Higher entropy conservation and numerical stability of compressible turbulence simulations

Journal of Computational Physics

Volumn 201, Issue 2, 2004, Pages 531-545

  Honein, Albert E ^a   Moin, Parviz ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Compressible turbulence simulations; Conservation properties; High order central schemes; Nonlinear numerical stability; Skew symmetric form

Indexed keywords

AERODYNAMICS; COMPUTATIONAL FLUID DYNAMICS; LARGE EDDY SIMULATION; MACH NUMBER; NUMERICAL METHODS; REYNOLDS NUMBER; TURBULENCE;

CENTRAL SCHEME; COMPRESSIBLE TURBULENCE; COMPRESSIBLE TURBULENCE SIMULATION; CONSERVATION PROPERTIES; HIGH ORDER CENTRAL SCHEME; HIGH-ORDER; HIGHER-ORDER; NONLINEAR NUMERICAL STABILITY; SKEW-SYMMETRIC FORMS; TURBULENCE SIMULATION;

ENTROPY;

EID: 8744273826     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.06.006     Document Type: Article

References (42)

1. Yee H.C. Vinokur M. Djomehri M.J. Entropy splitting and numerical dissipation J. Comput. Phys. 162 2000 33-81
2. Sandham N.D. Li Q. Yee H.C. Entropy splitting for high-order numerical simulation of compressible turbulence J. Comput. Phys. 178 2002 307-322
3. Nagarajan S. Lele S.K. Ferziger J.H. A robust high-order compact method for large eddy simulation J. Comput. Phys. 191 2 2003 392-419
4. Ducros F. Laporte F. Souleres T. Guinot V. Moinat P. Caruelle B. High-order fluxes for conservative skew-symmetric-like schemes in structured meshes J. Comput. Phys. 161 2000 114-139
5. Phillips N.A. An example of non-linear computational instability The Atmosphere and the Sea in Motion 1959 Rockefeller Institute Press and the Oxford University Press New York 501-504
6. Lilly D.K. On the computational stability of numerical solutions of time-dependent non-linear geophysical fluids dynamics problems Mon. Weather Rev. 93 1965 11-26
7. Ghosal S. An analysis of numerical errors in large-eddy simulations of turbulence J. Comput. Phys. 125 1 1996 187-206
8. Morinishi Y. Lund T.S. Vasilyev O.V. Moin P. Fully conservative higher order finite difference schemes for incompressible flow J. Comput. Phys. 143 1 1998 90-124
9. Moin P. Fundamentals of Engineering Numerical Analysis 2001 Cambridge University Press Cambridge
10. Zang T.A. On the rotation and skew-symmetric forms for incompressible flow simulations Appl. Numer. Math. 7 1 1991 27-40
11. Horiuti K. Comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow J. Comput. Phys. 71 2 1987 343-370
12. Mansour N.N. Moin P. Reynolds W.C. Ferziger J.H. Improved methods for large eddy simulations of turbulence Turbulent Shear Flows 1 1979 386-401
13. Harlow F.H. Welch J.E. Numerical calculation of time-dependent viscous incompressible flow of fluids with free surface Phys. Fluids 8 1965 2182-2189
14. Kim J. Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations J. Comput. Phys. 59 2 1985 308-323
15. Kravchenko A.G. Moin P. On the effect of numerical errors in large eddy simulations of turbulent flows J. Comput. Phys. 131 2 1997 310-322
16. C.D. Pierce, P. Moin, Progress-variable approach for large eddy simulation, Report TF-80, Flow Phys. Comput. Div., Mech. Eng., Stanford University, 2001
17. W.J. Feiereisen, W.C. Reynolds, J.H. Ferziger, Numerical simulation of a compressible, homogeneous, turbulent shear flow, Report TF-13, Thermosci. Div., Mech. Eng., Stanford University, 1981
18. Moin P. Squires K. Cabot W. Lee S. A dynamic subgrid-scale model for compressible turbulence and scalar transport Phys. Fluids A 3-11 1991 2746-2757
19. Dubois T. Domaradzki J.A. Honein A. The subgrid-scale estimation model applied to large eddy simulations of compressible turbulence Phys. Fluids 14 2002 1781-1801
20. Samtaney R. Pullin D.I. Kosovic B. Direct numerical simulation of decaying compressible turbulence and shocklet statistics Phys. Fluids 13 5 2001 1415-1430
21. Lee S. Lele S.K. Moin P. Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow Phys. Fluids A 4 7 1992 1521-1530
22. Blaisdell G.A. Spyropoulos E.T. Qin J.H. The effect of the formulation of non-linear terms on aliasing errors in spectral methods Appl. Numer. Math. 21 3 1996 207-219
23. S. Lee, Large eddy simulation of shock-turbulence interaction, Annual Research Briefs, Center for Turbulence Research, 1991, 73-84
24. Harten A. On the symmetric form of systems of conservation laws J. Comput. Phys. 49 1983 151-164
25. Tadmor E. Skew selfadjoint form for systems of conservation laws J. Math. Anal. Appl. 103 1984 428-442
26. P. Olsson, J. Oliger, Energy and maximum norm estimates for non linear conservation laws, RIACS Technical Report 94-01, NASA Ames Research Center, 1994
27. M. Gerritsen, Designing an efficient solution strategy for fluid flows, Ph.D. Thesis, Stanford University, 1996
28. Gerritsen M. Olsson P. Designing an efficient solution strategy for fluid flows. I. A stable high order finite difference scheme and sharp shock resolution for the Euler equations J. Comput. Phys. 129 1996 245-262
29. E.R. Van Driest, Investigation of laminar boundary layer in compressible fluids using the Crocco method, NACA TN 2597, 1952
30. Spyropoulos E.T. Blaisdell G.A. Evaluation of the dynamic model for simulations of compressible decaying isotropic turbulence AIAA J. 7 5 1996 27-40
31. A.E. Honein, Numerical aspects of compressible turbulence simulations, Ph.D. Thesis, Stanford University, 2004
32. G.A. Blaisdell, N.N. Mansour, W.C. Reynolds, Numerical simulations of compressible homogeneous turbulence, Report TF-50, Thermosci. Div., Mech. Eng., Stanford University, 1991
33. Strand B. Summation by parts for finite difference approximations for d/dx J. Comput. Phys. 110 1994 47-67
34. Lele S.K. Compact finite difference schemes with spectral-like resolution J. Comput. Phys. 103 1992 16
35. Lilly D.K. A proposed modification of the Germano subgrid-scale closure method Phys. Fluids A 4 3 1992 633-635
36. S. Lee, P. Moin, S.K. Lele, Interaction of isotropic turbulence with a shock wave, Report TF-52, Thermosci. Div., Mech. Eng., Stanford University, 1992
37. Kraichnan R.H. On the statistical mechanics of an adiabatically compressible fluid J. Acoust. Soc. Am. 27 3 1955 438-441
38. Onsager L. Statistical hydrodynamics Nuovo Cimento Suppl. 6 1949 279-286
39. Kraichnan R.H. Inertial ranges in two-dimensional turbulence Phys. Fluids 10 1967 1417-1423
40. Basdevant C. Sadourny R. Ergodic properties of inviscid truncated models of two-dimensional incompressible flows J. Fluid Mech. 69 1975 673-688
41. Kovasznay L.S.G. Turbulence in supersonic flow J. Aeronaut. Sci. 20 1953 657-674
42. Chu B.T. Kovasznay L.S.G. Nonlinear interactions in a viscous heat-conducting compressible gas J. Fluid Mech. 3 1958 494-514