×

Numerical solution of a free boundary problem in hypersonic flow theory: Nonequilibrium viscous shock layers. (English) Zbl 0778.76060

Numerical method for the viscous shock layer problem of hypersonic flow is considered. Because the position of the shock is not known, one has to solve a free-boundary problem. By introducing a reduced coordinate, the problem is transformed into a nonlinear eigenvalue problem. The new problem for an augmented set of variables is then solved with Newton iterations and adaptive gridding. New boundary conditions are also derived at the shock.
The proposed method which yields simultaneously the flow variables and the shock position has the advantage of coupling all the components of the dependent solution.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76K05 Hypersonic flows
76L05 Shock waves and blast waves in fluid mechanics
76V05 Reaction effects in flows

Software:

CHEMKIN; TRANSPORT
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Blottner, F. G., AIAA J., 7, 2281 (1969)
[2] Bush, W. B., J. Fluid Mech., 20, 353 (1964)
[3] Davis, R. T.; Flügge-Lotz, I., J. Fluid Mech., 20, 593 (1964)
[4] Davis, R. T., AIAA J., 8, 843 (1970)
[5] Davis, R. T., AIAA Paper 70-805 (1970), (unpublished)
[6] Murray, A. L.; Lewis, C. H., AIAA J., 16, 1279 ( (1978)
[7] Song, D. J.; Swaminathan, S.; Lewis, C. H., J. Spacecr. Rockets, 22, 614 (1985)
[8] Scott, C. D., Catalytic Recombination of Nitrogen and Oxygen on High Temperature Reusable Surface Insulation, (Crosbie, A. L., Aerothermodynamics and Planetary Entry. Aerothermodynamics and Planetary Entry, Progress in Astronautics and Aeronautics, Vol. 77 (1981), Am. Inst. Aeronaut. Astronaut: Am. Inst. Aeronaut. Astronaut New York)
[9] Anderson, D. A.; Tannehill, J. C.; Pletcher, R. H., Computational Fluid Mechanics and Heat Transfer (1984), Hemisphere: Hemisphere New York · Zbl 0569.76001
[10] Waskiewicz, J. D.; Murray, A. L.; Lewis, C. H., AIAA J., 16, 189 (1978)
[11] Allgower, E. L.; Böhmer, K.; Potra, F. A.; Rheinboldt, W. C., SIAM J. Numer. Anal., 23, 160 (1986)
[12] Deuflhard, P., Numer. Math., 22, 289 (1974)
[13] Giovangigli, V.; Smooke, M. D., Comb. Sci. Tech., 53, 23 (1987)
[14] Smooke, M. D., J. Comput. Phys., 48, 72 (1982)
[15] Russell, R. D.; Christiansen, J., SIAM J. Numer. Anal., 15, 59 (1978)
[16] Bortner, M. H., (AMRC Proc., 14 (1966)), Part 1
[17] Baulknight, C. W., (Proceedings, 2nd conference on Kinetics, Equilibria and Performance of High-Temperature Systems (1962), The Combustion Institute: The Combustion Institute Los Angeles, CA), (unpublished)
[18] Kee, R. J.; Miller, J. A.; Jefferson, T. H., CHEMKIN: A GeneralPurpose, Problem-Independent, Transportable, Fortran Chemical Kinetics Code Package, (SAND80-8003 (1983), SANDIA National Laboratories)
[19] Kee, R. J.; Warnatz, J.; Miller, J. A., A Fortran Computer Code Package for the Evaluation of Gas-Phase Viscosities, Conductivities, and Diffusion Coefficients, (SAND83-8209 (1983), SANDIA National Laboratories)
[20] Giovangigli, V., Impact of Computing in Science and Engineering, 3, 244 (1991)
[21] V. Giovangigli, “Mathematical Analysis of Viscous Shock Layer Equations,” submitted for publication.; V. Giovangigli, “Mathematical Analysis of Viscous Shock Layer Equations,” submitted for publication.
[22] Meyer, G. H., Numerical Methods for Free Boundary Value Problems: 1981 Survey, (Fasano, A.; Primicerio, M., Free Boundary Problems, Theory and Applications, Vol. II. Free Boundary Problems, Theory and Applications, Vol. II, Research Notes in Mathematics, Vol. 79 (1983), Pitman Advanced Publishing Program: Pitman Advanced Publishing Program Boston) · Zbl 0513.65076
[23] Korman, P., SIAM J. Math. Anal., 19, 814 (1988)
[24] Meyer, G. H., SIAM J. Numer. Anal., 18, 150 (1981)
[25] Giovangigli, V.; Smooke, M. D., Appl. Numer. Math., 5, 305 (1989)
[26] Giovangigli, V.; Darabiha, N., Vector Computers and Complex Chemistry Combustion, (Brauner, C.; Schmidt-Laine, C., Mathematical Modeling in Combustion and Related Topics. Mathematical Modeling in Combustion and Related Topics, NATO ASI Series, Vol. 140 (1988), Nijhoff: Nijhoff The Hague)
[27] Smooke, M. D., J. Opt. Theory Appl., 39, 489 (1983)
[28] Laboudigue, B., (Thesis No. 1990-30, Laboratoire E.M2.C., UPR 288 du CNRS (1990), Ecole Centrale Paris: Ecole Centrale Paris Chatenay-Malabry, France)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.