Treatments of stiff source terms in conservation laws by the method of space-time conservation element/solution element

35th Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 1997, Pages

  Yu, Sheng Tao ^a   Chang, Sin Chung ^a  

^a NASA GLENN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE ENGINEERING; SHOCK TUBES; TURBULENT FLOW;

CONSERVATION ELEMENTS; CONSERVATION LAW; CONSTANT TEMPERATURE BATHS; IMPLICIT FORMULATION; QUASI-ONE-DIMENSIONAL FLOW; SPACE TIME GEOMETRY; SPACE-TIME CONSERVATION ELEMENT; VOLUMETRIC INTEGRATION;

PHYSICAL PROPERTIES;

EID: 84982318972     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (41)

1. S.C. Chang and W.M. To, "A New Numerical Framework for Solving Conservation Laws - The Method of Space-Time Conservation Element and Solution Element," NASA TM 104495, August 1991.
2. S.C. Chang, "On an Origin of Numerical Diffusion: Violation of Invariance Under Space-Time Inversion", Proceedings of the 23rd Modeling and Simulation Conference, April 1992, Pittsburgh, PA, William G. Vogt and Marlin H. Mickle eds., Part 5, pp. 2727-2738. Also published as NASA TM 105776.
3. S.C. Chang and W.M. To, "A Brief Description of a New Numerical Framework for Solving Conservation Laws - The Method of Space-Time Conservation Element and Solution Element", Proceedings of the 13th International Conference on Numerical Methods in Fluid Dynamics, July 6-10, 1992, Rome, Italy, M. Napolitano and F. Sabetta, eds. Also published as NASA TM 105757.
4. S.C. Chang, "New Developments in the Method of Space-Time Conservation Element and Solution Element - Applications to the Euler and Navier-Stokes Equations", Presented at the Second U.S. National Congress on Computational Mechanics, August 16-18, 1993, Washington D.C. Published as NASA TM 106226.
5. S.C. Chang, X.Y. Wang and C.Y. Chow, "New Developments in the Method of Space-Time Conservation Element and Solution Element - Applications to Two-Dimensional Time-Marching Problems", NASA TM 106758, December 1994.
6. S.C. Chang, J. Comput. Phys., 119, (1995) pp. 295-324.
7. S.C. Chang, X.Y. Wang and C.Y. Chow, "The Method of Space-Time Conservation Element and Solution Element - Applications to One-Dimensional and Two-Dimensional Time-Marching Flow Problems", AIAA Paper 95-1754, the 12th AIAA CFD Conference, June 1995, San Diego, CA. Also published as NASA TM 106915.
8. S.C. Chang, X.Y. Wang, C.Y. Chow and A. Himansu, "The Method of Space-Time Conservation Element and Solution Element -Development of a New Implicit Solver", the Ninth International Conference on Numerical Methods in Laminar and Turbulent Flow, July 1995, Atlanta, GA. Also published as NASA TM 106897.
9. S.C. Chang, C.Y. Loh and S.T. Yu, "Computational Aeroacoustics via a New Global Conservation Scheme," the 15th International Conference on Numerical Methods in Fluid Dynamics, June 1996, Monterey, CA.
10. S.C. Chang, S.T. Yu, A. Himansu, X.Y. Wang, and C.Y. Loh, "The Method of Space-Time Conservation Element and Solution Element - A New Paradigm for Numerical Solution of Conservation Laws," to appear in Computational Fluid Dynamics Review 1996, Edited by M.M. Hafez and K. Oshima, John Wiley and Sons, West Sussex, UK.
11. C.Y. Loh, S.C. Chang, J.R. Scott and S.T. Yu, "Application of the Method of Space-Time Conservation Element and Solution Element to Aeroacoustics Problems," the 6th International Symposium of CFD, September 1995, Lake Tahoe, NV.
12. C.Y. Loh, S.C. Chang, J.R. Scott and S.T. Yu, "The Space-Time Conservation Element Method - A New Numerical Scheme for Computational Aeroacoustics," AIAA Paper 96-0276, the 34th AIAA Aerospace Sciences Meeting, January 1996, Reno, NV.
13. C.Y. Loh, S.C. Chang and J.R. Scott, "Computational Aeroacoustics via the Space-Time Conservation Element /Solution Element Method," AIAA Paper 96-1687, the 2nd AIAA/CEAS Aeroacoustics Conference, May 1996, State College, PA.
14. X.Y. Wang, C.Y. Chow and S.C. Chang, "Application of the Space-Time Conservation Element and Solution Element Method to Shock-Tube Problem," NASA TM 106806, December 1994.
15. X.Y. Wang, "Computational Fluid Dynamics Based on the Method of Space-Time Conservation Element and Solution Element," Ph.D. Dissertation, 1995, Department of Aerospace Engineering, University of Colorado, Boulder, CO.
16. X.Y. Wang, C.Y. Chow and S.C. Chang, "Application of the Space-Time Conservation Element and Solution Element Method to Two-Dimensional Advection-Diffusion Problems," NASA TM 106946, June 1995.
17. X.Y. Wang, C.Y. Chow and S.C. Chang, "High Resolution Euler Solvers Based on the Space-Time Conservation Element and Solution Element Method," AIAA Paper 96-0764, the 34th AIAA Aerospace Sciences Meeting, January 1996, Reno, NV.
18. X.Y. Wang, C.Y. Chow and S.C. Chang, "Numerical Simulation of Flows Caused by Shock-Body Interaction," AIAA Paper 96-2004, the 27th AIAA Fluid Dynamics Conference, June 1996, New Orleans, LA.
19. X.Y. Wang, C.Y. Chow and S.C. Chang, "An Euler Solver Based on the Method of Space-Time Conservation Element and Solution Element," the 15th International Conference on Numerical Methods in Fluid Dynamics, June 1996, Monterey, CA.
20. J.R. Scott and S.C. Chang, "A New Flux Conserving Newton’s Method Scheme for the Two-Dimensional, Steady Navier-Stokes Equations," NASA TM 106160, June 1993.
21. J.R. Scott, "A New Flux-Conserving Numerical Scheme for the Steady, Incompressible Navier-Stokes Equations," NASA TM 106520, April 1994.
22. J. R. Scott and S.C. Chang, Comp. Fluid Dyn., Vol. 5 (1995) pp. 189-212.
23. J.R. Scott and S.C. Chang, "The Space-Time Solution Element Method - A New Numerical Approach for the Navier-Stokes Equations," AIAA Paper 95-0763, the 33rd AIAA Aerospace Sciences Meeting, January 1995, Reno, NV.
24. J. R. Scott, "Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations," NASA TM 107190, March 1996.
25. H.F. Davis and A.D. Snider, "Introduction to Vector Analysis," 6th Ed., Wm. C. Brown Publishers, Dubuque IA (1991) pp. 274-281.
26. M. Vinokur, J. Comput. Phys., 81, pp. 1-52 (1989).
27. P. Colella, A. Majda, and V. Roytburd, SI AM J. Sci. Stat. Comput, 7, 4 (1986) pp. 1059-1080.
28. R.J. LeVeque and H.C. Yee, J. Comput. Phys., 86 (1990) pp. 187-210.
29. R.B. Pember, SIAM J. Appl. Math., 53, 5 (1993) pp. 1293-1330.
30. R.B. Pember, SIAM J. Sci. Comput, 14, 4 (1993) pp. 824-859.
31. T.P. Liu, Commun. Math. Phys., 108, pp. 153 (1987).
32. G.B. Whitham, Linear and Nonlinear Waves, (Wiley, New York, 1974).
33. S. Jin, J. Comput. Phys., 122 (1995) pp. 51-67.
34. P.L. Roe and M. Arora, Numer. Methods for Partial Dig. Equations, 9 (1993) pp.459-505.
35. M. Arora, "Explicit Characteristic-Based High-Resolution Algorithms for Hyperbolic Conservation Laws with Stiff Source Terms," Ph.D. dissertation, Aerospace Engineering and Scientific Computing, University Michigan (1996).
36. J. Bell, P. Colella, J. Trangenstein, and M. Welcome, "Adaptive Methods for High Mach Number Reacting Flows," AIAA Paper 87-1168, the 8th AIAA CFD Conference, Honolulu, HI, June 1987.
37. E. Harabetian, J. Comput. Phys., 103 (1992) pp.350-358.
38. A. Bourlioux and A.J. Majda, V. Roytburd, SIAM J. Appl. Math., 51, 2 (1991) pp.303-343.
39. A. Bourlioux and A.J. Majda, Phil. Trans. R. Soc. Lond. A, 350 (1995) pp. 29-68.
40. G.R. Shubin, A.B. Stephens, and H.M. Glaz, J. Comput. Phys., 39 (1981) pp. 364-374.
41. H.T. Huynh and P. Prashant, NASA Lewis Resaerch Center, Ohio and Coastal Carolina University, South Carolina, private communication.