Challenge of CIP as a universal solver for solid, liquid and gas
Corresponding Author
T. Yabe
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan===Search for more papers by this authorK. Takizawa
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Search for more papers by this authorM. Chino
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Search for more papers by this authorM. Imai
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Search for more papers by this authorC. C. Chu
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Search for more papers by this authorCorresponding Author
T. Yabe
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan===Search for more papers by this authorK. Takizawa
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Search for more papers by this authorM. Chino
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Search for more papers by this authorM. Imai
Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Search for more papers by this authorC. C. Chu
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Search for more papers by this authorAbstract
We review some recent progress of the CIP method that is known as a general numerical solver for solid, liquid, gas and plasmas. This method is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. Some applications to skimmer, swimming fish and laser cutting are presented. This method is recently extended to almost mesh-free system that is called ‘soroban grid’ that ensures the third-order accuracy both in time and space with the help of the CIP method. Copyright © 2005 John Wiley & Sons, Ltd.
REFERENCES
- 1 Takewaki H, Nishiguchi A, Yabe T. The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type 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, B Alder 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, KW Morton, MJ Baines (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.
10.1016/0021-9991(68)90007-7 Google Scholar
- 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, H Cerjak (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.
Citing Literature
Special Issue on Advances and Challenges in Flow Simulation and Modelling
28 February ‐ 10 March 2005
Pages 655-676