Abstract
A great number of phenomena can be modelled by using evolution equations. These equations can model different behaviors according to the problem of interest. The advection–diffusion equation models the dispersion of pollutants in water bodies such as rivers, lakes, and groundwater.In previous works, different results for the stability of generalized finite-difference applied to the advection equation and the diffusion equation have been presented.This paper deals with a study of the stability of a generalized finite-difference approximation of the advection–diffusion equation solved on non-rectangular and highly irregular regions using convex, logically rectangular grids. The discussed bounds for the time step are valid for any second-order finite difference scheme, regardless of a grid structure.
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