A generalized statement for advective-diffusive phenomena. Finite element model and applications
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A generalized statement for advective-diffusive phenomena. Finite element model and applicationsFecha
2000Resumen
[Abstract] Solving convective-diffusive transport problems is a frequent task in engineering, especially in
convection dominated situations. Moreover, the standard statement for the transport problem leads to
the result that mass can propagate at an infinite speed. This paradoxical result occurs as a consequence
of using Fick's law. It seems that this fact is related to the spurious oscillations that occur in the
numerical solution of the standard formulation of the transport problem when the Galerkin ¯nite
element method is used for the spatial discretization.
For these reasons, we propose to use Cattaneo's law instead of Fick's law for the formulation of the
advective-diffusive problem. Cattaneo's law has been previously applied to pure-diffusive problems
and it is a generalization of Fick's law. The formulation of the transport problem by using Cattaneo's
law leads to a hyperbolic system of partial differential equations which can be written in conservative
form. As a consequence of being a hyperbolic system, a finite diffusive velocity can be defined.
A Taylor-Galerkin procedure can be used to solve these equations. In this paper, several problems
in one and two-dimensional domains have been solved to show that this new approach can be used in
real engineering problems.
Palabras clave
Convection-diffusion
Cattaneo's equation
Taylor-Galerkin
Cattaneo's equation
Taylor-Galerkin
Descripción
Enviado a International journal for numerical methods in engineering
Versión del editor
Derechos
This is a preprint of an
article accepted for publication in International journal for numerical methods in engineering © copyright 2005 John Wiley & Sons