A Fully-coupled Newton-Krylov Solution Method for Parallel Unstructured Finite Element Fluid Flow, Heat and Mass Transfer Simulations

International Journal of Computational Fluid Dynamics

Volumn 12, Issue 3-4, 1999, Pages 199-211

  Shadid, J N ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

FEM; Iterative solvers; Parallel CFD; Unstructured grids

Indexed keywords

EID: 0033267340     PISSN: 10618562     EISSN: None     Source Type: Journal    
DOI: 10.1080/10618569908940825     Document Type: Article

References (23)

1. Hughes, J. R., Franca, L. P. and Balestra, M. (1986). "A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accomodating Equal-order Interpolations", Comp. Meth. App. Mech. and Eng., 59, 85-99.
2. Brooks, A. N. and Hughes, J. R. (1982). "Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations", Comp. Meth. App. Mech. and Eng., 32, 199-259.
3. Tezduyar, T. E. (1992). "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in App. Mech., 28, 1-44.
4. Elman, H. C. and Golub, G. H., "Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems", Technical Report, Numerical Analysis Project, #NA-93-02, June 1993.
5. Haroutunian, V., Engelman, M. S. and Hasbani, I. (1993). "Segregated Finite-Element Algorithms for the Numerical Solution of Large-Scale Incompressible Flow Problems", Int. J. Numer. Meth. Fluids, 17, 323-348.
6. Strigbreger, J., Baruzzi, G. and Habashi, W. (1993). "Some Special Purpose Preconditioners for Conjugate Gradient-like Methods Applied to CFD", Int. J. Numer. Meth. Fluids, 16, 581-596.
7. Vincent, C. and Boyer, R. (1992). "A Preconditioned Conjugate Gradient Uzawa-type Method for the Solution of the Stokes Problem by Mixed Q1-P0 stabilized Finite Elements", Int. J. Numer. Meth. Fluids, 14, 289-298.
8. Wille, S. O. (1994). "A Preconditioned Alternating Inner-Outer Iterative Solution Method for the Mixed Finite Element Formulation of the Navier-Stokes Equations", Int. J. Numer. Meth. Fluids, 18, 1135-1151.
9. Hendrickson, B. and Leland, R. (1993). "A User's Guide to Chaco, Version 1.0." Sandia National Laboratories Technical Report, SAND93-2339, Albuquerque, NM.
10. Shadid, J. N., Hutchinson, S. A., Hennigan, G. L., Moffat, H. K., Devine, K. D. and Salinger, A. G. (1997). "Efficient Parallel Computation of Unstructured Finite Element Reacting Flow Solutions", Parallel Computing 23, 1307-1325.
11. Eisenstat, S. C. and Walker, H. F. (1994). "Globally Convergent Inexact Newton Methods", SIAM J. Optimization, 4, 393-422.
12. Shadid, J. N., Tuminaro, R. S. and Walker, H. F. (1997). "An Inexact Newton Method for Fully-Coupled Solution of the Navier-Stokes Equations with Heat and Mass Transport", J. Comput. Phys., 137, 155-185.
13. McHugh, P. R., Knoll, D. A. and Keyes, D. E., "Application of a Newton-Krylov Schwarz Algorithm to Low Mach Number Compressible Combustion", AIAA J., 36(2), 290-292.
14. Hutchinson, S. A., Shadid, J. N. and Tuminaro, R. S. (1995). "Aztec User's Guide: Version 1.0." Sandia National Laboratories Technical Report, SAND95-1559, Albuquerque, NM.
15. Shadid, J. N. and Tuminaro, R. S., "A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine", SIAM J. Sci. Comput., 15(2), 440-459, March 1994.
16. Shadid, J. N., Moffat, H. K., Hutchinson, S. A., Hennigan, G. L., Devine, K. D. and Salinger, A. G. (1996). "MPSalsa: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theory Document". Sandia National Laboratories Technical Report, SAND95-2752, Albuquerque, NM.
17. de Vahl Davis, G. and Jones, C. P. (1983). "Natural Convection in a Square Cavity: a Comparison Exercise", Int. J. Numer. Meth. Fluids, 3.
18. Ghia, U., Ghia, K. N. and Shin, C. T. (1982). "High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method", J. Comput. Phys., 48, 387-411.
19. Schreiber, R. and Keller, H. B. (1983). "Driven Cavity Flows by Efficient Numerical Techniques", J. Comput. Phys., 49, 310-333.
20. Gartling, D. K. (1990). "Test Problem for Outflow Boundary Conditions-Flow over a Backward Facing Step", Int. J. Numer. Meth. Fluids, 11, 953-967.
21. Saad, Y. (1989). "Krylov Subspace Methods on Supercomputers", SIAM J. Sci. Stat. Comput., 10(6), 1200-1232.
22. Tuminaro, R. S., Shadid, J. N. and Hutchinson, S. A. (1998). "Parallel Sparse Matrix-Vector Multiply Software for Martrices with Data Locality", Technical Report, Sandia National Labs, SAND95-1540J, To appear in Concurrency: Practice and Experience. (1998).
23. Tuminaro, R. S., Walker, H. F. and Shadid, J. N., "On backtracking failure in Newton-GMRES methods", submitted to SIAM J on Optimization (3/1998).