Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows

Journal of Computational Physics

Volumn 185, Issue 1, 2003, Pages 1-26

  Sjogreen B ^a   Yee, H C ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b NASA AMES RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

ACM FILTERS; FINE GRIDS; GRID CONVERGENCE; HIGH-ORDER METHODS; HIGHER-ORDER METHODS; NAVIER-STOKES MODEL; NUMERICAL DISSIPATION CONTROLS; SECOND ORDERS; VISCOUS COMPRESSIBLE FLOWS; WAVELET FILTERS;

SHOCK TUBES;

EID: 0037429536     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(02)00044-X     Document Type: Article

References (49)

1. P. Alpert, Implicit filtering in conjunction with explicit filtering, J. Comput. Phys. 44 (1981) 212-219.
2. D.L. Brown, M.L. Minion, Performance of under-resolved two-dimensional incompressible flow simulations, J. Comput. Phys. 122 (1995) 165-183.
3. D.L. Brown, L. Margolin, D. Sharp, A.A. White, Predictability of Complex Phenomena, A White Paper, Los Alamos National Laboratory reprint, 1997.
4. J. Nordström, M.H. Carpenter, Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations, J. Comput. Phys. 148 (1999) 621-645.
5. M.H. Carpenter, D. Gottlieb, S. Abarbanel, Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes, J. Comput. Phys. 111 (1994) 220-236.
6. M.H. Carpenter, D. Gottlieb, S. Abarbanel, W.-S. Don, The theoretical accuracy of Runge-Kutta time discretizations for initial value problem: a study of the boundary error, SIAM J. Sci. Comput. 16 (1995) 1241-1252.
7. V. Daru, C. Tenaud, Evaluation of TVD high resolution schemes for unsteady viscous shocked flows, Comput. Fluids 30 (2000) 89-113.
8. W.S. Don, C.B. Quillen, Numerical simulation of shock-cylinder interactions, J. Comput. Phys. 122 (1995) 244-265.
9. W.S. Don, D. Gottlieb, Spectral simulation of supersonic reactive flows, SIAM J. Numer. Anal. 35 (1998) 2370-2384.
10. D.V. Gaitone, M.R. Visbal, Further Development of a Navier-Stokes Solution Procedure based on Higher-order Formulas, AIAA Paper 99-0557, Reno, NV, 1999.
11. M. Gerritsen, P. Olsson, Designing an efficient solution strategy for fluid flows, J. Comput. Phys. 129 (1996) 245-262.
12. D.F. Griffiths, P.K. Sweby, H.C. Yee, On spurious asymptotic numerical solutions of explicit Runge-Kutta schemes, IMA J. Numer. Anal. 12 (1992) 319-338.
13. J. Glimm, D. Sharp, Prediction and the Quantification of Uncertainty, Los Alamos National Laboratory LAUR-98-3391, 1998.
14. P.M. Gresho, D.K. Gartling, J.R. Torczynski, K.A. Cliffe, K.H. Winters, T.J. Garrett, A. Spence, J.W. Goodrich, Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable? Int. J. Numer. Meth. Fluids 17 (1993) 501-541.
15. B. Gustafsson, H.-O. Kreiss, J. Oliger, Time Dependent Problems and Difference Methods, Wiley, New York, 1995.
16. A. Harten, The artificial compression method for computation of shocks and contact discontinuities: III. Self-adjusting hybrid schemes, Math. Comp. 32 (1978) 363-389.
17. A. Harten, On the symmetric form of systems for conservation laws with entropy, J. Comput. Phys. 49 (1983) 151-164.
18. M. Johansson, Loss of High Order Spatial Accuracy due to Boundary Error Caused by Runge-Kutta Time Integration, Technical Report 2000-013, Department of Information Technology, Uppsala University, May 2000.
19. G.-S. Jiang, C.-W. Shu, Efficient Implementation of Weighted ENO Schemes, ICASE Report No. 95-73, 1995.
20. A. Lafon, H.C. Yee, Dynamical approach study of spurious steady-state numerical solutions for nonlinear differential equations, part III: the effects of nonlinear source terms in reaction-convection equations, Comp. Fluid Dyn. 6 (1996) 1-36.
21. A. Lafon, H.C. Yee, Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations, part IV: stability vs. numerical treatment of nonlinear source terms, Comput. Fluid Dyn. 6 (1996) 89-123.
22. S.A. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42.
23. R.J. LeVeque, H.C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys. 86 (1990) 187-210.
24. K. Mattsson, Imposing Boundary Conditions with the Injection, the Projection and the Simultaneous Approximation Term Methods, Proceedings of the First International Conference on CFD, July 10-14, Kyoto, Japan, 2000.
25. B.J. McBride, S. Heimel, J.G. Ehlers, S. Gorden, Thermodynamics Properties to 6000 K for 210 Substances Involving the first 18 elements, NASA SP-3002, 1963.
26. M.L. Minion, D.L. Brown, Performance of under-resolved two-dimensional incompressible flow simulations II, J. Comput. Phys. 138 (1997) 734-765.
27. W.L. Oberkampf, K.V. Diegert, K.F. Alvin, B.M. Rutherford, Variability, Uncertainty and Error in Computational Simulation, ASME Proceedings of the 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, HTD-vol. 357-2, 1998.
28. P. Olsson, J. Oliger, Energy and Maximum Norm Estimates for Nonlinear Conservation Laws, RIACS Technical Report 94.01, 1994.
29. P. Olsson, Summation by parts, projections, and stability. I, Math. Comp. 64 (1995) 1035-1065.
30. P. Olsson, Summation by parts, projections, and stability. II, Math. Comp. 64 (1995) 1473-1493.
31. P. Olsson, Summation by Parts, Projections, and Stability. III, RIACS Technical Report 95.06, 1995.
32. N.D. Sandham, H.C. Yee, Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence, RIACS Technical Report 00.10, June, 2000, Proceedings of the 1st International Conference on CFD, July 10-14, Kyoto, Japan, 2000.
33. B. Sjögreen, H.C. Yee, Multiresolution Wavelet based Adaptive Numerical Dissipation Control for Shock-Turbulence Computation, RIACS Report 01.01, NASA Ames Research Center, October 2000.
34. B. Sjögreen, H.C. Yee, Low Dissipative High Order Numerical Simulations of Supersonic Reactive Flows, RIACS Report 01-017, NASA Ames research center, May 2001, Proceedings of the ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, UK, September 4-7, 2001.
35. Special Section of the AIAA Journal, Credible computational fluid dynamics simulation, AIAA J. 36 (1998) 665-759.
36. B. Strand, Summation by parts for finite difference approximations for d/dx, J. Comput. Phys. 110 (1994) 47-67.
37. B. Strand, High-Order Difference Approximations for Hyperbolic Initial Boundary Value Problems, PhD thesis, Uppsala University, Department of Scientific Computing, 1996.
38. R.A. Svehla, Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, NASA Report TR R-132, 1962.
39. J.R. Torczynski, A grid refinement study of two-dimensional transient flow over a backward-facing step using a spectral-element method, in: J.C. Dutton, L.P. Purtell (Eds.), Separated Flows, FED-vol. 149, ASME, New York, 1993.
40. T.G. Trucano, Prediction and Uncertainty in Computational Modeling of Complex Phenomena: A Whitepaper, Sandia Report, SAND98-2776, 1998.
41. M. Vinokur, H.C. Yee, Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids, NASA TM 209598, June 2000.
42. R. Vichnevetsky, Numerical Filtering for Partial Differencing Equations, Numerical Applications Memorandum, Rutgers University, NAM 156, 1974.
43. C.R. Wilke, A viscosity equation for gas mixtures, Chem. Phys. 18 (1950) 517-519.
44. H.C. Yee, P.K. Sweby, D.F. Griffiths, Dynamical approach study of spurious steady-state numerical solutions for nonlinear differential equations, part I: the dynamics of time discretizations and its implications for algorithm development in computational fluid dynamics, NASA TM-102820, April 1990, J. Comput. Phys. 97 (1991) 249-310.
45. H.C. Yee, P.K. Sweby, Dynamics of Numerics and Spurious Behaviors in CFD Computations, Keynote paper, 7th ISCFD Conference, September 15-19, 1997, Beijing, China, RIACS Technical Report 97.06, June 1997.
46. H.C. Yee, P.K. Sweby, Some Aspects of Numerical Uncertainties in Time Marching to Steady-State Computations, AIAA-96-2052, 27th AIAA Fluid Dynamics Conference, June 18-20, 1996, New Orleans, LA, AIAA J., 36 (1998) 712-724.
47. H.C. Yee, J.R. Torczynski, S.A. Morton, M.R. Visbal, P.K. Sweby, On Spurious Behavior of CFD Simulations, AIAA 97-1869, Proceedings of the 13th AIAA Computational Fluid Dynamics Conference, June 29-July 2, 1997, Snowmass, CO., also International J. Numer. Meth. Fluids 30 (1999) 675-711.
48. H.C. Yee, N.D. Sandham, M.J. Djomehri, Low Dissipative high order shock-capturing methods using characteristic-based filters, J. Comput. Phys. 150 (1999) 199-238.
49. H.C. Yee, M. Vinokur, M.J. Djomehri, Entropy splitting and numerical dissipation, J. Comput. Phys. 162 (2000) 33-81.