An approximate solution of the Riemann problem for a realisable second-moment turbulent closure

Shock Waves

Volumn 11, Issue 4, 2002, Pages 245-269

  Berthon, C ^a   Coquel, F ^a   Herard J M ^b,c   Uhlmann, M ^d  

^a SORBONNE UNIVERSITÉ   (France)

^b Laboratoire National d'Hydraulique   (France)

^c AIX MARSEILLE UNIVERSITY   (France)

^d ECOLE CENTRALE DE LYON   (France)

Author keywords

Approximate Riemann solver; Riemann problem; Turbulent closure

Indexed keywords

EID: 20544436471     PISSN: 09381287     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001930100109     Document Type: Article

References (46)

1. Buffard T, Gallouët T, Hérard JM (1998) A naïve scheme to compute shallow water equations. C. R. Acad. Sci., Paris, I-326, pp. 385-390
2. Buffard T, Gallouët T, Hérard JM (1999) A naïve Riemann solver to compute a non-conservative hyperbolic system. Int. Series on Numerical Mathematics 129: 129-138
3. Buffard T, Gallouët T, Hérard JM (2000) A sequel to a rough Godunov scheme: application to real gases. Computers and Fluids 29(7): 813-847
4. Dal Maso G, Le Floch PG, Murat F (1995) Definition and weak stability of non-conservative products. J. Math. Pures Appl. 74: 483-548
5. Declercq-Xeuxet E (1999) Comparaison de solveurs numé riques pour le traitement de la turbulence bi fluide. PhD thesis, Université Evry Marne la Vallée, Paris, France, June 23
6. Eymard R, Gallouët T, Herbin R (2001) Finite volume methods. In: Ciarlet PG, Lions PL (eds) Handbook for numerical analysis, Vol. 7, pp. 729-1020. North Holland
7. Faucher E (2000) Simulation numérique des écoulements uni-dimensionnels instationnaires d'écoulements avec auto-vaporisation. PhD thesis, Université Paris Val de Marne, Paris, France, January 24
8. Favre A (1965) Equations des gaz turbulents compressibles. Jour. Mécanique 4: 391-421
9. Forestier A, Hérard JM, Louis X (1995) Exact or approximate Riemann solvers to compute a two-equation turbulent compressible model. In: Cecchi M, Morgan K, Periaux J, Schrefler BA, Zienkiewicz OC (eds) Finite elements in fluids. New trends and applications, vol. I, pp. 677-686
10. Forestier A, Hérard JM, Louis X (1997) A Godunov type solver to compute turbulent compressible flows. C. R. Acad. Sci., Paris, I-324, pp. 919-926
11. Fu S, Launder BE, Tselepidakis DP (1987) Accomodating the effects of high strain rates in modelling the pressure strain correlations. UMIST report TFD 87/5
12. Gallouët T, Masella JM (1996) A rough Godunov scheme. C. R. Acad. Sci., Paris, I-323, pp. 77-84
13. Gallouët T, Hérard JM, Seguin N (2000) Some recent finite volume schemes to compute Euler equations with real gas equations of state. Internal report LATP 00-21, Université de Provence, Marseille, France
14. Godlewski E, Raviart PA (1996) Numerical analysis of hyperbolic systems of conservation laws. Springer Verlag
15. Godunov SK (1959) A difference method for numerical calculation of discontinuous equations of hydrodynamics. Math. Sb. 47: 217-300
16. Harten A, Lax PD, Van Leer B (1983) On upstream differencing and Godunov type schemes for hyperbolic conservation laws. SIAM Review 25(1): 35-61
17. Hérard JM (1994) Basic analysis of some second moment closures. Part I: incompressible isothermal turbulent flows. Theoretical and Computational Fluid Dynamics 6(4): 213-233
18. Hérard JM (1995a) Suitable algorithms to preserve the realisability of Reynolds stress closures. ASME Fluids Engineering Division 215: 73-80
19. Hérard JM (1995b) Solveur approché pour un système hyperbolique non conservatif issu de la turbulence compressible. EDF report HE-41/95/009/A, Electricité de France, Chatou, France
20. Hérard JM (1996) Realisable non-degenerate second moment closures for incompressible turbulent flows. C. R. Acad. Sci., Paris, t.322, IIb, pp. 371-377
21. Hérard JM, Forestier A, Louis X (1995) A non-strictly hyperbolic system to describe compressible turbulence. Collection des Notes internes de la Direction des Etudes et Recherches d'EDF n7deg; 95NB00003, Electricité de France, Chatou, France
22. Le Floch P (1988) Entropy weak solutions to non-linear hyperbolic systems in non-conservative form. Comm. in Part. Diff. Eq. 13(6): 669-727
23. Le Floch P, Liu TP (1992) Existence theory for non-linear hyperbolic systems in non-conservative form. CMAP report 254, Ecole Polytechnique, Palaiseau, France
24. Liou M (1996) A sequel to AUSM: AUSM +. J. Comp. Physics 12(2): 364-382
25. Louis X (1995) Modélisation numérique de la turbulence compressible. PhD thesis, Université Paris VI, Paris, France, July 8
26. Lumley JL (1978) Computational modelling of turbulent flows. Advances in Applied Mechanics 18: 123-176
27. Lumley JL (1983) Turbulence modelling. J. of Applied Mechanics 50: 1097-1103
28. Masella JM (1997) Quelques méthodes numériques pour les écoulements diphasiques bi-fluide en conduites pétrolières. PhD thesis, Université Paris VI, Paris, France, May 5
29. Masella JM, Faille I, Gallouët T (1999) On a rough Godunov scheme. Int. J. for Computational Fluid Dynamics 12(2): 133-150
30. Page A, Uhlmann M (1996) Traitement de la partie hyperbolique du système des équations de Navier-Stokes moyénnées et des équations de transport issues d'une femeture au premier ordre pour un fluide compressible. Internal report 96-1, LMFA, Ecole Centrale de Lyon, Lyon, France
31. Périgaud G, Archambeau F (2000) Méthodes non conservatives multidimensionnelles pour modèle de turbulence compressible au second ordre. Internal EDF report HI-83/00/028/A, Electricité de France, Chatou, France
32. Pope SB (1985) PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11: 119-192
33. Ristorcelli J (1993) A representation for the turbulent mass flux contribution to Reynolds stress and two-equation closures for compressible turbulence. NASA ICASE Technical Report 93-88
34. Roe PL (1981) Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Physics 43: 357-372
35. Rusanov W (1961) Calculation of interaction of non steady shock waves with obstacles. J. Comp. Math. Physics USSR 1: 267-279
36. Sainsaulieu L (1995a) Finite volume approximation of two phase fluid flow based on approximate Roe type Riemann solver. J. Comp. Physics 121: 1-28
37. Sainsaulieu L (1995b) Contribution à la modélisation mathé matique et numérique des écoulements diphasiques constitués d'un nuage de particules dans un écoulement de gaz. Thèse d'habilitation, Université Paris VI, Paris, France, January 20
38. Seguin N (2000) Comparaison numérique de schémas Volumes Finis pour les équations d'Euler en gaz parfaits et reéls. EDF report HI-81/00/010/A, Electricité de France, Chatou, France
39. Shih T, Lumley JL (1985) Modeling of pressure corelation terms in Reynolds stress and scalar flux equations. Cornell University report FDA-85-3
40. Shih T, Shabbir A, Lumley JL (1994) Realisability in second moment turbulence closures revisited. NASA Technical Memorandum 106469
41. Smoller J (1983) Shock waves and reaction diffusion equations. Springer Verlag, New York
42. Speziale CG (1979) Invariance of turbulent closure models. Physics of Fluids A 22(6): 1033-1037
43. Toro EF (1997) Riemann solvers and numerical methods for fluid dynamics. Springer Verlag
44. Toro EF, Spruce M, Speares W (1994) Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4: 25-34
45. Uhlmann M (1997) Etude de modèles de fermeture au second ordre et contribution à la résolution numérique des écoulements turbulents compressibles. PhD thesis, Ecole Centrale de Lyon, Lyon, France, April 17
46. Vandromme D, Ha Minh H (1986) About the coupling of turbulence closure models with averaged Navier-Stokes equations. J. Comp. Physics 65(2): 386-409