Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 176, Issue -, Pages 301-311Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2020.01.020
Keywords
Stability analysis; Generalized finite-difference; Advection-diffusion equation; Irregular regions; Numerical solution of EDP's
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Funding
- CIC-UMSNH
- Aula-CIMNE Morelia
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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. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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