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A Highly Accurate Numerical Solution of the Advection-Diffusion Equation
P.F.C. Matsoukis

The numerical solution of the advection-diffusion equation of a pollutant concentration is an extremely important issue in the mathematical modelling of the physical processes involved in many environmental applications. The present work describes a numerical solution in one and two spatial dimensions that is based on the notion of characteristics and uses a finite difference scheme for the calculation of the concentration values. This solution is proven to be highly accurate compared to available analytical solutions, provided that the Peclet number is kept equal or close to 2 for the one-dimensional case and 2 (square root of 2) to for the two-dimensional case.

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