A study of the stability for a generalized finite-difference scheme applied to the advection-diffusion equation

摘要

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.