A Generalized Method For Advective-diffusive
Computations In Engineering
Author(s)
H. G´omez, I. Colominas, F. Navarrina & M. Casteleiro
Abstract
Besides the computational cost of solving advective-diffusive problems in convection
dominated situations, the standard statement for this phenomenon leads
to the result that mass can propagate at an infinite speed. This paradoxical result
occurs as a consequence of using Fick’s law [1] and it is related to the appearance
of boundary layers on outflow borders when convection dominates diffusion.
For these reasons we propose to use Cattaneo’s law [2] instead of Fick’s law as the
constitutive equation of the problem. This approach leads to a totally hyperbolic
system of partial differential equations. A finite diffusive velocity can be defined
by using this approach. Several problems have been solved to show that the proposed
formulation leads to stable results in convection dominated situations.
Keywords: advection-diffusion, Taylor–Galerkin, Cattaneo’s equation.
1 Introduction
Transport problems involving convective and diffusive processes in fluid media
have a great applicability in engineering. This kind of phenomena can be modeled
by using the so-called advective-diffusive equation. Unfortunately, it is very
complicated to obtain an accurate and stable solution for this equation when the
convective term becomes important. To overcome this problem, many interesting
numerical methods have been introduced, but completely satisfactory results have
not been achieved (for a detailed presentation of most of these methods see reference
[3]).
In this paper we review the formulation of the advective-diffusive equations
applied to the spillage of a pollutant into a fluid medium. In particular, we notice
that Fick’s law leads to the result that mass can propagate at an infinite speed.
This fact is related to the appearance of spurious oscillations in the numerical
Keywords
advection-diffusion, Taylor–Galerkin, Cattaneo’s equation.
Related Book
Other papers in this volume
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