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

15th AIAA Computational Fluid Dynamics Conference

Volumn , Issue , 2001, Pages

  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

EID: 84894410449     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (48)

1. Alpert, P., Implicit Filtering in Conjunction with Explicit Filtering, J. Comput. Phys. 44, 212-219 (1981).
2. Brown, D.L. and Minion, M.L., Performance of Under-resolved Two-Dimensional Incompressible Flow Simulations, J. Comput. Phys. 122, 165-183 (1995).
3. Brown, D.L., Margolin, L., Sharp, D. and White, A., Predictability of Complex Phenomena, A White Paper, Los Alamos National Laboratory reprint (1997).
4. Nordstrom, J. and Carpenter, M.H., Boundary and Interface Conditions for High-Order Finite-Difference Methods Applied to the Euler and Navier-Stokes Equations, J. Comput. Phys., 148, 621-645 (1999).
5. Carpenter, M.H., Gottlieb, D and Abarbanel, S., Time-Stable Boundary Conditions for Finite-Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Schemes, J. Comput. Phys., Ill, 220-236 (1994).
6. Carpenter, M.H., Gottlieb, D., Abarbanel S. and Don, W.-S., The Theoretical Accuracy of Runge-Kutta Time Discretizations for Initial Value Problem: A Study of the Boundary Error, SIAM J. Sci. Comput. 16, 1241-1252 (1995).
7. Daru, V. and Tenaud, C., Evaluation of TVD High Resolution Schemes for Unsteady Viscous Shocked Flows, Computers Fluids, 30 89-113 (2000).
8. Don, W.S. and Quillen, C. B., Numerical simulation of Shock-Cylinder Interactions, J. Comput. Phys. 122 244-265 (1995).
9. Don, W.S. and Gottlieb, D., Spectral Simulation of Supersonic Reactive Flows, SIAM J. Numer. Anal. 35 2370-2384 (1998).
10. Gaitone, D.V. and Visbal, M.R., Further Development of a Navier-Stokes Solution Procedure Based on Higher-Order Formulas, AIAA Paper 99-0557, Reno, NV, 1999.
11. Gerritsen, M. and Olsson, P., Designing an Efficient Solution Strategy for Fluid Flows, J. Comput. Phys. 129 245-262 (1996).
12. Griffiths, D.F., Sweby, P.K. and Yee, H.C., On Spurious Asymptotic Numerical Solutions of Explicit Runge-Kutta Schemes, IMA J. Numer. Anal, 12 319-338 (1992).
13. Glimm, J., and Sharp, D., Prediction and the Quantification of Uncertainty, Los Alamos National Laboratory LAUR-98-3391 (1998).
14. Gresho, P.M., Gartling, D.K., Torczynski, J.R., Cliffe, K.A., Winters, K.H., Garrett, T.J., Spence, A. and Goodrich, J.W., Is the Steady Viscous Incompressible Two-Dimensional Flow Over a Backward-facing Step at Re=800 Stable?, Intern. J. Numer. Meth. Fluids 17 501-541 (1993).
15. Gustafsson, B., Kreiss, H.-O., Oliger, J., Time Dependent Problems and Difference Methods, John Wiley & Sons, New York (1995).
16. Harten, A., The Artificial Compression Method for Computation of Shocks and Contact Discontinuities: III. Self-Adjusting Hybrid Schemes, Math. Comp. 32 363-389 (1978).
17. Harten, A., On the Symmetric Form of Systems for Conservation Laws with Entropy, J. Comput. Phys. 49, 151-164 (1983).
18. Johansson, M., Loss of High Order Spatial Accuracy due to Boundary Error Caused by Runge-Kutta Time Integration, Technical report 2000-013, Dept. Info. Tech., Uppsala University, May 2000.
19. Jiang, G.-S. and Shu, C.-W., Efficient Implementation of Weighted ENO schemes, ICASE Report No. 95-73, (1995).
20. Lafon, A. and Yee, H.C., 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 1-36 (1996).
21. Lafon, A. and Yee, H.C., 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 89-123 (1996).
22. Lele, S.A., Compact Finite Difference Schemes with Spectral-Like Resolution, J. Comput. Phys., 103, 16-42 (1992).
23. LeVeque, R.J. and Yee, H.C., A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms, J. Comput. Phys. 86 187-210 (1990).
24. Mattsson, K., 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, 2000, Kyoto, Japan.
25. McBride, B.J., Heimel, S., Ehlers, J.G. and Gorden, S., Thermodynamics Properties to 6000° K for 210 Substances Involving the first 18 elements, NASA SP-3002 (1963)
26. Minion, M.L. and Brown, D.L., Performance of Under-resolved Two-Dimensional Incompressible Flow Simulations II, J. Comput. Phys. 138, 734-765 (1997).
27. Oberkampf, W.L., Diegert, K.V., Alvin, K.F., and Rutherford, B.M., 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. Olsson, P. and Oliger, J., Energy and Maximum Norm Estimates for Nonlinear Conservation Laws, RIACS Technical Report 94.01 (1994).
29. Olsson, P., Summation by Parts, Projections, and Stability. I, Math. Comp. 64 (1995), pp. 1035-1065.
30. Olsson, P., Summation by Parts, Projections, and Stability. II,Math. Comp. 64, pp. 1473-1493 (1995).
31. P. Olsson, Summation by Parts, Projections, and Stability. Ill, RIACS Technical Report 95.06 (1995).
32. Sandham, N.D. and Yee, H.C., Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence, RIACS Technical Report 00.10, June, 2000, Proceedings of the 1st Intern. Conf. on CFD, July 10-14, 2000, Kyoto, Japan.
33. B. Sjogreen and H. C. Yee, Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computation, RIACS Report 01-01, NASA Ames research center (Oct 2000).
34. Special Section of the AIAA Journal, Credible Computational Fluid Dynamics Simulation, AIAA J. 36, 665-759 (1998).
35. Strand, B., Summation by Parts for Finite Difference Approximations for d/dx, J. Comput. Phys. 110 (1994), pp. 47-67.
36. Strand, B., High-Order Difference Approximations for Hyperbolic Initial Boundary Value Problems, PhD thesis, Uppsala University, Department of Scientific Computing, 1996.
37. Svehla, R.A., Estimated Viscosities and Thermal Conductivities of Gases at High temperatures, NASA Report TR R-132 (1962).
38. Torczynski, J.R., A Grid Refinement Study of Two-Dimensional Transient Flow Over a Backward-facing Step Using a Spectral-Element Method, FED-Vol. 149, Separated Flows, ASME, J.C. Dutton and L.P. Purtell, Eds. (1993).
39. Trucano, T.G., Prediction and Uncertainty in Computational Modeling of Complex Phenomena: A Whitepaper, Sandia Report, SAND98-2776 (1998).
40. Vinokur, M. and Yee, H.C., Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids, NASA TM 209598, June 2000.
41. Vichnevetsky, R., Numerical Filtering for Partial Differencing Equations, Numerical Applications Memorandum, Rutgers University, NAM 156 (1974).
42. Wilke, C.R., A Viscosity Equation for Gas Mixtures, Chem. Phs. 18 517-519, (1950).
43. Yee, H.C., Sweby, P.K. and Griffiths, D.F., 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. 97 249-310 (1991).
44. Yee, H.C. and Sweby, P.K., Dynamics of Numerics & Spurious Behaviors in CFD Computations, Keynote paper, 7th ISCFD Conference, Sept. 15-19, 1997, Beijing, China, RIACS Technical Report 97.06, June 1997.
45. Yee, H.C. and Sweby, P.K., 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., 36 712-724 (1998).
46. Yee, H.C., Torczynski, J.R., Morton, S.A., Visbal, M.R. and Sweby, P.K., 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. Num. Meth. Fluids, 30, 675-711 (1999).
47. H. C. Yee, N. D. Sandham, and M. J. Djomehri, Low Dissipative High Order Shock- Capturing Methods Using Characteristic-Based Filters, J. Comput. Phys., 150 199-238 (1999).
48. Yee, H.C., Vinokur, M., and Djomehri, M.J., Entropy Splitting and Numerical Dissipation, J. Comput. Phys. 162, 33-81 (2000).