A finite volume method for the solution of convection—diffusion 2d problems by a quadratic profile with smoothing

Abstract

A new finite volume (FV) method is proposed for the solution of convection‐diffusion equations defined on 2D convex domains of general shape. The domain is approximated by a polygonal region; a structured non‐uniform mesh is defined; the domain is partitioned in control volumes. The conservative form of the problem is solved by imposing the law to be verified on each control volume. The dependent variable is approximated to the second order by means of a quadratic profile. When, for the hyperbolic equation, discontinuities are present, or when the gradient of the solution is very high, a cubic profile is defined in such a way that it enjoys unidirectional monotonicity. Numerical results are given.

Citation

De Biase, L., Feraudi, F. and Pennati, V. (1996), "A finite volume method for the solution of convection—diffusion 2d problems by a quadratic profile with smoothing", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 6 No. 4, pp. 3-24. https://doi.org/10.1108/09615539610123414