Abstract

FREY, S.; MARTINS-COSTA, M. L.  and  SALDANHA DA GAMA, R. M.. Petrov-Galerkin approximation for advective-diffusive heat transfer in saturated porous media. Lat. Am. appl. res. [online]. 2008, vol.38, n.2, pp.169-178. ISSN 0327-0793.

This article studies the heat transport in a flow through a saturated rigid porous medium. The mechanical model is based on the Continuum Theory of Mixtures which considers the fluid and the porous matrix as overlapping continuous constituents of a binary mixture. A Petrov-Galerkin formulation is employed to approximate the resulting system of partial differential equations, overcoming the classical Galerkin method limitation in dealing with advective-dominated flows. The employed method is built in order to remain stable and accurate even for very high advective-dominated flows. Taking advantage of an appropriated upwind strategy, the applied finite element method proved to generate accurate approximations even for very high Péclet regime. Some two-dimensional simulations of the advective-diffusive heat transfer in a flow through a porous flat channel employing lagrangean bilinear and serendipity biquadratic elements have been performed attesting the reliability of the employed Petrov-Galerkin formulation as well as the poor performance of Galerkin one even when mesh refining is considered.

Keywords : Porous Media; Mixture Theory; Computational Heat Transfer; Finite Elements; Petrov-Galerkin Formulation.

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