An artificial-viscosity finite-difference scheme is introduced for stabilizing the solutions of advection-diffusion equations. Although only the linear one-dimensional case is discussed, the method is easily susceptible to generalization. Some theory and comparisons with other well-known schemes are carried out. The aim is, however, to explain the construction of the method, rather than considering sophisticated applications.
A note on second-order finite-difference schemes on uniform meshes for advection-diffusion equations / Funaro, Daniele. - In: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0749-159X. - STAMPA. - 15:(1999), pp. 581-588.
A note on second-order finite-difference schemes on uniform meshes for advection-diffusion equations
FUNARO, Daniele
1999
Abstract
An artificial-viscosity finite-difference scheme is introduced for stabilizing the solutions of advection-diffusion equations. Although only the linear one-dimensional case is discussed, the method is easily susceptible to generalization. Some theory and comparisons with other well-known schemes are carried out. The aim is, however, to explain the construction of the method, rather than considering sophisticated applications.
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