Large-scale stabilized FE computational analysis of nonlinear steady-state transport/reaction systems

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 13-16, 2006, Pages 1846-1871

  Shadid, J N ^a   Salinger, A G ^a   Pawlowski, R P ^a   Lin, P T ^a   Hennigan, G L ^a   Tuminaro, R S ^a   Lehoucq, R B ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Bifurcation; Continuation; Domain decomposition; Multilevel; Newton Krylov; Parallel; Stability analysis; Stabilized finite elements; Steady state; Transport reaction

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); CHEMICAL REACTIONS; FINITE ELEMENT METHOD; HEAT TRANSFER; MASS TRANSFER; NAVIER STOKES EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY;

DOMAIN DECOMPOSITION; NEWTON-KRYLOV TECHNIQUES; STABILITY ANALYSIS; STABILIZED FINITE ELEMENTS;

COMPUTATIONAL FLUID DYNAMICS;

ALGORITHMS; BIFURCATION (MATHEMATICS); CHEMICAL REACTIONS; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; HEAT TRANSFER; MASS TRANSFER; NAVIER STOKES EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY;

EID: 30944432365     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.047     Document Type: Article

References (75)

1. T. Barth P. Bochev M. Gunzburger J. Shadid A taxonomy of consistently stabilized finite element methods for the Stokes problem SIAM J. Sci. Comput. 25 5 2004 1585-1607
2. M. Benzi Preconditioning techniques for large linear systems: A survey J. Comput. Phys. 182 2002 418-477
3. A.S. Bodke D.A. Olschki L.D. Schmidt E. Ranzi High selectivities to ethylene by partial oxidation of ethane Science 258 1999 712-715
4. F. Brezzi On existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers RAIRO Model. Math. Anal. Numer. 21 1974 129-151
5. A.N. Brooks T.J.R. Hughes Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 32 1982 199-259
6. P.N. Brown Y. Saad Convergence theory of nonlinear Newton-Krylov algorithms SIAM J. Optim. 4 1994 297-330
7. E. Burman A. Ern Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation Comput. Methods Appl. Mech. Engrg. 191 2002 3833-3855
8. E.A. Burroughs R.B. Lehoucq L.A. Romero A.G. Salinger Linear stability of flow in a differentially heated cavity via large-scale eigenvalue calculations Int. J. Numer. Methods Heat Fluid Flow 14 6 2004 803-822
9. X.-C. Cai, An additive Schwarz algorithm for nonselfadjoint elliptic equations, T.F. Chan, G. Roland, P. Jacques, O.B. Widlund, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, 1989, pp. 232-244.
10. X.-C. Cai W.D. Gropp D.E. Keyes Convergence rate estimate for a domain decomposition method Numer. Math. 61 2 1992 153-169
11. S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability 1961 Oxford University Press
12. K.A. Cliffe A. Spence S.J. Tavener The numerical analysis of bifurcation problems with application to fluid mechanics Acta Numer. 2000 39-131
13. R. Codina Comparison of some finite element methods for solving the diffusion-convection-reaction equations Comput. Methods Appl. Mech. Engrg. 156 1998 185-210
14. M.O. Conaire H.J. Curran J.M. Simmie W.J. Pitz C.K. Westbrook A comprehensive modeling study of hydrogen oxidation Int. J. Chem. Kinet. 36 11 2004 603-622
15. G.D. Davis I.P. Jones Natural convection in a square cavity: A comparison exercise Int. J. Numer. Methods Fluids 3 3 1983 227-248
16. J.W. Demmel, J.R. Gilbert, X.S. Li, Superlu users' guide, Technical Report LBNL-44289, Lawrence Berkeley National Laboratory, September 1999.
17. V.A. Denshchikov V.N. Kontratev A.N. Romashev Interaction between two opposed jets Fluid Dyn. 6 1978 924-926
18. V.A. Denshchikov V.N. Kontratev A.N. Romashev V.M. Chubarov Auto-oscillations of planar colliding jets Fluid Dyn. 3 1983 460-462
19. S.C. Eisenstat H.F. Walker Globally convergent inexact Newton methods SIAM J. Optim. 4 1994 393-422
20. A. Ern J.L. Guermond Theory and Practice of Finite Elements 2004 Springer-Verlag New York
21. C. Farhat N. Maman G.W. Brown Mesh partitioning for implicit computations via iterative domain decomposition - impact and optimization of the subdomain aspect ratio Int. J. Numer. Methods Engrg. 38 6 1995 989-1000
22. W.D. Gropp D.K. Kaushik D.E. Keyes B.F. Smith High-performance parallel implicit cfd Parallel Comput. 27 2001 337-362
23. J. Guckenheimer P. Holmes Nonlinear Oscillations, Dynamical Systems, Bifurcations of Vector Fields 1983 Springer-Verlag
24. M. Gunzburger Finite Element Methods for Viscous Incompressible Flows 1989 Academic Press Boston
25. B. Hendrickson, R. Leland, An improved spectral graph partitioning algorithm for mapping parallel computations, Technical Report SAND 92-1460, Sandia National Laboratories, Albuquerque, NM, 1992.
26. B.A. Hendrickson Load balancing fictions, falsehoods and fallacies Appl. Math. Model. 25 2 2000 99-108
27. B.A. Hendrickson T.G. Kolda Graph partitioning models for parallel computing Parallel Comput. 26 12 2000 1519-1534
28. M. Huff L.D. Schmidt Ethylene formation by oxidative dehydrogenation of ethane over monoliths at very short contact times J. Phys. Chem. 97 1993 11815
29. M. Huff L.D. Schmidt Elementary step model of ethane oxidative dehydrogenation on pt-coated monoliths AIChE J. 42 12 1996 3484-3497
30. T.J.R. Hughes L.P. Franca G.M. Hulbert A new finite element formulation for computational fluid dynamics: VII. the Galerkin/Least-Squares method for advective-diffusive equations Comput. Methods Appl. Mech. Engrg. 73 1989 173-189
31. T.J.R. Hughes T.E. Tezduyar Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations Comput. Methods Appl. Mech. Engrg. 45 1984 217-284
32. T.J.R. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Engrg. 127 1995 387-401
33. T.J.R. Hughes, A. Brooks, A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline-upwind procedure, in: R.H. Gallagher et al., (Ed.), Finite Elements in Fluids, vol. 4, J. Willey & Sons, 1982, pp. 47-65.
34. T.J.R. Hughes A.N. Brooks A multidimensional upwind scheme with no cross-wind diffusion T.J.R. Hughes Finite Element Methods for Convection Dominated Flows, AMD vol. 34 1979 ASME New York 19-35
35. T.J.R. Hughes L. Franca A new finite element formulation for computational fluid dynamics: VII, The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity pressure spaces Comput. Methods Appl. Mech. Engrg. 65 1987 85-96
36. T.J.R. Hughes L. Franca M. Balestra A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations Comput. Methods Appl. Mech. Engrg. 59 1986 85-99
37. T.J.R. Hughes M. Mallet A new finite element formulation for computational fluid dynamics: III, The generalized streamline operator for multidimensional advective-diffusive systems Comput. Methods Appl. Mech. Engrg. 58 1986 305-328
38. T.J.R. Hughes M. Mallet A. Mizukami A new finite element formulation for computational fluid dynamics: II. Beyond SUPG Comput. Methods Appl. Mech. Engrg. 54 1986 341-355
39. S.A. Hutchinson, L. Prevost, J.N. Shadid, C. Tong, R.S. Tuminaro, Aztec user's guide version 2.0, Technical Report SAND 99-8801J, Sandia National Laboratories, 1999.
40. R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics, Technical Report SAND 89-8009, Sandia National Laboratories, 1989.
41. H.B. Keller Numerical solution of bifurcation and nonlinear eigenvalue problems P.H. Rabinowitz Application of Bifurcation Theory 1977 Dekker New York 45-52
42. D.A. Knoll D.E. Keyes Jacobian-free Newton-Krylov methods: A survey of approaches and applications J. Comput. Phys. 193 2 2004 357-397
43. S. Kommu G.M. Wilson B. Khomami A theoretical/experimental study of silicon epitaxy in horizontal single-wafer chemical vapor deposition reactors J. Elec. Chem. Soc. 147 4 2000 1538-1550
44. M. Kubicek M. Marek Computational Methods in Bifurcation Theory and Dissipative Structures, Computational Physics 1983 Springer-Verlag New York, NY
45. R.B. Lehoucq K. Meergbergen Using generalized Cayley transformations within an inexact rational Krylov sequence method SIAM J. Matrix Anal. Appl. 20 1 1998 131-148
46. R.B. Lehoucq A.G. Salinger Massively parallel linear stability analysis with P_ARPACK for 3D fluid flow modeled with MPSalsa Lecture Notes Comput. Sci. 1541 1998 286-295
47. R.B. Lehoucq D.C. Sorensen C. Yang ARPACK USERS GUIDE: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods 1998 SIAM Phildelphia, PA
48. R.B. Lehoucq A.G. Salinger Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers Int. J. Numer. Methods Fluids 36 2001 309-327
49. C.C. Lin The Theory of Hydrodynamic Stability 1955 Cambridge Univ. Press
50. K. Meerbergen A. Spence D. Roose Shift-invert and Cayley transforms for the detection of rightmost eigenvalues of nonsymmetric matrices BIT 34 1994 409-423
51. R.P. Pawlowski, A.G. Salinger. Numerical simulation of the partial catalytic oxidation of ethane to ethylene in short contact time reactors, Technical Report Sand 2001-1338, Sandia National Laboratories, Albuquerque NM, 87185, 1996.
52. R.P. Pawlowski, A.G. Salinger, J.N. Shadid, T.J. Mountziaris, Stability analysis of laminar isothermal impinging jet flows, J. Fluid Mech., submitted for publication.
53. R.P. Pawlowski, J.N. Shadid, J.P. Simonis, H.F. Walker, Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations, SIAM Rev., submitted for publication.
54. Y. Saad Krylov subspace methods for solving large unsymmetric linear systems Math. Comput. 37 155 1981 105-126
55. Y. Saad Iterative Methods for Sparse Linear Systems 1996 PWS Publishing Company Boston
56. A.G. Salinger E.A. Burroughs R.P. Pawlowski E.T. Phipps L.A. Romero Bifurcation tracking algorithms and software for large scale applications Int. J. Bifurcat. Chaos 15 3 2005 1015-1032
57. A.G. Salinger R.B. Lehoucq R.P. Pawlowski J.N. Shadid Computational bifurcation and stability studies of the 8:1 thermal cavity problem Int. J. Numer. Methods Fluids 40 2002 1059-1073
58. A.G. Salinger R.P. Pawlowski J.N. Shadid B.G. van Bloemen Waanders Computational analysis and optimization of a chemical vapor deposition reactor with large-scale computing Ind. Engrg. Chem. Res. 43 2004 4612-4623
59. J.N. Shadid, A.G. Salinger, R.C. Schmidt, S.A. Hutchinson, G.L. Hennigan, K.D. Devine, H.K. Moffat, MPSalsa: A finite element computer program for reacting flow problems Part 1: Theoretical development, Technical Report Sand 98-2864, Sandia National Laboratories, Albuquerque NM, 87185, January 1999.
60. J.N. Shadid R.S. Tuminaro H.F. Walker An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport J. Comput. Phys. 137 1997 155-185
61. J.N. Shadid A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations Int. J. CFD 12 1999 199-211
62. J.N. Shadid S.A. Hutchinson G.L. Hennigan H.K. Moffet K.D. Devine A.G. Salinger Efficient parallel computation of unstructured finite element reacting flow solutions Parallel Comput. 23 1997 1307-1325
63. J.N. Shadid R.S. Tuminaro K.D. Devine G.L. Hennigan P.T. Lin Performance of fully-coupled domain decomposition preconditioners for finite element transport/reaction simulations J. Comput. Phys. 205 2005 24-47
64. F. Shakib, Finite element analysis of the compressible Euler and Navier-Stokes equations. Ph.D. thesis, Division of Applied Mathematics, Stanford University, 1989.
65. F. Shakib, Personal Communication, 1997.
66. F. Shakib T.J.R. Hughes Z. Johan A new finite element formulation for computational fluid dynamics: X, the compressible Euler and Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 89 1991 141-219
67. B. Smith P. Bjorstad W. Gropp Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations 1996 Cambridge University Press
68. A. Tamir Impinging stream reactors, fundamentals and applications Transport Processes in Engineering vol. 7 1994 Elsevier Science
69. T.E. Tezduyar Stabilized finite element formulations for incompressible flow calculations Adv. Appl. Mech. 28 1992 1-44
70. T.E. Tezduyar Y.J. Park Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction problems Comput. Methods Appl. Mech. Engrg. 59 1986 307-325
71. R.S. Tuminaro C.H. Tong J.N. Shadid K.D. Devine D.M. Day On a multilevel preconditioning module for unstructured mesh Krylov solvers: Two-level Schwarz Commun. Numer. Method. Engrg. 18 2002 383-389
72. G. Veser L.D. Schmidt Ignition and extinction in the catalytic oxidation of hydrocarbons over platinum AIChE J. 42 4 1996 1077-1087
73. C. Vincent R. Boyer A preconditioned conjugate gradient Uzawa-type method for the solution of the Stokes problem by mixed Q1-P0 stabilized finite elements Int. J. Numer. Methods Fluids 14 1992 289-298
74. S.O. Wille A preconditioned alternating inner-outer solution method for the mixed finite element formulation of the Navier-Stokes equations Int. J. Numer. Methods Fluids 18 1994 1135-1151
75. K.H. Winters, K.A. Cliffe, C.P. Jackson, The prediction of instabilities using bifurcation theory, in: R.W. Lewis, E. Hinton, P. Beltess, B.A. Schrefler (Eds.), Numerical Methods in Transient and Coupled Systems, 1987, pp. 179-198.