A quasi-two-dimensional benchmark problem for low mach number compressible codes

Journal of Computational Physics

Volumn 146, Issue 2, 1998, Pages 691-706

  Tomboulides, Ananias G ^a   Orszag, Steven A ^b  

^a BOSTON UNIVERSITY   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

Backward differentiation; Combustion; Compressible reactive flows; Splitting errors; Time stepping

Indexed keywords

AERODYNAMICS; BENCHMARKING; ERRORS; MACH NUMBER;

ASYMPTOTIC ESTIMATES; BACKWARD DIFFERENTIATION; BENCHMARK PROBLEMS; COMPRESSIBLE REACTIVE FLOW; LOW MACH NUMBERS; REACTIVE FLOW; SPLITTING ERRORS; TIME-STEPPING; TWO DIMENSIONAL MODEL; TWO-DIMENSIONAL;

NUMERICAL METHODS;

EID: 0032209661     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6079     Document Type: Article

References (22)

1. 1. B. T. Chu and L. S. G. Kovasznay, Non-linear interactions in a viscous heat-conducting compressible gas, J. Fluid Mech. 3, 494 (1958).
2. 2. G. J. Sivashinsky, Hydrodynamics theory of flame propagation in an enclosed volume, Acta Astronaut. 6, 631 (1979).
3. 3. G. R. Rehm and H. R. Baum, The equations of motion for thermally driven flows, J. Res. Natl. Bur. Standards 83(3), 297 (1978).
4. 4. E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow (Elsevier Science, New York, 1987).
5. 5. M. Smooke, R. Mitchell, and D. Keyes, Numerical solution of two-dimensional axisymmetric laminar diffusion flames, Combust. Sci. Technol. 67, 85 (1989).
6. 6. T. Poinsot, S. Candel, and A. Trouvé, Applications of direct numerical simulation to premixed turbulent combustion, Prog. Energy Combust. Sci. 21, 531 (1996).
7. 7. P. A. McMurtry, W. H. Jou, J. J. Riley, and R. W. Metcalfe, Direct numerical simulations of a reacting mixing layer with chemical heat release, AIAA J. 24(6), 962 (1986).
8. 8. R. I. Issa, B. Ahmadi-Befrui, K. R. Beshay, and A. D. Gosman, Solution of the implicitly discretised reacting flow equations by operator-splitting, J. Comput. Phys. 93(2), 388 (1991).
9. 9. J. Hilditch and P. Colella, A projection method for low Mach number fast chemistry reacting flow, in AIAA Aerospace Sciences Meeting, Jan. 6-10, Reno, NV., 1997.
10. 10. S. Lele, Compact finite difference schemes with spectral like resolution, J. Comput. Phys. 103, 16 (1992).
11. 11. T. Poinsot and S. Lele, Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys. 101, 104 (1992).
12. 12. N. Yanenko, The Method of Fractional Steps (Springer-Verlag, Berlin, New York, 1971).
13. 13. S. A. Orszag, M. Israeli, and M. O. Deville, Boundary conditions for incompressible flows, J. Sci. Comput. 1, 75 (1986).
14. 14. A. G. Tomboulides, J. Lee, and S. A. Orszag, Numerical simulation of low mach number reactive flows, J. Sci. Comput. 12, 139 (1997).
15. 15. J. Lee, A. G. Tomboulides, S. A. Orszag, R. Yetter, and F. Dryer, A transient two-dimensional chemically reactive flow model: Fuel particle combustion in a non-quiescent environment, in Twenty-sixth Symposium(International) on Combustion/The Combustion Institute, 1996.
16. 16. J. Lee, Simulations of Two-Dimensional Chemically Reactive Flows, Ph.D. thesis, Princeton University, 1996.
17. 17. M. Israeli and A. Sidi, personal communication, Arnoldi-type eigensolvers provided.
18. 18. G. E. Karniadakis, M. Israeli, and S. A. Orszag, High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys. 97, 414 (1991).
19. 19. D. Gottlieb, and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (SIAM, Philadelphia, 1977).
20. 20. C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, New York/Berlin, 1987).
21. 21. A. T. Patera, A spectral element method for fluid dynamics; Laminar flow in a channel expansion, J. Comput. Phys. 54, 468 (1984).
22. 22. Y. Maday and A. T. Patera, Spectral element methods for the Navier-Stokes equations, in ASME, State-of-the-Art Surveys in Computational Mechanics, 1987.