A finite volume scheme for two-dimensional chemically reactive hypersonic flow

International Journal of Numerical Methods for Heat and Fluid Flow

Volumn 8, Issue 8, 1998, Pages 888-933

  Bertolazzi, Enrico ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL REACTIONS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; CONSTRAINT THEORY; ENERGY CONSERVATION; FINITE VOLUME METHOD; LINEAR SYSTEMS; MATRIX ALGEBRA; PHASE EQUILIBRIA; PROBLEM SOLVING; THERMAL EFFECTS; VECTORS; VELOCITY; ALGORITHMS; EFFICIENCY; SHOCK WAVES;

DIATOMIC SPECIES; MASS DENSITY; TRANSLATIONAL TEMPERATURES; VIBRATIONAL ENERGIES;

HYPERSONIC FLOW;

FINITE VOLUME TECHNIQUE; FLUID FLOW; HEAT TRANSFER; HYPERSONIC FLOW; MATHEMATICAL ANALYSIS;

EID: 0032309071     PISSN: 09615539     EISSN: None     Source Type: Journal    
DOI: 10.1108/09615539810241114     Document Type: Article

References (71)

1. Abgrall, R., Fezoui, L. and Talandier, J. (1992), "An extension of Osher's Riemann solver for chemical and vibrational non-equilibrium gas flows", International Journal of Numerical Methods in Fluids, Vol. 14, pp. 935-60.
2. Anderson, J. Jr (1990a), Hypersonic and High Temperature Gas Dynamics, McGraw-Hill, New York, NY.
3. Anderson, J. Jr (1990b), Modern Compressible Flow, McGraw-Hill, New York, NY.
4. Argyris, J., Doltsinis, I.S., Friz, H. and Urban, J. (1991), "An exploration of chemically reacting viscous hypersonic flow", Computer Methods in Applied Mechanics and Engineering, Vol. 89, pp. 85-128.
5. Ben-Dor, G. and Glass, I.I. (1979), "Domains and boundary on non-stationary oblique shock-wave reflexions. 1. Diatomic gas", Journal of Fluid Mechanics, Vol. 92, pp. 459-96.
6. Ben-Dor, G. and Glass, I.I. (1980), "Domains and boundary on non-stationary oblique shock-wave reflexions. 2. Monatomic gas", Journal of Fluid Mechanics, Vol. 96, pp. 735-56.
7. Bertolazzi, E. (1995), Risoluzione Numerica di Flussi Ipersonici Chimicamente Reattivi, PhD thesis, Trento University, Italy.
8. Bertolazzi, E. (1996), "Positive and conservative schemes for mass action kinetics", Computers and Mathematics with Applications, Vol. 32, pp. 29-43.
9. Bertolazzi, E. and Casulli, V. (1993), "Fast, positive and conservative scheme for chemically reactive hypersonic flow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 3, pp. 379-98.
10. Boris, J.P. and Book, D.L. (1973), "Flux-corrected transport", Journal of Computational Physics, Vol. 11, pp. 38-69.
11. Candler, G. (1988), "The computation of weakly ionized hypersonic flows in thermo-chemical nonequilibrium", PhD thesis, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA.
12. Chiang, T.L. and Hoffmann, K.A., "Determination of computational timestep for chemically reacting flows", AIAA-89-1855.
13. Cinnella, P. and Grossman, B., "Flux-split algorithms for flows with multiple translational temperature", ICAM Report 90-06-01, Virginia Polytechnic Institute and State University, Petersburg, VA.
14. Colella, P. (1984), "The piecewise parabolic method (PPM) for gas-dynamical simulation", Journal of Computational Physics, Vol. 54, pp. 174-201.
15. Colella, P. and Glaz, H.M. (1985), "Efficient solution algorithms for the riemann problem for real gases", Journal of Computational Physics, Vol. 59, pp. 264-89.
16. Collatz, L. (1960), The Numerical Treatment of Differential Equations, Springer, Berlin.
17. Deschambault, R.L. and Glass, I.I. (1983), "An update on non-stationary oblique shock-wave reflections: actual isopicnics and numerical experiments", Journal of Fluid Mechanics, Vol. 131, pp. 27-57.
18. Dunn, M.G. and Kang, S.W. (1973), "Theoretical and experimental studies of reentry plasmas", NASA CR2232.
19. Edwards, J.R. and McRae, D.S. (1993), "Nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equation", AIAA Journal, Vol. 31.
20. Glaz, H.M., Colella, P., Glass, I.I. and Deschambault, R.L. (1985), "A numerical study of oblique shock-wave reflections with experimental comparisons", Proc of the Royal Society of London, Vol. 398, pp. 117-40.
21. Grossman, B. and Cinnella, P. (1988), "The computation of non-equilibrium, chemically-reacting flows", Computers and Structures, Vol. 30, Pergamon Press, Oxford, pp. 79-93.
22. Groth, C.P.T. and Gottlieb, J.J. (1993), "VD finite-difference methods for computing high-speed thermal and chemical non-equilibrium flows with strong shocks", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 3, pp. 483-516.
23. Groth, C.P.T., Gottlieb, J.J. and Sullivan, P.A. (1991), "Numerical investigation of high-temperature effects in the UTIAS-RPI hypersonic impulse tunnel", Canadian Journal of Physics, Vol. 69, pp. 897-918.
24. Harten, A. (1977), "The artificial compression method for computation of shocks and contact discontinuities, I single conservation laws", Communications on Pure and Applied Mathematics, Vol. XXX, pp. 611-38.
25. Harten, A. (1983), "High resolution schemes for hyperbolic conservation laws", Journal of Computational Physics, Vol. 49, pp. 357-93.
26. Harten, A. (1984), "On a class of high resolution total-variation-stable finite-difference schemes", SIAM Journal of Numerical Analysis, Vol. 21, pp. 1-23.
27. Harten, A. (1987), "Uniformly high order accurate essentially non-oscillatory schemes, III", Journal of Computational Physics, Vol. 71, pp. 231-303.
28. Harten, A., Hyman, J.M. and Lax, P.D. (1976), "On finite-difference approximation and entropy conditions for shocks", Communications on Pure and Applied Mathematics, Vol. XXIX, pp. 297-322.
29. Häuser, J., Vinckier, A., Zemsch, S. and Paap, H.G. (1989), "Supercomputing in hypersonic flow with non-equilibrium effects", Supercomputing in Fluid Flow, Lowell, MA, pp. 3-5.
30. Hirsch, C. (1991), Numerical Computations Of Internal And External Flows, Wiley & Sons, New York, NY.
31. Hornung, H.G. (1972), "Non-equilibrium dissociating nitrogen flow over spheres and circular cylinders", Journal of Fluid Mechanics, Vol. 53, pp. 149-76.
32. Hornung, H.G. (1976),"Non-equilibrium ideal-gas dissociation after a curved shock wave",Journal of Fluid Mechanics, Vol. 74, pp. 143-59.
33. Jameson, A. (1995), "Positive schemes and shock modelling for compressible flows", International Journal of Numerical Methods in Fluids, Vol. 20, pp. 743-76.
34. Jorgenson, P. and Turkel, E. (1993), "Central difference TVD schemes for time dependent and steady state problems", Journal of Computational Physics, pp. 297-308.
35. Larrouturou, B. (1954), "How to preserve mass fraction positivity when computing compressible multi-component flows", Journal of Computational Physics, Vol. 95, pp. 59-84.
36. Lax, P.D. (1954), "Wak solutions of nonlinear hyperbolic equations and their numerical computations", CPAM, Vol. 7, pp. 159-93.
37. Lee, J.-H. (1984), "Basic governing equation for the flight regimes of aeroassisted orbital transfer vehicles", AIAA-84-1729, Snowmass, CO, June, pp. 25-8.
38. LeVeque, R.J. (1990), Numerical Methods for Conservation Laws, Birkhäuser Verlag, Berlin.
39. Majda, A. and Osher, S. (1979), "Numerical viscosity and the entropy condition", Communications on Pure and Applied Mathematics, Vol. XXXII, pp. 797-838.
40. Millikan, R.C. and White, D.R. (1963), "Systematics of vibrational relaxation", The Journal of Chemical Physics, Vol. 39, pp. 3209-12.
41. Ortega, J. M. (1988), "Efficient implementation of certain iterative methods", SIAM Journal on Scientific and Statistical Computing, Vol. 9.
42. Osher, S. (1984), "Riemann solvers, the entropy condition, and difference approximations", SIAM Journal on Scientific and Statistical Computing, Vol. 21, pp. 217-35.
43. Osher, S. and Chakravarthy, S. (1984), "High resolution schemes and the entropy conditions", SIAM Journal on Scientific and Statistical Computing, Vol. 21, pp. 955-84.
44. Park, C. (1984), "Problems of rate chemistry in the flight regimes of aeroassisted orbital transfer vehicles", AIAA-84-1730, AIAA, Snowmass, CO, 25-28 June.
45. Park, C. (1985), "On convergence of computation of chemically reacting flows" AIAA-85-0247.
46. Park, C. (1990), Nonequilibrium Hypersonic Aerothermodynamics, John Wiley & Son, New York, NY.
47. Rider, W.J. (1993), "Methods for extending high-resolution schemes to non-linear system of hyperbolic conservation laws", International Journal of Numerical Methods in Fluids, Vol. 17, pp. 861-85.
48. Roe, P.L. (1981), "Approximate Riemann solvers, parameter vectors, and difference schemes", Journal of Computational Physics, Vol. 43, pp. 357-72.
49. Rose, M.E. (1983), "Compact finite difference schemes for the Euler and Navier-Stokes equations", Journal of Computational Physics, Vol. 49, pp. 420-42.
50. Saltzman, J. (1994), "An unsplit 3D upwind methods for hyperbolic conservation laws", Journal of Computational Physics, Vol. 115, pp. 153-68.
51. Schröder, W. and Hartman, G. (1992), "Implicit solution of three-dimensional viscous hypersonic flows", Computers and Fluids, Vol. 21, pp. 109-32.
52. Shu, C.-W. (1987), "TVB uniformly high-order schemes for conservation laws", Mathematics of Computation, Vol. 49, pp. 105-21.
53. Shuen, S. and Yoon, S. (1989), "Numerical study of chemically reacting flows using lower-upper symmetric successive overrelaxation scheme", AAIA Journal, Vol. 27.
54. Shuen, J.S., Liou, M.S. and Van Leer, B. (1990), "Inviscid flux-splitting algorithms for real gases with non-equilibrium chemistry", Journal of Computational Physics, Vol. 90, pp. 371-95.
55. Sod, G.A. (1978), "A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws", Journal of Computational Physics, Vol. 27, pp. 1-31.
56. Steger, J.L. and Warming, R.F. (1981), "Flux vector splitting of the inviscid gas dynamic equations with application to finite-difference methods", Journal of Computational Physics, Vol. 40, pp. 263-93.
57. Swanson, R.C. and Turkel, E. (1992), "On central-difference and upwind schemes", Journal of Computational Physics, Vol. 101, pp. 292-306.
58. Sweby, P.K. (1984), "High resolution schemes using flux limiters for hyperbolic conservation laws", SIAM Journal of Numerical Analysis, Vol. 21, pp. 995-1011.
59. Tadmor, E. (1984), "Numerical viscosity and the entropy condition for conservative difference schemes", Mathematics of Computation, Vol. 41, pp. 369-81.
60. Tadmor, E. (1987), "The numerical viscosity of entropy stable schemes for systems of conservation laws. I", Mathematics of Computation, Vol. 49, pp. 91-103.
61. Toon, S. and Kwak, D. (1992), "Implicit Navier-Stokes solver for three-dimensional compressible flows", AIAA Journal, Vol. 30.
62. Van Leer, B. (1979), "Toward the ultimate conservative difference scheme", Journal of Computational Physics, Vol. 32, pp. 101-36.
63. Vincenti, W.G. and Kruger, C.H. Jr (1967), Introduction to Physical Gas Dynamics, Krieger Publishing Company, Malabar, FL.
64. Vinckier, A. (1990), "Qoneq, A first step towards 2d nonequilibrium flow", Institut für Luftfahrttechnik und Leichtbau, Universiät der Bundeswehr, München.
65. Vol'pert, A.I. and Hudjaev, S.I. (1985), Analysis In Classes of Discontinuous Functions and Equations of Mathematical Physics, Martinus Nijoff Publishers, Dordrecht.
66. Walpot, L. (1991), "Quasi one dimensional inviscid nozzle flow in vibrational and chemical non-equilibrium", T.U.DELFT Department of Aerospace Engineering High Speed Aerodynamics Kluyverweg 2 2629, WL Delft, The Netherlands.
67. Williams, F.A. (1985), Combustion Theory 2nd Ed., Benjamin/Cummings Pub., Menlo Park, CA.
68. Witte, D.W., Tatum, K.E. and Willias, S.B. (1996), "Computation of thermally perfect compressible flow properties", AIAA-96-0681, December.
69. Wüthrich, S. and Sawley, M.L. (1992), "Coupled Euler/boundary-layer methods for non-equilibrium, chemically reacting hypersonic flows", AIAA Journal, Vol. 30, December, pp. 2836-44.
70. Yu, S.T., McBridge, B.J., Hsiesh, K.C. and Shuen, J.S. (1988), "Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry", AIAA-88-0273.
71. Zeidler, E. (1986), Nonlinear Functional Analysis and its Applications I, Springer-Verlag, New York, NY.