Development of direct multifrontal solvers for combustion problems

Numerical Heat Transfer, Part B: Fundamentals

Volumn 53, Issue 3, 2008, Pages 189-205

  Raju, Mandhapati P ^a   T'ien, James S ^a  

^a Case Western Reserve University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARKING; COMPUTATIONAL METHODS; LINEAR SYSTEMS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING;

COMBUSTION PROBLEMS; MULTIFRONTAL SOLVERS;

COMBUSTION;

EID: 38349106532     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790701790168     Document Type: Article

References (21)

1. Pascau, C. Perez, and F. J. Seron, A Comparison of Segregated and Coupling Methods for the Solution of the Incompressible Navier-Stokes Equation, Commun. Numer. Meth. Eng., vol. 12, pp. 617-630, 1996.
2. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.
3. P. R. Mchugh and D. A. Knoll, A Fully Implicit Direct Newton Method for the SteadyState Navier-Stokes Equations, Int. J. Numer. Meth. Fluids, vol. 17, pp. 449-461, 1993.
4. P. R. Mchugh and D. A. Knoll, Fully Coupled Finite-Volume Solutions of the Incompressible Navier-Stokes and Energy Equations Using an Inexact Newton Method, Int. J. Numer. Meth. Fluids, vol. 19, pp. 439-455, 1994.
5. D. W. Peaceman and H. H. Rachford, The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Ind. Appl. Math., vol. 3, p. 28, 1955.
6. H. L. Stone, Iterative Solution of Implicit Approximations of Multi-Dimensional Partial Differential Equations, SIAM J. Numer Anal., vol. 5, p. 530, 1968.
7. T. A. Davis, Algorithm 832: UMFPACK V4.3-An Unsymmetric-Pattern Multifrontal Method, ACM Trans. Math. Software, vol. 30, pp. 196-199, 2004.
8. T. A. Davis, A Column Pre-ordering Strategy for the Unsymmetric-Pattern Multifrontal Method, ACM Trans. Math. Software, vol. 30, pp. 165-195, 2004.
9. T. A. Davis and I. S. Duff, A Combined Unifrontal/Multifrontal Method for Unsymmetric Sparse Matrices, ACM Trans. Math. Software, vol. 25, pp. 1-19, 1999.
10. T. A. Davis and I. S. Duff, An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization, SIAM J. Matrix Anal. Appl., vol. 18, pp. 140-158, 1997.
11. Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Non-symmetric Linear Systems, SIAM J. Sci. Stat. Comput., vol. 7, pp. 856-869, 1986.
12. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, 2003.
13. Brandt, Multi-level Adaptive Solutions to Boundary Value Problems, Math. Comput., vol. 31, pp. 333-390, 1977.
14. S. P. Vanka, Block-Implicit Calculation of Steady Turbulent Recirculating Fluid Flows, Int. J. Heat Mass Transfer, vol. 28, pp. 2093-2103, 1985.
15. S. P. Vanka, A Calculation Procedure for Three-Dimensional Steady Recirculating Flows Using Multigrid Methods, Comput Meth. Appl. Mech. Eng., vol. 55, pp. 321-338, 1986.
16. P. K. Gupta and K. V. Pagalthivarthi, Application of Multifrontal and GMRES Solvers for Multisize Particulate Flow in Rotating Channels, Prog. Comput Fluid Dynam., vol. 7, pp. 323-336, 2007.
17. M. P. Raju and J. T'ien, Two phase Flow inside an Externally Heated Axisymmetric Porous Wick, J. Porous Media, in press.
18. Alsairafi, S. T. Lee, and J. S. T'ien, Modeling Gravity Effect on Diffusion Flames Stabilized around a Cylindrical Wick Saturated with Liquid Fuel, Combustion Sci. Technol., vol. 176, pp. 2165-2191, 2004.
19. Alsairafi, A Computational Study on the Gravity Effect on Wick-Stabilized Diffusion Flames, Ph.D. thesis, Case Western Reserve University, Cleveland, OH, 2003.
20. M. P. Raju and J. T'ien, Modeling of Candle Burning with a Self Trimmed Wick, Combustion Theory Model., in press.
21. D. L. Deitrich, H. D. Ross, Y. Shu, P. Chang, and J. S. T'ien, Candle Flames in Non-buoyant Atmospheres, Combustion Sci. Technol., vol. 156, pp. 1-24, 2000.