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A discontinuous Galerkin method for a hyperbolic model for convection–diffusion problems in CFD
Author(s) -
Gómez H.,
Colominas I.,
Navarrina F.,
Casteleiro M.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1996
Subject(s) - convection–diffusion equation , classification of discontinuities , computational fluid dynamics , discontinuous galerkin method , galerkin method , generalization , upwind scheme , mathematics , convection , spurious relationship , diffusion , fourier transform , mechanics , finite element method , mathematical analysis , physics , thermodynamics , statistics , discretization
This paper proposes a hyperbolic model for convection–diffusion transport problems in computational fluid dynamics (CFD). The hyperbolic model is based on the so‐called Cattaneo's law. This is a time‐dependent generalization of Fick's and Fourier's laws that was originally proposed to solve pure‐diffusive heat transfer problems. We show that the proposed model avoids the infinite speed paradox that is inherent in the standard parabolic model. A high‐order upwind discontinuous Galerkin (DG) method is developed and applied to classic convection‐dominated test problems. The quality of the numerical results is remarkable, since the discontinuities are very well captured without the appearance of spurious oscillations. These results are compared with those obtained by using the standard parabolic model and the local DG (LDG) method and with those given by the parabolic model and the Bassi–Rebay scheme. Finally, the applicability of the proposed methodology is demonstrated by solving a practical case in engineering. We simulate the evolution of pollutant being spilled in the harbour of A Coruña (northwest of Spain, EU). Copyright © 2007 John Wiley & Sons, Ltd.