A simple algebraic interface capturing scheme using hyperbolic tangent function

International Journal for Numerical Methods in Fluids

Volumn 48, Issue 9, 2005, Pages 1023-1040

  Xiao, F ^a,b   Honma, Y ^a   Kono, T ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b STATE KEY LABORATORY OF SEVERE WEATHER   (China)

Author keywords

Advection scheme; Computational fluid dynamics; Interface capturing; Moving interface; Multi phase flow

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; FUNCTIONS; NUMERICAL ANALYSIS;

ALGEBRIC INTERFACES; TANGENT OF HYPERBOLA FOR INTERFACE CAPTURING (THINC); VOLUME OF FLUIDS (VOF) METHODS;

COMPUTATIONAL METHODS;

COMPUTATIONAL FLUID DYNAMICS; MATHEMATICAL METHOD; MULTIPHASE FLOW;

EID: 22244434665     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.975     Document Type: Article

References (29)

1. Unverdi SO, Tryggvason G. A front-tracking method for viscous, incompressible multi-fluid flow. Journal of Computational Physics 1992; 100:25-37.
2. Glimm J, Graham MJ, Grove J, Li XL, Smith TM, Tan D, Tangerman F, Zhang Q. Front tracking in two and three dimensions. Journal of Computational Mathematics 1998; 7:1-12.
3. Hirt CW, Nichols BD. Volume of fluid (VOF) methods for the dynamics of free boundaries. Journal of Computational Physics 1981; 39: 201-225.
4. Lafaurie B, Nardone C, Scardovell R, Zaleski S, Zanetti G. Modeling merging and fragmentation in multiphase flows with SURFER. Journal of Computational Physics 1994; 113:134-147.
5. Ubink C, Issa RI. A method for capturing sharp fluid interfaces on arbitrary meshes. Journal of Computational Physics 1999; 153: 26-50.
6. Noh WF, Woodward P. SLIC (simple line interface method). Lecture Notes in Physics 1976; 24:330-340.
7. Youngs DL. Time-dependent multi-material flow with large fluid distortion. In Numerical Methods for Fluid Dynamics, Morton KW, Baines MJ (eds), vol. 24. Academic Press: New York, 1982; 273-285.
8. Ashgriz A, Poo JP. FLAIR: flux line-segment model for advection and interface reconstruction. Journal of Computational Physics 1991; 93:449-468.
9. Puckett EG, Almgren AS, Bell JB, Marcus DL, Rider WJ. A high-order projection method for tracking fluid interface in variable density incompressible flows. Journal of Computational Physics 1997; 130:269-282.
10. Rider WJ, Kothe DB. Reconstructing volume tracking. Journal of Computational Physics 1998; 141:112-152.
11. Harvie DJE, Fletcher DF. A new volume of fluid advection algorithm: the stream scheme. Journal of Computational Physics 2000; 162: 1-32.
12. Pan D, Chang CH. The capturing of free surfaces in incompressible multi-fluid flows. International Journal for Numerical Methods in Fluids 2000; 30:203-222.
13. Rudman M. Volume-tracking methods for interfacial flow calculations. International Journal for Numerical Methods in Fluids 1997; 24: 671-691.
14. Xiao F, Ikebata A. An efficient method for capturing free boundaries in multi-fluid simulations. International Journal for Numerical Methods in Fluids 2003; 42:187-210.
15. Yang H. An artificial compression method for ENO schemes: the slope modification method. Journal of Computational Physics 1990; 89: 125-160.
16. Allen DN de G, Southwell RV. Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quarterly Journal of Mechanics and Applied Mathematics 1955; 18: 129-145.
17. El-Mistikawy TM, Werle MJ. Numerical method for boundary layers with blowing-the exponential box scheme. AIAA Journal 1978; 16: 749-751.
18. Schrfetter DL, Gummel HK. Large-signal analysis of a silicon read diode oscillator. IEEE Transactions on Electron Devices 1969; ED-16: 64-77.
19. Ramos JI. On diffusive methods and exponential fitted techniques. Applied Mathematics and Computation 1999; 103:69-96.
20. 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; 62:2537-2540.
21. Yabe T, Aoki T. A universal solver for hyperbolic-equations by cubic-polynomial interpolation. 1. One-dimensional solver. Computer Physics Communications 1991; 66:219-232.
22. Rider WJ, Kothe DB. Stretching and tearing interface tracking methods. Los Alamos National Laboratory Report, LA-UR-95-1145 (AIAA-95-1717), 1995.
23. Xiao F. Unified formulation for compressible and incompressible flows by using multi-integrated moments I: one-dimensional inviscid compressible flow. Journal of Computational Physics 2004; 195:629-654.
24. Xiao F, Ikebata A, Hasegawa T. Numerical simulations of free-interface fluids by a multi-integrated moment method. Computers and Structures 2005; 83:409-423.
25. Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. Journal of Computational Physics 1992; 100: 335-354.
26. Martin JC, Moyce WJ. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions of the Royal Society of London Series A 1952; 244:312-324.
27. Hnat JG, Buckmaster JD. Spherical cap bubbles and skirt formation. Physics of Fluids 1976; 19:182-194.
28. Gueyffier D, Li J, Nadim A, Scardovelli R, Zaleski S. Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. Journal of Computational Physics 1999; 152:423-456.
29. Sussman M, Smereka P. Axisymmetric free boundary problems. Journal of Fluid Mechanics 1997; 341: 269-294.