Resolución Numérica de la Ecuación Unidimensional de Convección-Difusión. Aplicación al Transporte de Contaminantes en Cursos de Agua

Abstract

The application of a numeric methodology for the solution of the one dimensional covection-diffusion equation is described in the present paper. It is well known tbefuct that the resolution of this equation is frequently associated with problems of numerical diffusion and oscillations due to the numerical schemes. In order to avoid these problems, a split opemtoc approach which sepo:mtes the complete equation into a convective term (hyperbolic type) and a ditfusive term (pambolic type) is used. In this approoch both terms are considered as alternating processes during short time periods. The convective term is modelled by the chamcteristics method combined with a high order interpolation. The diffusive
term is modelled by a generalized Crank Nicolson scheme. The effets of variation on the model parameters: Courant number, Peclet number and weighing metor theta, are nnalized. The computational implementation of the model in TURBO PASCAL is descnbed. The behaviour of the model is compared with results of a classic Crank Nicolson scheme applied to the compiete equation. Applications are made to theoretical situations and to a natural stream of the region. Final conclusions are exposed.