Review of numerical computation of compressible flows with artificial interfaces

Computers and Fluids

Volumn 36, Issue 10, 2007, Pages 1657-1679

  Wu, Zi Niu ^a   Xu, Shan Shu ^a   Gao, Bo ^a   Zhuang, Li Shen ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; COMPUTATIONAL GEOMETRY; GRID COMPUTING; NUMERICAL METHODS; PARALLEL PROCESSING SYSTEMS; SHOCK WAVES;

ARTIFICIAL INTERFACE; OVERLAPPING GRID INTERFACE;

COMPUTATIONAL FLUID DYNAMICS;

COMPRESSIBLE FLOW; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL GEOMETRY; GRID COMPUTING; NUMERICAL METHODS; PARALLEL PROCESSING SYSTEMS; SHOCK WAVES;

EID: 34548506265     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2007.03.001     Document Type: Article

References (92)

1. Rai M.M. A conservative treatment of zonal boundaries for Euler equation calculations. J Comput Phys 62 (1986) 472-503
2. Rai M.M. A implicit, conservative, zonal-boundary scheme for Euler equation calculations. Comput Fluids 14 (1986) 295-319
3. Enander R. Analysis of a grid patching technique. Uppsala University, Department of Scientific Computing, Report No. 112, March, 1990.
4. Gustafsson B, The Euler and Navier-Stokes equations. Wellposedness, stability and composite grids. Computational Fluid Dynamics, von Karman Institute for Fluid Dynamics, Lecture Series 1991-01, 18-22, FEB, 1991.
5. Lerat A., and Wu Z.N. Stable conservative multidomain treatments for implicit Euler solvers. J Comput Phys 123 (1996) 45-64
6. Catalano L.A., Depalma P., Napolitano M., et al. Cell-vertex adaptive euler method for cascade flows. AIAA J 33 12 (1995) 2299-2304
7. Thakur S., Wright J., Wei S.Y., et al. Development of pressure-based composite multigrid methods for complex fluid flows. Prog Aerosp Sci 32 4 (1996) 313-375
8. Wang T.S. Analysis of linear aerospike plume-induced X-33 base-heating environment. J Spacecr Rockets 36 6 (1999) 777-783
9. Kwon H.B., Jang K.H., Kim Y.S., et al. Nose shape optimization of high-speed train for minimization of tunnel sonic boom. JSME Int J Ser C Mech Syst Mach Elem Manuf 44 3 (2001) 890-899
10. Kwon H.B., Kim T.Y., Lee D.H., et al. Numerical simulation of unsteady compressible flows induced by a high-speed train passing through a tunnel. Proc Inst Mech Eng, F J Rail Rapid Transit 217 2 (2003) 111-124
11. Steger J.L., and Benek J.A. On the use of composite grid schemes in computational aerodynamics. Comput Methods Appl Mech Eng 64 (1987) 301-320
12. Chesshire G., and Henshaw D. Composite overlapping meshes for the solution of partial differential equations. J Comput Phys 90 (1990) 1-64
13. Gustafsson B. The Euler and Navier-Stokes equations. Wellposedness, stability and composite grids. Computational Fluid Dynamics, von Karman Institute for Fluid Dynamics, Lecture Series 1991-01, 18-22, FEB, 1991.
14. Sherer S.E., and Scott J.N. High-order compact finite-difference methods on general overset grids. J Comput Phys 210 2 (2005) 459-496
15. Thuné M. Stability of difference approximations of hyperbolic systems on substructured domains. Uppsala University, Department of Scientific Computing, Report No. 106, DEC, 1986.
16. Pärt-Enander E, Sjögreen B. Shock waves and overlapping grids. Uppsala University, Department of Scientific Computing, Report No. 131, JAN, 1991.
17. Pärt-Enander E., and Sjögreen B. Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems. Comput Fluids 23 (1994) 551-574
18. Berger M. On conservation at grid interfaces. SIAM J Numer Anal 24 (1987) 967-983
19. Wang Z.J. A fully conservative interface algorithm for overlapping grids. J Comput Phys 112 (1995) 96-106
20. Tang H.S., and Zhou T. On nonconservative algorithms for grid interfaces. SIAM J Numer Anal 37 1 (1999) 173-193
21. Wu Z.N. Steady and unsteady shock waves on overlapping grids. SIAM J Sci Comput 20 (1999) 1850-1874
22. Wu Z.N. Transmission of a slowly moving shock across a nonconservative interface. J Comput Phys 171 2 (2001) 579-615
23. Wu Z.N. Convergence study of an implicit multidomain method for compressible flow computations. Comput Fluids 25 (1996) 181-196
24. Wu Z.N. Uniqueness of steady state solutions for difference equations on overlapping grids. SIAM J Numer Anal 33 (1996) 1336-1357
25. Wang LX, Caughey D. Multiblock/multigrid Euler method to simulate 2D and 3D compressible flow. AIAA Paper, 93-0332, 1993.
26. Gee K, Rizk YM, Murmann SM, Lanser WR, Meyer LR, Schiff LB. Analysis of pnenmatic forebody flow control concept about a full aircraft geometry. AIAA Paper, 92-2678-cp, 1992.
27. Sides J., Pahlke K., and Costes M. Numerical simulation of flows around helicopters at DLR and ONERA. Aerosp Sci Technol 5 (2001) 35-53
28. Lijewski L.E., and Suhs N.E. Time-accurate computational fluid-dynamics approach to transonic store separation trajectory prediction. J Aircraft 31 (1994) 886-891
29. Croba D., and Kueny J.L. Numerical calculation of 2D, unsteady flow in centrifugal pumps: impeller and volute interaction. Int J Numer Methods Fl 22 (1996) 467-481
30. RenzoniP P., D'Alascio A., Kroll N., et al. EROS - a common European Euler code for the analysis of the helicopter rotor flowfield. Prog Aerosp Sci 36 5-6 (2000) 437-485
31. Zheng Y., and Liou M.S. A novel approach of three-dimensional hybrid grid methodology: Part 1. Grid generation. Comput Methods Appl Mech Eng 192 37-38 (2003) 4147-4171
32. Cinnella P., Palma P.D., Pascazio G., et al. A numerical method for turbomachinery aeroelasticity. J Turbomach 126 2 (2004) 310-316
33. Henshaw W.D., and Schwendeman D.W. Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow. J Comput Phys 216 2 (2006) 744-779
34. Keyes DE. Domain decomposition: a bridge between nature and parallel computers. ICASE Report No. 92-44, 1992.
35. Roose D, Driessche RV. Parallel computers and parallel algorithms for CFD: an introduction. AGARD-R-807, 1-23, 1995.
36. Chan TF, Goovearts D, Schwartz S. Overlapping versus non-overlapping domain decomposition. Technical Reports, CAM 88-21, UCLA, 1988.
37. Wang H. A parallel solver for tridiagonal solvers. ACM Trans Math Softw 7 (1981) 170-183
38. Kuznetsov Y. New algorithms for approximate realization of implicit difference scheme. Sov J Numer Math Modell 3 (1988) 99-114
39. Wu Z.N., and Zou H. Grid overlapping for implicit parallel computations of compressible flows. J Comput Phys 157 (2000) 2-43
40. Wu Z.N., and Zou H. Efficient parallel method for implicit upwind schemes approximating the Euler equations in gas dynamics. J Comput Phys 187 2 (2003) 683-715
41. Sawley M.L., and Tegnér J.K. A comparison of parallel programming models for multiblock flow computations. J Comput Phys 122 (1995) 280-290
42. Kim C.S., Kim C., and Rho O.H. Parallel computations of high-lift airfoil flows using two-equation turbulence models. AIAA J 38 8 (2000) 1360-1368
43. Rokicki J., Drikakis D., Majewski J., et al. Parallel performance of Chimera overlapping mesh technique. Lect Notes Comput Sci 1593 (1999) 1015-1024
44. Prewitt N.C., Belk D.M., and Shyy W. Parallel computing of overset grids for aerodynamic problems with moving objects. Prog Aerosp Sci 36 2 (2000) 117-172
45. Bird G.A. Molecular gas dynamics and the direct simulation of gas flows (1994), Clarendon Press, Oxford
46. Cercignani C. Rarefied gas dynamics: from basic concepts to actual calculations (2000), Cambridge University Press
47. Wadsworth DC, Erwin DA. One-dimensional hybrid continuum/particle simulation approach for rarefied hypersonic flows. AIAA paper 90-1690, 1990.
48. Wadsworth DC, Erwin DA. Two-dimensional hybrid continuum/particle simulation approach for rarefied flows. AIAA paper 92-2975, 1992.
49. Hash D.B., and Hassan H.A. Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods. J Thermophys Heat Transfer 10 (1996) 242-249
50. Hash DB, Hassan HA. Two-dimensional coupling issues of hybrid DSMC/Navier-Stokes solvers. AIAA paper, 97-2507, 1997.
51. Roveda R., Goldstein D.B., and Varghese P.L. Hybrid Euler/particle approach for continuum/rarefied flows. J Spacecr Rockets 35 3 (1998) 258-265
52. Roveda R., Goldstein D.B., and Varghese P.L. Hybrid Euler/direct simulation Monte Carlo calculation of unsteady slit flow. J Spacecr Rockets 37 6 (2000) 753-760
53. Garcia A.L., Bell J.B., Crutchfield W.Y., and Alder B.J. Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J Comput Phys 154 (1999) 134-155
54. Aktas O., and Aluru N.R. A combined continuum/DSMC technique for multiscale analysis of microfluidics filters. J Comput Phys 178 (2002) 342-372
55. Wang WL, Boyd ID. Hybrid DSMC-CFD Simulations of hypersonic flow over sharp and blunted bodies. AIAA 2003-3644, 2003.
56. Sun Q., Boyd I.D., and Candler G.V. A hyprid continuum/particle approach for modeling subsonic, rarefied gas flows. J Comput Phys 194 (2004) 256-277
57. Schwartzentruber T.E., and Boyd I.D. A hybrid particle-continuum method applied to shock waves. J Comput Phys 215 (2006) 402-416
58. Lian YY, Wu JS, Cheng G, Koomullil R. Development of a parallel hybrid method for the DSMC and NS solver. AIAA 2005-435, 2005.
59. Ladeinde F, Cai X, Agarwal R. Stability of higher-order continuum (HOC) equations for hybrid HOC/DSMC solvers. ADA445985, 2005.
60. Titov EV, Zeifman M, Levin DA. Application of the kinetic and continuum techniques to the multi-scale flows in MEMS devices. AIAA 2005-1399, 2005.
61. Papp JL, Yellin KA, Dash SM. Plume and divert jet effects on missile flowfields at higher altitudes. 42nd AIAA Aerospace Sciences Meeting and Exhibit; 2004. p. 6913-25.
62. Hadjiconstantinou N.G. Hybrid atomistic-continuum formulations and the moving contact-line problem. J Comput Phys 154 (1999) 245-265
63. Nedea S.V., Frijns A.J.H., Steenhoven A.A.V., Markvoort A.J., and Hilbers P.A.J. Hybrid method coupling molecular dynamics and Monte Carlo simulations to study the properties of gases in microchannels and nanochannels. Phys Rev E 72 (2005) 016705
64. Bourgat J.F., Tallec P.L., and Tidriri M.D. Coupling Boltzmann and Navier-Stokes equations by friction. J Comput Phys 127 (1996) 227-245
65. Tallec P.L., and Mallinger F. Coupling Boltzmann and Navier-Stokes equations by half fluxes. J Comput Phys 136 (1997) 51-67
66. Guermond J.L., Huberson S., and Shen W.Z. Simulation of 2D external viscous flows by means of a domain decomposition method. J Comput Phys 108 (1993) 343-352
67. Cottet G.H., and Koumoutsakos P.D. Vortex methods: theory and practice (2000), Cambridge University Press
68. Chorin A.J. Numerical study of slightly viscous flow. J Fluid Mech 57 (1973) 785-796
69. Fedkiw R.P., Aslam T., and Xu S. The ghost fluid method for deflagration and detonation discontinuities. J Comput Phys 154 (1999) 393-427
70. Fedkiw R.P., Aslam T., Merriman B., and Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows. J Comput Phys 152 (1999) 457-492
71. Fedkiw R.P. Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method. J Comput Phys 175 (2002) 200-224
72. Hui W.H., Li P.Y., and Li Z.W. A unified coordinate system for solving the two-dimensional Euler equations. J Comput Phys 153 (1999) 596-637
73. Hui W.H., and Koudriakov A. A unified coordinate system for solving the three-dimensional Euler equations. J Comput Phys 172 (2001) 235-260
74. Hui WH, Wu ZN, Gao B. Preliminary extension of the unified coordinate system approach to computation of viscous flows. J Scientific Comput, in press.
75. Starius G. On composite mesh difference methods for hyperbolic differential equations. Numer Math 35 (1980) 241-255
76. Gustafsson B., Kreiss H.O., and Sundström A. Stability theory of difference approximations for mixed initial-boundary value problems II. Math Comput 26 (1972) 649-686
77. Ciment M. Stable difference schemes with uneven mesh spacings. Math Comput 114 (1971) 219-226
78. Ciment M. Stable matching of difference schemes. Math Comput 9 (1972) 695-701
79. Lax P., and Wendroff B. System of conservation laws. Commun Pure Appl Math XIII (1960) 217-237
80. Engquist B., and Gustafsson B. Steady state computations for wave propagation problems. Math Comput 49 (1987) 39-64
81. Nordström J. The influence of open boundary conditions on the convergence to steady state for the Navier-Stokes equations. J Comput Phys 85 (1989) 210-244
82. Gustafsson B. The choice of numerical boundary conditions for hyperbolic systems. J Comput Phys 48 (1982) 270-283
83. Wagner W. A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation. J Stat Phys 66 (1992) 1011-1044
84. Boyd ID, Chen G, Cander GV. Predicting the failure of the continuum fluid equations in transitional hypersonic flows. AIAA Paper, 94-2352, 1994.
85. Wang W.L., and Boyd I.D. Predicting continuum breakdown in hypersonic viscous flows. Phys Fluids 15 (2003) 91-100
86. Bird G.A. Breakdown of transitional and rotational equilibrium in gaseous expansions. AIAA J 8 (1970) 1998
87. Tiwari S. Coupling the Boltzmann and Euler equations with automatic domain decomposition. J Comput Phys 144 (1998) 710-726
88. Hash DB, Hassan HA. A decoupled DSMC/Navier-Stokes analysis of transitional flow. AIAA Paper, 96-0353, 1996.
89. Sun Q., and Boyd I.D. Evaluation of macroscopic properties in the direct simulation Monte Carlo method. J Thermophys Heat Transfer 19 3 (2005) 329-335
90. Fan J., and Shen C. Statistical simulation of low-speed rarefied gas flows. J Comput Phys 167 (2001) 393-412
91. Sun Q., and Boyd I.D. A direct simulation method for subsonic, microscale gas flows. J Comput Phys 179 (2002) 400-425
92. Garcia A.L., and Alder B.J. Generation of the Chapman-Enskog distribution. J Comput Phys 140 (1998) 66-70