Challenge of CIP as a universal solver for solid, liquid and gas

International Journal for Numerical Methods in Fluids

Volumn 47, Issue 6-7, 2005, Pages 655-676

  Yabe, Takashi ^a   Takizawa, K ^a   Chino, M ^a   Imai, M ^a   Chu, C C ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

CIP; Fish; Mesh free; Semi Lagrangian schemes; Stone skipping

Indexed keywords

FLUIDS; LAGRANGE MULTIPLIERS; LIQUIDS; NUMERICAL METHODS; PLASMAS; SOLIDS;

CIP METHOD; COMPRESSIBLE FLUIDS; MESH-FREE SYSTEMS; SEMI-LAGRANGIAN SCHEMES;

INCOMPRESSIBLE FLOW;

INCOMPRESSIBLE FLOW; LAGRANGIAN ANALYSIS; MATHEMATICAL ANALYSIS; MODEL;

EID: 14344265531     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.830     Document Type: Review

References (32)

1. Takewaki H, Nishiguchi A, Yabe T. The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolictype equations. Journal of Computational Physics 1985; 61:261.
2. Takewaki H, Yabe T. Cubic-interpolated pseudo particle (CIP) method-application to nonlinear or multi-dimensional problems. Journal of Computational Physics 1987; 70:355.
3. Yabe T, Takei E. A new higher-order Godunov method for general hyperbolic equations. Journal of the Physical Society of Japan 1988; 57:2598.
4. Yabe T, Aoki T. A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver. Computer Physics Communications 1991; 66:219.
5. Yabe T, Ishikawa T, Wang PY, Aoki T, Kadota Y, Ikeda F. A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers. Computer Physics Communications 1991; 66:233.
6. Nakamura T, Yabe T. Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space. Computer Physics Communications 1999; 120:122.
7. Utsumi T, Yabe T, Koga J, Aoki T, Ogata Y, Matsunaga E, Sekine M. A note on the basis set approach in the constrained interpolation profile method. Journal of Computational Physics 2004; 196:1.
8. Yabe T, Mizoe H, Takizawa K, Moriki H, Im HN, Ogata Y. Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme. Journal of Computational Physics 2004; 194:57.
9. Leith CE. Numerical simulation of the Earth's atmosphere. In Methods in Computational Physics, Alder B et al. (eds), vol. 4. Academic Press: New York, 1965; 1-28.
10. Yabe T, Xiao F, Utsumi T. Constrained interpolation profile method for multiphase analysis. Journal of Computational Physics 2001; 169 556.
11. Colella P, Woodward PR. The piecewise parabolic method (PPM) for gas-dynamical simulations. Journal of Computational Physics 1984; 54:174.
12. Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 1981; 39 201.
13. Youngs DL. Time-dependent multi-material flow with large fluid distortion. In Numerical Methods for Fluids and Dynamics, Morton KW, Baines MJ (eds). 1982; 273.
14. Osher S, Sethian JA. Front propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1988; 79:12.
15. Unverdi SO, Tryggvasson GA. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics 1992; 100:25.
16. Tezduyar TE. Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering 2001; 8:83.
17. Yabe T, Xiao F. Description of complex and sharp interface during shock wave interaction with liquid drop. Journal of the Physical Society of Japan 1993; 62:2537.
18. Yabe T, Xiao F. Description of complex and sharp interface with fixed grids in incompressible and compressible fluid. Computers and Mathematics with Applications 1995; 29:15.
19. Yabe T et al. The next generation CIP as a conservative semi-Lagrangian solver for solid, liquid and gas. Journal of Computational and Applied Mathematics 2002; 149:267.
20. Chino M, Takizawa K, Yabe T. Experimental research on rotating simmer. Proceedings of FEDSM'03, 4th ASME-JSME Joint Fluids Engineering Conference FEDSM2003-45171, Honolulu, Hawaii, USA, 6-11 July 2003.
21. Clanet C, Hersen F, Bocquet L. Secrets of successful stone-skipping. Nature 2004; 427:29.
22. Yabe T, Xiao F, Zhang Y. Strategy for unified solution of solid, liquid, gas and plasmas, AIAA Paper No.99-3509, 30th AIAA Fluid Dynamics Conference, Norfolk, USA, 28 June-1 July 1999.
23. Harlow FH, Welch JE. Numerical calculation of time dependent viscous incompressible flow with free surface. Physics of Fluids 1965; 8:2182.
24. Harlow FH, Amsden AA. Numerical simulation of almost incompressible flow. Journal of Computational Physics 1968; 3:80.
25. Yabe T, Wang PW. Unified numerical procedure for compressible and incompressible fluid. Journal of the Physical Society of Japan 1991; 60:2105.
26. Xiao F et al. An efficient model for driven flow and application to a gas circuit breaker. Computer Modelling and Simulation Engineering 1996; 1:235.
27. Yabe T. Simulation of laser-induced melting and evaporation dynamics by the unified solver CIP for solid, liquid and gas. In Mathematical Modeling of Weld Phenomena 4, Cerjak H (ed.). The University Press: Cambridge, 1998; 26-36.
28. Wang PY, Yabe T, Aoki T. A general hyperbolic solver-the CIP method-applied to curvilinear coordinate. Journal of the Physical Society of Japan 1993; 62:1865.
29. Aoki T. Multi-dimensional advection of CIP (cubic-interpolate propagation) scheme. CFD Journal 1995; 4:279.
30. Nishiguchi A, Yabe T. Second order fluid particle scheme. Journal of Computational Physics 1983; 52:390.
31. Zalesak ST. Fully multidimensional flux-corrected transport algorithm for fluids. Journal of Computational Physics 1979; 31:335.
32. Berger MJ, Oliver J. Adaptive mesh refinement for hyperbolic partial differential equations. Journal of Computational Physics 1984; 53:484.