for the numerical solution of three-dimensional advection-diffusion equations, which arise, among others, in air pollution modelling. The technique is based on directional operator splitting, which results in one-dimensional advection-diffiision equations. Then upstream-type difference approximations are applied for the first-order derivatives and non-standard difference approximations for the second-order derivatives. This approach leads to significant qualitative improvements in the behaviour of the numerical solutions.

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