×

Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations. (English) Zbl 0593.76096

Formulations which complement the streamline-upwind/Petrov-Galerkin procedure are presented. These formulations minimize the oscillations about sharp internal and boundary layers in convection-dominated and reaction-dominated flows. The proposed methods are tested on various single- and multi-component transport problems.

MSC:

76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics
Full Text: DOI

References:

[1] Brooks, A. N.; Hughes, T. J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Meths. Appl. Mech. Engrg., 32, 199-259 (1982) · Zbl 0497.76041
[2] Deans, H. A.; Lapidus, L., A computational model for predicting and correlating the behavior of fixed bed reactors: I. Derivation of model for nonreactive systems, AIChEJ., 656-663 (1960)
[3] Deans, H. A.; Lapidus, L., A computational model for predicting and correlating the behavior of fixed-bed reactors: II. Extension to chemically reactive systems, AIChEJ., 663-668 (1960)
[4] Finlayson, B. A., Packed bed reactor analysis by orthogonal collection, Chem. Engrg. Sci., 26, 1082-1091 (1971)
[5] Fromont, G. F.; Bischoff, K. B., Chemical Reactor Analysis and Design (1979), Wiley: Wiley New York
[6] Heinemann, R. F.; Poore, A. B., Multiplicity, stability, and oscillatory dynamics of the tubular reactor, Chem. Engrg. Sci., 36, 1411-1419 (1981)
[7] Hughes, T. J.R.; Brooks, A. N., A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline upwind procedure, (Norrie, D. N.; Oden, J. T.; Zienkiewicz, O. C.; Gallagher, R. H., Finite Elements in Fluids (1982), Wiley: Wiley London), 46-65
[8] Hughes, T. J.R.; Mallet, M.; Taki, Y.; Tezduyar, T.; Zanutta, R., A one-dimensional shock capturing finite element method and multi-dimensional generalizations, (Angrand, F.; Dervieux, A.; Desideri, J. A.; Glowinski, R., Numerical Methods for the Euler Equations of Fluid Dynamics (1985), SIAM: SIAM Philadelphia, PA), 371-408 · Zbl 0608.76059
[9] Hughes, T. J.R.; Mallet, M.; Mizukami, A., A new finite element formulation for computational fluid dynamics: II. Beyond SUPG, Comput. Meths. Appl. Mech. Engrg., 54, 341-355 (1986) · Zbl 0622.76074
[10] Hughes, T. J.R.; Mallet, M.; Franca, L., New finite element methods for the compressible Euler equations, (Glowinski, R.; Lions, J. L., Computing Methods in Applied Sciences and Engineerings VII (1986), North-Holland: North-Holland Amsterdam) · Zbl 0678.76069
[11] Hughes, T. J.R.; Brooks, A., A multidimensional upwind scheme with no crosswind diffusion, (Hughes, T. J.R., Finite Element Methods for Convection Dominated Flows (1979), ASME: ASME New York), 19-35 · Zbl 0423.76067
[12] Jensen, K. F.; Ray, W. H., The bifurcation behavior of tubular reactors, Chem. Engrg. Sci., 37, 2, 199-222 (1982)
[13] Mihail, R.; Iordache, C., Performances of some numerical techniques used for simulation of fixed bed catalystic reactors, Chem. Engrg. Sci., 31, 83-86 (1976)
[14] Pinjala, V., Wrong-way behavior in fixed-bed catalystic reactors: Pseudo-homogeneous dispersion model, (Ph.D. Thesis (1985), Chemical Engineering Department, University of Houston: Chemical Engineering Department, University of Houston Houston, TX)
[15] Tezduyar, T. E.; Hughes, T. J.R., Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations, (Proceedings AIAA 21st Aerospace Sciences Meeting. Proceedings AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125 (1983)), Reno, NV · Zbl 0535.76074
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.