Multi-dimensional courant number insensitive CE/SE Euler solvers for applications involving highly nonuniform meshes

39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit

Volumn , Issue , 2003, Pages

  Chang, S C ^a   Wang, X Y ^a  

^a NASA GLENN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CE/SE SCHEMES; CFL NUMBER; COURANT NUMBERS; EULER SOLVER; NON-UNIFORM MESH; NUMERICAL DISSIPATION; PERFORMANCE SENSITIVITY; SPATIAL MESH;

PROPULSION;

EID: 84897586299     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (44)

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 and W.M. To, A brief description of a new numerical framework for solving con-servation laws-The method of space-time con-servation element and solution element, in Proceedings of the Thirteenth International Confer-ence on Numerical Methods in Fluid Dynamics, Rome, Italy, 1992, edited by M. Napoli-tano and F. Sabetta, Lecture Notes in Physics 414, (Springer-Verlag, New York/Berlin, 1992), p. 396.
3. S.C. Chang, The method of space-time conservation element and solution Element-A new approach for solving the Navier-Stokes and Euler equations, J. Comput, Phys., 119, 295 (1995).
4. S.C. Chang, S.T. Yu, A. Himansu, X.Y. Wang, C.Y. Chow, and C.Y. Loh, The method of space-time conservation element and solution element-A new paradigm for numerical solution of conservation laws, in Computational Fluid Dynamics Review 1998 edited by M.M. Hafez and K. Oshima (World Scientific, Singapore), Vol. 1, p. 206.
5. T. Molls and F. Molls, "Space-Time Conservation Method Applied to Saint Venant Equations, " J. of Hydraulic Engr., 124(5), 501 (1998).
6. C. Zoppou and S. Roberts, "Space-Time Con-servation Method Applied to Saint Venant Equations: A Discussion, " J. of Hydraulic Engr, 125(8), 891 (1999).
7. S.C. Chang, X.Y. Wang, and C.Y. Chow, The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws, " J. Comput, Phys, 156, 89 (1999).
8. X.Y. Wang, and S.C. Chang, A 2D nonsplitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element method, Computational Fluid Dynamics Journal, 8(2), 309 (1999).
9. S.C. Chang, X.Y. Wang and W.M. To, Application of the space-time conservation element and solution element method to onedimensional convection-diffusion problems, J, Comput. Phys, 165, 189 (2000).
10. J. Qin, S.T. Yu, Z.C. Zhang, and M.C. Lai, Direct Calculations of Cavitating Flows by the Space-Time CE/SE Method, J. Fuels & Lubricants, SAE Transc., 108(4), 1720 (2000).
11. C.Y. Loh, L.S. Hultgren and S.C. Chang, Wave computation in compressible flow using the space-time conservation element and solution element method, AIAA J., 39(5), 794 (2001).
12. Z.C. Zhang, S.T. Yu, and S.C. Chang, A Space-Time Conservation Element and Solution Element Method for Solving the Two-and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes, J. Comput, Phys, 175, 168 (2002).
13. K.B.M.Q. Zaman, M.D. Dahl, T.J. Bencic, and C.Y. Loh, Investigation of A 'Transonic Res-onance' with Convergent-Divergent Nozzles, J. Fluid Mech, 463, 313 (2002).
14. C.Y. Loh and K.B.M.Q. Zaman, Numerical Investigation of 'Transonic Resonance' with A Convergent-Divergent Nozzle, AIAA J. 40(12), 2393 (2002).
15. X.Y. Wang, C.Y. Chow, and S.C. Chang, Nu-merical Simulation of Flows Caused by Shock-Body Interaction, AIAA Paper 96-2004 (1996).
16. S.C. Chang, A. Himansu, C.Y. Loh, X.Y., Wang, S.T., Yu, and P. Jorgenson, Robust and Simple Non-Reflecting Boundary Conditions for the Space-Time Conservation Element and Solution Element Method, in A Collection of Technical Papers, 13th AIAA CFD Conference, June 29-July 2, 1997, Snowmass, Colorado, AIAA Paper 97-2077.
17. C.Y. Loh, L.S. Hultgren and S.C. Chang, Vortex Dynamics Simulation in Aeroacoustics by the Space-Time Conservation Element and Solution Element Method, AIAA Paper 99-0359 (1999)
18. X.Y. Wang, S.C. Chang and P.C.E. Jorgenson, Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves, AIAA Paper 2000-0474 (2000).
19. C.Y. Loh, L.S. Hultgren, S.C. Chang and P.C.E. Jorgenson, Noise Computation of a Supersonic Shock-Containing Axisymmetric Jet by the CE/SE Method, AIAA Paper 2000-0475 (1999).
20. C.Y. Loh, X.Y. Wang, S.C. Chang, and P.C. E, Jorgenson, Computation of Feedback Aeroa-coustic System by the CE/SE Method, in Proceedings of the First International Conference on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Sato-fuka, (Springer-Verlag Berlin Heidelberg 2001), p. 555.
21. C.Y. Loh, L.S. Hultgren and P.C.E. Jorgenson, Near Field Screech Noise Computation for An Underexpanded Supersonic Jet by the CE/SE Method, AIAA Paper 2001-2252 (2001).
22. X.Y. Wang, S.C. Chang, and P.C.E. Jorgenson, Numerical Simulation of Aeroacoustic Field in a 2D Cascade Involving a Downstream Moving Grid Using the Space-Time CE/SE method, in Proceedings of the First Internationa1 Confer-ence on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Sato-fuka, (Springer-Verlag Berlin Heidelberg 2001), p. 543.
23. X.Y. Wang, S.C. Chang, A. Himansu, and P.C.E. Jorgenson, Gust Acoustic Response of A Single Airfoil Using the Space-Time CE/SE Method, AIAA Paper 2002-0801 (2002).
24. S.T. Yu and S.C. Chang, Treatments of Stiff Source Terms in Conservation Laws by the Method of Space-Time Conservation Element and Solution Element, AIAA Paper 97-0435 (1997).
25. S.T. Yu and S.C. Chang, Applications of the Space-Time Conservation Element / Solution Element Method to Unsteady Chemically Re-active Flows, " AIAA Paper 97-2099, in A Col-lection of Technical Papers, 13th AIAA CFD Conference, June 29-Julv 2, 1997, Snowmass, CO.
26. S.T. Yu, S.C. Chang, P.C.E. Jorgenson, S.J. Park and M.C. Lai, "Treating Stiff Source Terms in Conservation Laws by the SpaceTime Conservation Element and Solution Element Method, " in Proceedings of the 16th In-ternational Conference on Numerical Method in Fluid Dynamics, Arcachon, France, 6-10 July, 1998, edited by C.H. Bruneau, (Springer-Verlag Berlin Heidelberg 1998), p. 433.
27. X.Y. Wang and S.C. Chang, A 3D struc-tured/unstructured Euler solver based on the space-time conservation element and solution element method, in A Collection of Technical Papers, 14th AIAA CFD Conference, June 28-July 1, 1999, Norfolk, Virginia, AIAA Paper 99-3278.
28. N.S. Liu and K.H. Chen, Flux; An Alternative Flow Solver for the National Combustion Code, AIAA Paper 99-1079.
29. G. Cook, High Accuracy Capture of Curved Shock Front Using the Method of Conservation Element and Solution Element, AIAA Paper 99-1008.
30. S.C. Chang, Y. Wu, X.Y. Wang, and V. Yang, Local Mesh Refinement in the Space-Time CE/SE Method, in Proceedings of the First In-ternational Conference on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Satofuka, (Springer-Verlag Berlin Heidelberg 2001), p. 61.
31. S.C. Chang, Z.C. Zhang, S.T. John Yu, and P.C.E. Jorgenson, A Unified Wall Boundary Treatment for Viscous and Inviscid Flows in the CE/SE Method, in Proceedings of the First International Conference on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Satofuka, (Springer-Verlag Berlin Heiderberg 2001), p. 671.
32. Z.C. Zhang, S.T. John Yu, S.C. Chang, and P.C.E. Jorgenson, Calculations of Low-Mach-Number Viscous Flows without Preconditioning by the Space-Time CE/SE method, in Proceedings of the First International Conference on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Satofuka, (Springer-Verlag Berlin Heiderberg 2001), p. 127.
33. A. Himansu, P.C.E. Jorgenson, X.Y. Wang, and S.C. Chang, Parallel CE/SE Computational via Domain Decomposition, in Proceedings of the First International Conference on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Satofuka, (Springer-Verlag Berlin Heiderberg 2001), p. 423.
34. Y. Wu, V. Yang, and S.C. Chang, SpaceTime Method for Chemically Reacting Flows with Detailed Kinetics, in Proceedings of the First International Conference on Computational Fluid Dynamics, Kyoto, Japan, 10-14 July, 2000, edited by N. Satofuka, (Springer-Verlag Berlin Heiderberg 2001), p. 207.
35. S.C. Chang, Courant Number Insensitive CE/SE Schemes, AIAA Paper 2002-3890 (2002).
36. M. Zhang, S.T. Yu, and S.C. Chang, CFL Number Insensitive CESE Schemes For TwoDimensional Euler Equations, AIAA Paper 2003-3840 (2003).
37. Other CE/SE references are posted on: http://www.grc.nasa.gov/www/microbus.
38. B. van Leer, Toward the Ultimate Conservative Difference Scheme. IV. A New Approach to Nu-merical Convection, J, Comput, Phys, 23, 276 (1977).
39. G.D. van Albada, B. van Leer, and W.W. Robert, A Comparative Study of Computational Methods in Cosmic Gas Dynamics, Astionom. and Astrophys., 108, 76 (1982).
40. To appear in a NASA Technical Memorandum.
41. G.A. Sod, A Survey of several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws, J. Comput, Phys., 27, 1 (1978).
42. Chau-Lyan Chang, private communication.
43. Y.I. Lim, S.C. Chang, and S.B. Jorgensen, A Novel Partial Differential Algebraic Equation (PDAE) Solver: Iterative Space-Time Conservation Element/Solution Element (CE/SE) Method, submitted for publication in Comp, Chem. Eng.
44. X.Y. Wang, S.C. Chang, and P.C.E. Jorgenson, Prediction of Sound Waves Propagating through a Nozzle without/with a Shock Wave Using the Space-time CE/SE Method, AIAA Paper 2000-0222 (2000).