Time-derivative preconditioning methods for multicomponent flows-part I: Riemann problems

Journal of Applied Mechanics, Transactions ASME

Volumn 76, Issue 2, 2009, Pages 1-13

  Housman, Jeffrey A ^a   Kiris, Cetin C ^b   Hafez, Mohamed M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NASA AMES RESEARCH CENTER   (United States)

Author keywords

Dual time stepping; Hybrid conservative nonconservative method; Split coefficient matrix (SCM) method; Time derivative preconditioning methods

Indexed keywords

CHARACTERISTIC-BASED METHOD; COEFFICIENT MATRIX; COMPONENT INTERFACES; DENSITY RATIO; DUAL TIME STEPPING; EXACT SOLUTION; FLUID INTERFACE; HYBRID APPROACH; HYBRID CONSERVATIVE/NONCONSERVATIVE METHOD; HYBRID FORMULATIONS; HYBRID METHOD; INCOMPRESSIBLE LIMIT; INDEPENDENT STABILITY; LARGE DENSITY RATIO; LOW SPEED; MULTICOMPONENT FLOW; MULTICOMPONENTS; NUMERICAL SIMULATION; PRECONDITIONING METHOD; RIEMANN PROBLEM; ROE METHOD; SOLUTION STRATEGY; STABILITY PROBLEM; SYSTEM OF EQUATIONS; TIME MARCHING; TIME STEP; VELOCITY OSCILLATIONS; WEAK SOLUTION;

AIR; COMPRESSIBLE FLOW; COMPUTER SIMULATION; FLUIDITY; MULTIPHASE FLOW; NUMBER THEORY; PHASE INTERFACES; SYSTEM STABILITY;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77955253955     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3072905     Document Type: Article

References (40)

1. Kiris, C., Kwak, D., Chan, W., and Housman, J., 2008, "High Fidelity Simulations for Unsteady Flow Through Turbopumps and Flowliners,"Comput. Fluids, 37, pp. 536-546.
2. Kiris, C., Chan, W., Kwak, D., and Housman, J., "Time-Accurate Computational Analysis of the Flame Trench,"ICCFD5, Seoul, Korea, Jul. 7-11.
3. J. Housman, C. Kiris, and M. Hafez, "Preconditioned Methods for Simulations of Low Speed Compressible Flows,"Comput. Fluids (to be published).
4. Merkle, C. L., and Choi, Y. H., 1985, "Computation of Low Speed Compressible Flows With Time-Marching Methods,"Int. J. Numer. Methods Eng., 25, pp. 292-311.
5. Turkel, E., 1987, "Preconditioning Methods for Solving Incompressible and Low-Speed Compressible Equations,"J. Comput. Phys., 72, pp. 277-298.
6. Karni, S., 1994, "Multicomponent Flow Calculations by a Consistent Primitive Algorithm,"J. Comput. Phys., 112, pp. 31-43.
7. Abgrall, R., 1996, "How to Prevent Pressure Oscillations in Multicomponent Flows,"J. Comput. Phys., 125, pp. 150-160.
8. Karni, S., 1996, "Hybrid Multifluid Algorithms,"SIAM J. Sci. Comput. (USA), 17, pp. 1019-1039.
9. Jenny, P., Muller, B., and Thomann, H., 1997, "Correction of Conservative Euler Solvers for Gas Mixtures,"J. Comput. Phys., 132, pp. 91-107.
10. Abgrall, R., and Karni, S., 2001, "Computations of Compressible Multifluids,"J. Comput. Phys., 169, pp. 594-623.
11. Chakravarthy, S. R., Anderson, D. A., and Salas, M. D., 1980, "The Split-Coefficient Matrix Method for Hyperbolic Systems of Gas Dynamics,"18th AIAA Aerospace Sciences Meeting, Paper No. AIAA-80-0268.
12. Wren, G. P., Ray, S. E., Aliabadi, S. K., and Tezduyar, T. E., 1997, "Simulation of Flow Problems With Moving Mechanical Components, Fluid-Structure Interactions and Two-Fluid Interfaces,"Int. J. Numer. Methods Fluids, 24, pp. 1433-1448.
13. Chorin, A. J., 1967, "A Numerical Method for Solving Incompressible Viscous Flow Problems,"J. Comput. Phys., 2, pp. 12-26.
14. Kwak, D., Chang, J., Shanks, S., and Chakravarthy, S. R., 1986, "A Three-Dimensional Incompressible Navier-Stokes Solver Using Primitive Variables,"AIAA J., 24, pp. 390-396.
15. Merkle, C. L., and Athavale, M., 1987, "Time-Accurate Unsteady Incompressible Flow Algorithms Based on Artificial Compressibility,"AIAA Paper No. 87-1137.
16. Rogers, S. E., Kwak, D., and Kiris, C., 1989, "Numerical Solution of the Incompressible Navier-Stokes Equations for Steady-State and Time-Dependent Problems,"27th AIAA Aerospace Sciences Meeting, Reno, NV, Paper No. AIAA-89-0463.
17. Rehm, R. G., and Baum, H. R., 1978, "The Equations of Motion for Thermally Driven Buoyant Flows,"J. Res. Natl. Bur. Stand., 83, pp. 297-308.
18. Klainerman, S., and Majda, A., 1981, "Singular Limits of Quasilinear Hyperbolic Systems With Large Parameters and the Incompressible Limit of Compressible Fluids,"Commun. Pure Appl. Math., 34, pp. 481-524.
19. Klainerman, S., and Majda, A., 1982, "Compressible and Incompressible Fluids,"Commun. Pure Appl. Math., 35, pp. 629-653.
20. Briley, W. R., McDonald, H., and Shamroth, S. J., 1983, "A Low Mach Number Euler Formulation and Application to Time-Iterative LBI Schemes,"AIAA J., 21, pp. 1467-1469.
21. Viviand, H., 1985, "Pseudo-Unsteady Systems for Steady Inviscid Calculations,"Numerical Methods for the Euler Equations of Fluid Dynamics, F. Angrand et al., eds., SIAM, Philadelphia, PA.
22. Guerra, J., and Gustafsson, B., 1986, "A Numerical Method for Incompressible and Compressible Flow Problems With Smooth Solutions,"J. Comput. Phys., 63, pp. 377-397.
23. Lindau, J. W., Kunz, R. F., Venkateswaran, S., and Merkle, C. L., 2001, "Development of a Fully-Compressible Multi-Phase Reynolds-Averaged Navier-Stokes Model,"15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, Paper No. AIAA-2001-2648.
24. Edwards, J. R., 2001, "Toward Unified CFD Simulation of Real Fluid Flows,"15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, Paper No. AIAA-2001-2524.
25. Li, D., Venkateswaran, S., Lindau, J. W., and Merkle, C. L., 2005, "A Unified Computational Formulation for Multi-Component and Multi-Phase Flows,"43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. AIAA-2005-1391.
26. Edwards, J. R., and Liou, M.-S., 2006, "Simulation of Two-Phase Flows Using Low-Diffusion Shock-Capturing Schemes,"44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. AIAA-2006-1288.
27. Neaves, M. D., and Edwards, J. R., 2006, "All-Speed Time-Accurate Underwater Projectile Caculations Using a Precoditioned Algorithm,"ASME J. Fluids Eng., 128, pp. 284-296.
28. McDaniel, K. S., Edwards, J. R., and Neaves, M. D., 2006, "Simulation of Projectile Penetration Into Water and Sand,"44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. AIAA-2006-1289.
29. Housman, J., 2007, "Time-Derivative Preconditioning Method for Multicomponent Flow,"Ph.D. thesis, University of California Davis, Davis, CA.
30. Lax, P. D., and Wendroff, B., 1960, "Systems of Conservation Laws,"Commun. Pure Appl. Math., 13, pp. 217-237.
31. Moretti, G., 1979, "The Lambda-Scheme,"Comput. Fluids, 7, pp. 191-205.
32. van Leer, B., Lee, W. T., and Roe, P. L., 1991, "Characteristic Time-Stepping or Local Preconditioning of the Euler Equations,"AIAA Computational Fluid Dynamics Conference, Honolulu, HI, Paper No. AIAA-91-1552-CP.
33. Roe, P. L., 1981, "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,"J. Comput. Phys., 43, pp. 357-372.
34. Lombard, C. K., Bardina, J., Vankatapathy, E., and Oliger, J., 1983, "Multi-Dimensional Formulation of CSCM-An Upwind Flux Difference Eigenvector Split Method for the Compressible Navier-Stokes Equations,"Sixth AIAA Computational Fluid Dynamics Conference, Danvers, MA, Paper No. AIAA-83-1895.
35. Daywitt, J. E., Szostowski, D. J., and Anderson, D. A., 1983, "A Split-Coefficient/Locally Monotonic Scheme for Multishocked Supersonic Flow,"AIAA J., 21, pp. 871-880.
36. Harabetian, E., and Pego, R., 1993, "Nonconservative Hybrid Shock Capturing Schemes,"J. Comput. Phys., 105, pp. 1-13.
37. Toro, E. F., 1995, "On Adaptive Primitive-Conservative Schemes for Conservation Laws,"Sixth International Symposium on Computational Fluid Dynamics: A Collection of Technical Papers, Vol. 3, M. M. Hafez, ed., pp. 1288-1293.
38. Quirk, J. J., 1993, "Godunov-Type Schemes Applied to Detonation Flows,"NASA/ICASE Contractor Report No. 191447.
39. Ivings, M. J., Causon, D. M., and Toro, E. F., 1997, "On Hybrid High Resolution Upwind Methods for Multicomponent Flows,"Z. Angew. Math. Mech., 77, pp. 645-668.
40. Chang, C.-H., and Liou, M.-S., 2005, "A Conservative Compressible Multifluid Model for Multiphase Flow: Shock-Interface Interaction Problems,"17th AIAA Computational Fluid Dynamics Conference, Paper No. AIAA 2005-5344.