Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows

Journal of Computational Physics

Volumn 213, Issue 1, 2006, Pages 31-56

  Xiao, Feng ^a,b   Akoh, Ryosuke ^a   Ii, Satoshi ^a  

^a Tokyo Institute of Technology ^*  (Japan)

^b STATE KEY LABORATORY OF SEVERE WEATHER   (China)

Author keywords

Compressible and incompressible flows; Conservative scheme; Euler conservation laws; Multi dimensional simulation; Pressure projection; Shock capturing; Unified method

Indexed keywords

AERODYNAMICS; FINITE VOLUME METHOD; MACH NUMBER; METHOD OF MOMENTS;

CONSERVATION LAW; CONSERVATIVE SCHEMES; EULER CONSERVATION LAW; FINITE-VOLUME METHOD; MULTI DIMENSIONAL; MULTIDIMENSIONAL SIMULATION; PRESSURE PROJECTION; SHOCK-CAPTURING; UNIFIED METHOD; VOLUME INTEGRATED AVERAGES;

INCOMPRESSIBLE FLOW;

EID: 31744440190     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.08.002     Document Type: Article

References (31)

1. H. Bijl P. Wesseling A unified method for computing incompressible and compressible flows in boundary-fitted coordinates J. Comput. Phys. 141 1998 153
2. A. Clappier A correction method for use in multidimensional time-splitting advection algorithms: Application to two- and three-dimensional transport Mon. Weather Rev. 126 1998 223
3. A. Chorin Numerical solution of the Navier-Stokes equations Math. Comput. 22 1968 745
4. U.K. Ghia N. Ghia C.T. Shin High-Re solution for incompressible flow using the Navier-Stokes equations end a multi-grid method J. Comput. Phys. 48 1982 387
5. H. Guillard C. Viozat On the behavior of upwind schemes in the low Mach number limit Comput. Fluids 28 1999 63
6. F. Harlow E. Welch Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface Phys. Fluids 8 1965 2182
7. F. Harlow A. Amsden Numerical calculation of almost incompressible flows J. Comput. Phys. 3 1968 80
8. F. Harlow A. Amsden A numerical fluid dynamics calculation method for all flow speeds J. Comput. Phys. 8 1971 197
9. R. Issa Solution of the implicitly discretized fluid flow equations by operator-splitting J. Comput. Phys. 62 1986 40
10. R. Issa D. Gosman A. Watkins The computation of compressible and incompressible flows by a non-iterative implicit scheme J. Comput. Phys. 62 1986 66
11. C. Karki S. Patankar Pressure based calculation procedure for viscous flows at all speed in arbitrary configurations AIAA J. 27 1989 1167
12. J. Kim P. Moin Application of a fractional step method to incompressible Navier-Stokes equations J. Comput. Phys. 59 1985 308
13. B. Koren B. van Leer Analysis of preconditioning and multi-grid for Euler flows with low-subsonic regions Adv. Comput. Meth. 4 1995 127-144
14. T.G. Liu B.C. Khoo K.S. Yeo The numerical simulations of explosion and implosion in air: Use of a modified Harten's TVD scheme Int. J. Numer. Meth. Fluid 31 1999 661
15. J. McGuirk J. Page Shock capturing using a pressure correction method AIAA J. 28 1990 1751
16. W. Shyy, E. Braaten, Adaptive grid computation for inviscid compressible flows using a pressure correction method, AIAA Paper 88-3566, 1988.
17. G.A. Sod A numerical study of a converging cylindrical shock J. Fluid Mech. 83 1977 785
18. E. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics 1997 Springer Berlin
19. E. Turkel Review of preconditioning techniques for fluid dynamics Appl. Numer. Math. 21 1993 257
20. E. Turkel R. Radespiel H. Kroll Assessment of preconditioning methods for multidimensional aerodynamics Comput. Fluids 26 1997 613
21. D.R. van der Heul C. Vuik P. Wesseling A conservative pressure-correction method for flow at all speeds Comput. Fluids 32 2003 1113
22. M. Weiss A. Smith Preconditioning applied to variable and constant density flows AIAA J. 22 1995 745
23. P. Wesseling Principles of Computational Fluid Dynamics 2000 Springer Berlin
24. F. Xiao Unified formulation for compressible and incompressible flows by using multi integrated moments I: One-dimensional inviscid compressible flow J. Comput. Phys. 195 2004 629
25. F. Xiao A. Ikebata T. Hasegawa Numerical simulations of free-interface fluids by a multi integrated moment method Comput. Struct. 83 2005 409
26. F. Xiao T. Yabe Completely conservative and oscillation-less semi-Lagrangian schemes for advection transportation J. Comput. Phys. 170 2001 498
27. F. Xiao T. Yabe X. Peng H. Kobayashi Conservation and oscillation-less transport schemes based on rational functions J. Geohys. Res. 107 2002 4609
28. T. Yabe T. Aoki A universal solver for hyperbolic-equations by cubic-polynomial interpolation. 1. One-dimensional solver Comput. Phys. Commun. 66 1991 219
29. T. Yabe R. Tanaka T. Nakamura F. Xiao Exactly conservative semi-Lagrangian scheme (CIP-CSL) in one dimensionm Mon. Weather Rev. 129 2001 332
30. T. Yabe P. Wang Unified numerical procedure for compressible and incompressible fluid J. Phys. Soc. Jpn. 60 1991 2105
31. T. Yabe F. Xiao T. Utsumi The constrained interpolation profile method for multiphase analysis J. Comput. Phys. 169 2001 556