The Constrained Interpolation Profile Method for Multiphase Analysis

Journal of Computational Physics

Volumn 169, Issue 2, 2001, Pages 556-593

  Yabe, Takashi ^a   Xiao, Feng ^a,c   Utsumi, Takayuki ^b,c  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b JAPAN ATOMIC ENERGY AGENCY   (Japan)

^c JAPAN AGENCY FOR MARINE EARTH SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Fluid dynamics; Interface capturing; Mass conservation; Multiphase flows; Numerical algorithm; Rheological materials; Semi Lagrangian schemes; Surface tension

Indexed keywords

ELASTOPLASTICITY; INCOMPRESSIBLE FLOW; INTERPOLATION; LAGRANGE MULTIPLIERS; LIQUEFIED GASES; NUMERICAL METHODS; PHASE INTERFACES;

CONSTRAINED INTERPOLATION PROFILES; FLUID-DYNAMICS; INTERFACE-CAPTURING; MASS CONSERVATION; MULTIPHASES; NUMERICAL ALGORITHMS; NUMERICAL SOLVERS; PROFILE METHOD; RHEOLOGICAL MATERIAL; SEMI-LAGRANGIAN SCHEME;

SURFACE TENSION;

EID: 0001531042     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6625     Document Type: Article

References (74)

1. Amsden A. A., Harlow F. H. A simplified MAC technique for incompressible fluid flow calculations. J. Comput. Phys. 6:1970;322.
2. Aoki T. Multi-dimensional advection of CIP (cubic-interpolated propagation) scheme. CFD J. 4:1995;279.
3. Bell J. B., Marcus D. L. A second-order projection method for variable-density flows. J. Comput. Phys. 101:1992;334.
4. Bermejo R., Staniforth A. The conversion of semi-Lagrangian advection schemes to quasi-monotone schemes. Mon. Weather Rev. 120:1992;2622.
5. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 100:1992;335.
6. Colella P., Woodward P. R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54:1984;174.
7. Ghia U., Ghia K. N., Shin C. T. High-resolution for incompressible flow using the Navier-Stokes equations and a multi-grid method. J. Comput. Phys. 48:1982;387.
8. Harlow F. H., Shannon J. P. The splash of a liquid drop. J. Appl. Phys. 38:1967;3855.
9. Harlow F. H., Amsden A. A. Numerical simulation of almost incompressible flow. J. Comput. Phys. 3:1968;80.
10. Harlow F. H., Welch J. E. Numerical calculation of time-dependent viscous incompressible flow with free surface. Phys. Fluids. 8:1965;2182.
11. Hirt C. W., Nichols B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39:1981;201.
12. Issa R. I. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62:1985;40.
13. D. Jacqmin, A variational approach to deriving smeared interface surface tension models, in, Barriers and Challenges in CFD, edited by, V. Venkatakrishnan, et al., Kluwer Academic, Dordrecht/Norwell, MA, 1998, p, 231.
14. Karki K. C., Patankar S. V. Pressure-based calculation procedure for viscous flows at all speeds in arbitrary configurations. AIAA J. 27:1989;1167.
15. Karni S. Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112:1994;31.
16. Kothe D. B., Rider W. J., Mosso S. J., Brock J. S. Volume tracking of interfaces having surface tension in two and three dimensions. 1996.
17. Kudoh T., Matsumoto R., Shibata K. Magnetically driven jets from accretion disks. III. 2.5-dimensional nonsteady simulations for thick disk case. Astrophys. J. 508:1998;186.
18. C. E. Leith, Numerical simulation of the earth's atmosphere, in, Methods in Computational Physics, Vol. 4, edited by, B. Alder, et al., Academic Press, New York, 1965, p, 1.
19. McMaster W. H. 1984 Computer codes for fluid-structure interactions. 1984.
20. Mutsuda H., Yasuda T. Physical mechanism based on numerical simulations of strongly turbulent air-water mixing layer within surf-zone. Proceedings 27th Int. Conf. on Coastal Eng., Sydney. 1999.
21. Nakamura T., Yabe T. Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space. Comput. Phys. Commun. 120:1999;122.
22. Von Neumann J., Richtmyer R. D. A method for the numerical calculation of the hydrodynamic shocks. J. Appl. Phys. 21:1950;232.
23. Ogata Y., Yabe T. Shock capturing with improved numerical viscosity in primitive Euler representation. Comput. Phys. Commun. 119:1999;179.
24. Osher S., Sethian J. A. Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79:1988;12.
25. Pan Y., Banerjee S. Numerical simulation of particle interactions with wall turbulence. Phys. Fluids. 8:1996;2733.
26. Pan Y., Banerjee S. Numerical investigation of the effects of large particles on wall-turbulence. Phys. Fluids. 9:1997;3786.
27. Patanker S. V. Numerical Heat Transfer and Fluid Flow. 1980.
28. Patanker S. V., Spalding D. B. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer. 15:1972;1787.
29. Peng D., Merriman B., Osher S., Zhao H. K., Kang M. A PDE-based fast local level-set method. J. Comput. Phys. 155:1999;410.
30. Peskin C. S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25:1977;220.
31. Peskin C. S., McQueen D. M. A three-dimensional computational model for blood flow in the heart. I. Immersed elastic fibers in viscous incompressible fluid. J. Comput. Phys. 81:1989;372.
32. Puckett E. G., Almgren A. S., Bell J. B., Marcus D. L., Rider W. J. A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys. 130:1997;269.
33. Puckett E. G., Saltzman J. S. A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics. Physica D. 60:1992;84.
34. Purnell D. K. Solution of the advective equation by upstream interpolation with a cubic spline. Mon. Weather Rev. 104:1975;42.
35. Rider W. J., Kothe D. B. Stretching and Tearing Interface Tracking Methods. 1995.
36. Shapiro S. L., Teukolsky S. A. Black Holes, White Dwarfs, and Neutron Stars. 1983.
37. Staniforth A., Côtè J. Semi-Lagrangian integration scheme for atmospheric model - A review. Mon. Weather Rev. 119:1991;2206.
38. Sussman M., Smereka P., Osher S. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114:1994;146.
39. Sweby P. K. High-resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21:1984;995.
40. Takewaki H., Nishiguchi A., Yabe T. The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations. J. Comput. Phys. 61:1985;261.
41. Takewaki H., Yabe T. Cubic-interpolated pseudo particle (CIP) method - application to nonlinear or multi-dimensional problems. J. Comput. Phys. 70:1987;355.
42. Tanaka R., Nakamura T., Yabe T., Wu H. A class of conservative formulation of the CIP method. CFD J. 8:1999;1.
43. Tanaka R., Nakamura T., Yabe T. Constructing an exactly conservative scheme in a non-conservative form. Comput. Phys. Commun. 126:2000;232.
44. Toro E. T. Riemann Solvers and Numerical Methods for Fluid Dynamics. 1997.
45. Unverdi S. O., Tryggvasson G. A. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100:1992;25.
46. Utsumi T., Kunugi T., Aoki T. Stability and accuracy of the cubic interpolated propagation scheme. Comput. Phys. Commun. 101:1996;9.
47. Wakisaka T., Takeuchi S., Chung J. H. A numerical study on the mixture formation process in fuel injection engines by means of the CIP method. CFD J. 8:1999;82.
48. Wang P. Y., Yabe T., Aoki T. A general hyperbolic solver - the CIP method - applied to curvilinear coordinates. J. Phys. Soc. Japan. 62:1993;1865.
49. Wilkins M. L. Use of artificial viscosity in multidimensional fluid dynamic calculations. J. Comput. Phys. 36:1980;281.
50. Wilkins M. L. Computer Simulation of Dynamic Phenomena. 1999.
51. Williamson D. L., Rasch P. J. Two-dimensional semi-Lagrangian transport with shape-preserving interpolation. Mon. Weather Rev. 117:1989;102.
52. Woodward P. R., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:1984;115.
53. Xiao F. Numerical Scheme for Advection Equation and Multi-Layered Fluid Dynamics. 1996.
54. Xiao F., Yabe T., Ito T. Constructing an oscillation-preventing scheme for the advection equation by a rational function. Comput. Phys. Commun. 93:1996;1.
55. Xiao F., Yabe T., Nizam G., Ito T. Constructing a multi-dimensional oscillation-preventing scheme for the advection equation by a rational function. Comput. Phys. Commun. 94:1996;103.
56. Xiao F. An Efficient model for driven flow and application to a gas circuit breaker. Comput. Model. Sim. Eng. 1:1996;235.
57. Xiao F., Yabe T., Ito T., Tajima M. An algorithm for simulating solid objects suspended in stratified flow. Comput. Phys. Commun. 102:1997;147.
58. Xiao F., Yabe T. Computation of complex flows containing rheological bodies. CFD J. 8:1999;43.
59. Xu X., Nadim A. Deformation and orientation of an elastic slender body sedimenting in viscous liquid. Phys. Fluids. 6:1994;2889.
60. Yabe T., Takei E. A new higher-order Godunov method for general hyerbolic equations. J. Phys. Soc. Japan. 57:1988;2598.
61. Yabe T., Aoki T. A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver. Comput. Phys. Commun. 66:1991;219.
62. Yabe T., Ishikawa T., Wang P. Y., Aoki T., Kadota Y., Ikeda F. A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers. Comput. Phys. Commun. 66:1991;233.
63. Yabe T., Wang P. Y. Unified numerical procedure for compressible and incompressible fluid. J. Phys. Soc. Japan. 60:1991;2105.
64. Yabe T., Xiao F. Description of complex and sharp interface during shock wave interaction with liquid drop. J. Phys. Soc. Japan. 62:1993;2537.
65. Yabe T., Xiao F. Description of complex and sharp interface with fixed grids in incompressible and compressible fluid. Computer Math. Applic. 29:1995;15.
66. Yabe T. Interface capturing and universal solution of solid, liquid and gas by CIP method. Proceedings Conf. High-Performance Computing on Multi-phase Flow. 1997.
67. Yabe T., Zhang Y., Xiao F. A numerical procedure - CIP - to solve all phases of matter together. Lecture Note in Physics. 1998;439.
68. T. Yabe, 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, edited by, H. Cerjak, cambridge Univ. Press, Cambridge, U.K, 1998, p, 26.
69. Yabe T., Xiao F., Zhang Y. Strategy for unified solution of solid, liquid, gas and plasmas. 1999.
70. Yoon S. Y., Yabe T. The unified simulation for incompressible and compressible flow by the predictor-corrector scheme based on the CIP method. Comput. Phys. Commun. 119:1999;149.
71. D. L. Youngs, Time-dependent multi-material flow with large fluid distortion, in, Numerical Methods for Fluid Dynamics, edited by, K. W. Morton and M. J. Baines, Academic Press, New York, 1982, p, 273.
72. Zhang Y., Yabe T. Effect of ambient gas on three-dimensional breakup in coronet formation. CFD J. 8:1999;378.
73. Zienkiewicz O. C., Wu J. A general explicit or semi-explicit algorithm for compressible and incompressibe flows. Int. J. Num. Meth. Eng. 35:1992;457.
74. Zalesak S. T. Fully multidimensional flux-corrected transport algorithm for fluids. J. Comput. Phys. 31:1979;335.