A FINITE-VOLUME METHOD FOR THE SOLUTION OF CONVECTION-DIFFUSION 2D PROBLEMS BY A QUADRATIC PROFILE WITH SMOOTHING

A new finite volume (FV) method is proposed for the solution of convec tion-diffusion equations defined on 2D convex domains of general shape . The domain is approximated by a polygonal region; a structured nonun iform mesh is defined; the domain is partitioned in control volumes. T he conservative form of the problem is solved by imposing the law to b e verified on each control volume. The dependent variable is approxima ted to the second order by means of a quadratic profile. When, for the hyperbolic equation, discontinuities are present, or when the gradien t of the solution is very high, a cubic profile is defined in such a w ay that it enjoys unidirectional monotonicity. Numerical results are g iven.