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A stabilized finite element approach for advective-diffusive transport problems

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Title
A stabilized finite element approach for advective-diffusive transport problems
Author(s)
Figueroa Álvarez, Carlos Alberto
Colominas, Ignasi
Mosqueira Martínez, Gonzalo
Navarrina, Fermín
Casteleiro, Manuel
Date
1999
Citation
19th. Iberian-latin American Congress on Computational Methods in Engineering, São Paulo, November, 1999 (CD-ROM), editors, P.M. Pimenta, R.M.L.R.F. Brasil and E.S. Almeida N.
Abstract
[Abstract] As it is well-know, the numerical simulation in fluid mechanics is quite difficult specially when the velocity of the fluid is important. These problems are reflected in the apparearance of numerical oscillations when Finite Element approaches with Galerkin weighting are used. In last years, some alternative formulations have been proposed in order to overcome these problems: Streamline Upwind Petrov Galerkin Methods, Space-time Galerkin Least Squares Methods, Subgrid Scale Methods, Characteristic Galerkin Method, etc. In this paper, we focuse our attention in the advective-diffusive transport differential equation, and its application to engineering problems. Thus, we present a brief review of the causes of appaerance of these numerical oscillations and a short revision of the numerical schemes proposed for the stabilization of advective-dominant problems. Then, a numerical formulation based on a Petrov Galerkin scheme and a procedure to obtain stabilization parameters for 1D, 2D and 3D problems are proposed. Finally, we present different numerical test problems, and we show the feasibility of this formulation with its application to an engineering problem: the evolution of a water pollutant spilt in a harbour area.
Keywords
Advective-diffusive transport
Petrov-Galerkin weighting
Stabilization parameters
 
ISBN
85-901027-1-8

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