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

Tezduyar, T. E.; Park, Y. J.

Comput. Methods Appl. Mech. Eng. 59, 307-325 (1986).

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

Keywords:

streamline-upwind/Petrov-Galerkin procedure; oscillations about sharp internal and boundary layers; convection-dominated and reaction-dominated flows; multi-component transport problems; electrophoresis separation phenomena

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 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, (), 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, (), 371-408
[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, () · Zbl 0678.76069
[11]	Hughes, T.J.R.; Brooks, A., A multidimensional upwind scheme with no crosswind diffusion, (), 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, ()
[15]	Tezduyar, T.E.; Hughes, T.J.R., Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations, (), Reno, NV · Zbl 0535.76074