Viscous fluid flow at all speeds: Analysis and numerical simulation

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 54, Issue 6, 2003, Pages 1010-1049

  Meister, Andreas ^a  

^a UNIVERSITY OF LÜBECK   (Germany)

Author keywords

Asymptotic expansion; Finite volume method; Low Mach number limit

Indexed keywords

EID: 0344824456     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-2025-8     Document Type: Article

References (70)

1. T. J. Barth, D. C. Jesperson, The Design and Application of Upwind Schemes on Unstructured Meshes. AIAA paper, 89-0366, 1989.
2. W. R. Briley, H. McDonald, S. J. Shamroth, A Low Mach Number Euler Formulation and Application to Time-Iterative LSI Schemes. AIAA J. 21 (10) (1983), 1467-1469.
3. D. Choi, C. L. Merkle, The Application of Preconditioning in Viscous Flows. J. Comput. Phys. 105 (1993), 207-223.
4. A. J. Chorin, A Numerical Method for Solving Incompressible Viscous Flow Problems. J. Comput. Phys. 2 (1967), 12-26.
5. (Eds.) A. Dervieux, B. van Leer, J. Periaux, A. Rizzi, Numerical Simulation of Compressible Euler Flows, number 26 in Notes on Numerical Fluid Mechanics, Braunschweig, Vieweg, Wiesbaden, 1989.
6. (Eds.) J.-A. Désidéri, R. Glowinski, J. Périaux, Hypersonic Flows for Reentry Problems, volume II, Antibes, Springer 1990.
7. B. Edney, Anomalous Heat Transfer and Pressure Distributions on Blunt Bodies at Hypersonic Speeds in the Presence of an Impinging Shock. FFA Report 115, Stockholm, 1968.
8. O. Friedrich, A new method for generating inner points of triangulations in two dimensions. Comp. Meth. Appl Mech and Eng. 104 (1993), 77-86.
9. O. Friedrich, Weighted Essential Non-Oscillatory Schemes for the Interpolation of Mean Values on Unstructured Grids. J. Comput. Phys. 144 (1998), 194-212.
10. O. Friedrich, Gewichtete wesentlich nicht-oszillierende Verfahren auf unstrukturierten Gittern. Dissertation, Fachbereich Mathematik, Schwerpunkt Differentialgleichungen und Dynamische Systeme, Universität Hamburg, 1999.
11. O. Friedrich, D. Hempel, A. Meister, Th. Sonar, Adaptive Computation of Unsteady Flow Fields with the DLR- τ -Code, in: 77th AGARD Fluid Dynamics Panel Meeting and Symposium on Progress and Challenges in CFD Methods and Algorithms, AGARD-CP-578, Sevilla, 1995.
12. E. Godlewski, P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, volume 118 of Applied Mathematical Sciences. Springer, New York, Berlin, Heidelberg, 1996.
13. S. K. Godunov, A Finite Difference Method for the Numerical Computation of Discontinuous Solutions of the Equations of Fluid Dynamics. Mat. Sb. 47 (1959), 357-393.
14. H. Guillard, C. Viozat, On the Behaviour of Upwind Schemes in the Low Mach Number Limit. Computers and Fluids 28 (1999), 63-86.
15. D. Hänel, R. Schwane, An implicit flux-vector splitting scheme for the computation of viscous hypersonic flow. AIAA Paper (1989), 89-0274.
16. D. Hänel, R. Schwane, G. Seider, On the accuracy of upwind schemes for the solution of the Navier-Stokes equations. AIAA Paper (1987), 87-1105.
17. V. Hannemann, Numerische Simulation von Stoβ-Stoβ- Wechselwirkungen unter Berücksichtigung von chemischen und thermischen Nichtgleichgewichtseffekten. Dissertation, Universität Göttingen, 1996.
18. V. Hannemann, D. Hempel, Th. Sonar, Dynamic Adaptivity and Residual Control in Unsteady Compressible Flow Computation. Mathematical and Computer Modelling 20 (1994), 201-213.
19. G. Hauke, T. J. R. Hughes, A Comparative Study of Different Sets of Variables for Solving Compressible and Incompressible Flows. Comput. Methods Appl. Mech. Engrg 153 (1998) 1-44.
20. D. Hietel, A. Meister, Th. Sonar, On the comparison of four different implementations of an third-order ENO scheme of box type for the computation of compressible flow. Numerical Algorithms 13 (1996), 77-105.
21. C. Hirsch, Numerical computation of internal and external flows, volume 1. Wiley & Sons, Chicester, New York, 1988.
22. C. Hirsch, Numerical computation of internal and external flows, volume 2. Wiley & Sons, Chicester, New York, 1988.
23. L. Hoffmann, Ein zeitlich selbstadaptives numerisches Verfahren zur Berechnung von Strömungen aller Mach-Zahlen basierend auf Mehrskalenasymptotik und diskreter Datenanalyse. Dissertation, Fachbereich Mathematik, Schwerpunkt Differentialgleichungen und Dynamische Systeme, Universität Hamburg, 2000.
24. L. Hoffmann, A. Meister, A Numerical Scheme for Low Mach Number Flow based on Asymptotic Analysis with Time-Dependent Adaptation of the Asymptotic Sequence. In Proceedings of the Fourth ECCOMAS Computational Fluid Dynamics Conference, (Eds.) C. Hirsch, et. al. Pandolfi, M., volume 1, Part 1, pp. 567-572, Athens, 1998.
25. L. Hoffmann, A. Meister, The Extension of a Compressible Flow Solver to the Low Mach Number Regime. In Proceedings of the and Seminar on Euler and Navier-Stokes Equations, Prague, 1998.
26. L. Hoffmann, A. Meister, A Compressible Low Mach Number Scheme based on Image Processing and Asymptotic Analysis. Computational Fluid Dynamics Journal 9 (2001), 399-410.
27. M.S. Holden, A.R. Wieting, J.R. Moselle, C. Glass, Studies of Aerothermal Loads Generated in Regions of Shock/Shock Interaction in Hypersonic Flow. AIAA 26th Aerospace Sciences Meeting, AIAA-88-0477, January 1988.
28. C. Hu, C.-W. Shu, Weighted Essentially Non-oscillatory Schemes on Triangular Meshes. J. Comput. Phys. 150 (1999), 97-127.
29. A. Jameson, Computational Transonics. Comm. Pure Appl. Math. 41 (1988), 507-549.
30. S. Klainerman, A. Majda, Singular limits of quasilinear hyperbolic system with large parameters and the incompressible limit of compressible fluids. Comm. Pure Appl. Math. 34 (1981), 481-524.
31. S. Klainerman, A. Majda, Compressible and incompressible fluids. Comm. Pure Appl. Math. 35 (1982), 629-651.
32. R. Klein, Semi-Implicit Extension of a Godunov-Type Scheme Based on Low Mach Number Asymptotics I: One-Dimensional Flow. J. Comput. Phys. 121 (1995), 213-237.
33. R. Klein, N. Botta, T. Schneider, C.D. Munz, S. Roller, A. Meister, L. Hoffmann, Th. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics. Journal of Engineering Mathematics, 9 (2001), 261-343.
34. D. Kröner, Numerical Schemes for Conservation Laws. Teubner, Stuttgart, 1997.
35. R. J. LeVeque, Numerical Methods for Conservation Laws. Birkhäuser, Basel, 1990.
36. M.-S. Liou, C.J. Steffen, A New Flux Splitting Scheme. NASA Technical Memorandum 104404, Cleveland, Ohio, May 1991. also in J. Comput. Phys. 107 (1993), 23-39.
37. M.-S. Liou, C.J. Steffen, A New Flux Splitting Scheme. NASA Technical Memorandum 104404, Cleveland, Ohio, May 1991. also in J. Comput. Phys. 107 (1993), 23-39.
38. A. Meister, Ein Beitrag zum DLR- τ -Code: Ein explizites und implizites Finite-Volumen-Verfahren zur Berechnung instationärer Strömungen auf unstrukturierten Gittern. DLR-IB 221 - 94 A 36, Göttingen, 1994.
39. A. Meister, Development of an Implicit Finite Volume Scheme for the Computation of Unsteady Flow Fields on Unstructured Moving Grids. In Numerical Methods for Fluid Dynamics V, pp. 481-488, Oxford, 1995. Clarendon Press. Ed. K.W. Morton and M.J. Baines.
40. A. Meister, Zur zeitgenauen numerischen Simulation reibungsbehafteter, kompressibler, turbulenter Strömungsfelder mit einer impliziten Finite-Volumen-Methode vom Box-Typ, Dissertation, Technische Hochschule Darmstadt, 1996.
41. A. Meister, Comparison of Different Krylov Subspace Methods Embedded in an Implicit Finite Volume Scheme for the Computation of Viscous and Inviscid Flow Fields on Unstructured Grids. J. Comput. Phys. 140 (1998), 311-345.
42. A. Meister, Asymptotic Single and Multiple Scale Expansions in the Low Mach Number Limit. SIAM J. Appl. Math. 60 (1999), 256-271.
43. A. Meister, Analyse und Anwendung Asymptotik-basierter numerischer Verfahren zur Simulation reibungsbehafteter Strömungen in allen Mach-Zahlbereichen, Habilitationsschrift, Universität Hamburg, 2001.
44. A. Meister, Asymptotic based preconditioning technique for low Mach number flows. Z. Angew. Math. Mech. 83(1) (2003), 3-25.
45. A. Meister, M. Oevermann, Computation of Laminar and Turbulent Compressible Flow Fields on Unstructured Grids with an Implicit Finite Volume Scheme. In Proceedings of the 2nd Seminar on Euler and Navier-Stokes Equations, Prague, 1996.
46. A. Meister, M. Oevermann, An Implicit Finite Volume Approach of the k - ε Turbulence Model on Unstructured Grids. Z. Angew. Math. Mech. 78 (1998), 743-757.
47. A. Meister, Th. Sonar, Finite-volume schemes for compressible fluid flow. Surv. Math. Ind. 8 (1998), 1-36.
48. A. Meister, C. Vömel, Efficient Preconditioning of Linear Systems arising from the Discretization of Hyperbolic Conservation Laws. Advances in Computational Mathematics 14 (2001), 49-73.
49. A. Meister, J. Witzel, Krylov Subspace Methods in Computational Fluid Dynamics. Surv. Math. Ind. 10 (2002), 231-267.
50. C. L. Merkle, Y.-H. Choi, Computation of Low-Speed Compressible Flows with Heat Addition. AIAA J. 25 (1987), 831-838.
51. C. L. Merkle, Y.-H. Choi, Computation of Low-Speed Compressible Flows with Time-Marching Procedure. Int. J. Num. Meth. Eng. 25 (1998), 293-311.
52. M. Oevermann, Ein Finite-Volumen-Verfahren auf unstrukturierten Dreiecksgittern zur Berechnung turbulenter Diffusionsflammen in kompressiblen Strömungsfeldern. Dissertation, RWTH Aachen, 1997.
53. S. Osher, F. Solomon, Upwind Schemes for Hyperbolic Systems of Conservation Laws, Math. Comput. 38 (1982), 339-377.
54. J. J. Quirk, A Contribution to the Great Riemann Solver Debate. ICASE Report 92-64, Hampton, Virginia, 1992.
55. P. L. Roe, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes. J. Comput. Phys. 43 (1981), 357-372.
56. J. Sesterhenn, Zur numerischen Berechnung kompressibler Strömungen bei kleinen Mach-Zahlen. PhD thesis, Swiss Federal Institute of Technology, Diss. ETH No. 11334, 1995.
57. C.-W. Shu, S. Osher, Efficient Implementation of Essentially Nonoscillatory Shock-Capturing Schemes, J. Comput. Phys. 77 (1988), 439-471.
58. J.-S. Shuen, K.-H. Chen, Y. Choi, A Coupled Implicit Method for Chemical Non-equilibrium Flows at All Speeds. J. Comput. Phys. 106 (1993), 306-318.
59. Th. Sonar, Mehrdimensionale ENO-Verfahren. Teubner Verlag, Stuttgart, 1997.
60. Th. Sonar, On the Construction of Essentially Non-Oscillatory Finite Volume Approximations to Hyperbolic Conservation Laws on General Triangulations: Polynomial Recovery, Accuracy, and Stencil Selection. Comp. Meth. Appl. Mech. Eng. 140 (1997), 157-181.
61. J. L. Steger, R. F. Warming, Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite-Difference Methods. J. Comput. Phys. 40 (1981), 263-293.
62. E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin, Heidelberg, New York, 1997.
63. E. Turkel, Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations. J. Comput. Phys. 72 (1987), 277-298.
64. H. A. van der Vorst, BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (1992), 631-644.
65. B. van Leer, Flux-vector splitting for the Euler equations. In Eighth International Conference on Numerical Methods in Fluid Dynamics, (Ed.) E. Krause, number 170 in Lecture Notes in Physics, pp. 507-512, Springer Verlag, Berlin, 1982.
66. J. Vierendeels, K. Riemslagh, E. Dick, A Multigrid Semi-implicit Line- Method for Viscous Incompressible and Low-Mach-Number Flows on High Aspect Ratio Grids. J. Comput. Phys. 154 (1999), 310-341.
67. G. Volpe, Performance of Compressible Flow Codes at Low Mach Numbers. AIAA J. 31 (1993), 49-56.
68. Y. Wada, M.-S. Liou, A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities. AIAA Paper (1994), 94-0083.
69. J. M. Weiss, W. A. Smith, Preconditioning Applied to Variable and Constant Density Flows. AIAA J. 33 (1995), 2050-2057.
70. A.R. Wieting, M.S. Holden, Experimental Study of Shock Wave Interference Heating on a Cylindrical Leading Edge at Mach 6 and 8. AIAA 22nd Thermophysics Conference, AIAA-87-1511, June 1987.