Modeling of two-phase flows with surface tension by finite pointset method (FPM)

Journal of Computational and Applied Mathematics

Volumn 203, Issue 2 SPEC. ISS., 2007, Pages 376-386

  Tiwari, Sudarshan ^a   Kuhnert, Jörg ^a  

^a FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

Author keywords

Incompressible Navier Stokes equations; Least squares approximation; Meshfree method; Projection method; Two phase flows

Indexed keywords

CONTINUUM MECHANICS; LAGRANGE MULTIPLIERS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; SURFACE TENSION; TWO PHASE FLOW;

CONTINUUM SURFACE FORCE (CSF); FINITE POINTSET METHOD (FPM); MESHFREE METHOD; PROJECTION METHOD;

FINITE DIFFERENCE METHOD;

EID: 33947629720     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.04.048     Document Type: Article

References (26)

1. Brackbill J.U., Kothe D.B., and Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 354-355
2. Chorin A. Numerical solution of the Navier-Stokes equations. J. Math. Comput. 22 (1968) 745-762
3. Cummins S.J., and Rudmann M. An SPH projection method. J. Comput. Phys. 152 (1999) 284-607
4. Daly B.J. Phys. Fluid 12 (1969) 1340
5. G.A. Dilts, Moving least squares particle hydrodynamics I, consistency and stability, Hydrodynamics Methods Group Report, Los Alamos National Laboratory, 1996.
6. Drazin P.G., and Reid W.H. Hydrodynamic Stability (1981), Cambridge University Press, Cambridge, UK
7. Gingold R.A., and Monaghan J.J. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices Roy. Astronom. Soc. 181 (1997) 375-389
8. Ginzburg I., and Wittum G. Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolant. J. Comput. Phys. 166 (2001) 302-335
9. D. Hietel, M. Junk, S. Tiwari, J. Kuhnert, Meshless methods for conservation laws, in: G. Warnecke (Ed.), Analysis and Numerical Methods for Conservation Laws, Springer, Berlin, 2005.
10. Iliev O., and Tiwari S. A generalized (meshfree) finite difference discretization for elliptic interface problems. Springer Lecture Notes in Computer Sciences vol. 2542 (2003), Springer, Berlin
11. J. Kuhnert, General smoothed particle hydrodynamics, Ph.D. Thesis, Kaiserslautern University, Germany, 1999.
12. Kuhnert J. An upwind finite pointset method for compressible Euler and Navier-Stokes equations. Springer Lecture Notes in Computational Science and Engineering: Meshfree Methods for Partial Differential Equations I vol. 26 (2002), Springer, Berlin
13. J. Kuhnert, A. Tramecon, P. Ullrich, Advanced air bag fluid structure coupled simulations applied to out-of position cases, EUROPAM Conference Proceedings 2000, ESI group, Paris, France, 2000.
14. Liszka T., and Orkisz J. The finite difference method on arbitrary irregular grid and its application in applied mechanics. Comput. & Structures 11 (1980) 83-95
15. Monaghan J.J. Simulating free surface flows with SPH. J. Comput. Phys. 110 (1994) 399
16. Monaghan J.J., and Kocharyan A. SPH simulation of multi-phase flow. Comput. Phys. Comm. 87 (1995) 225-235
17. Morris J.P. Simulating surface tension with smoothed particle hydrodynamics. Internat. J. Numer. Methods Fluids 33 (2000) 333-353
18. Morris J.P., Fox P.J., and Zhu Y. Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136 (1997) 214-226
19. M. Oevermann, R. Klein, M. Berger, J. Goodman, A projection method for two-phase incompressible flow with surface tension and sharp interface resolution, Konrad-Zuse Zentrum, Berlin, Germany, 2000, preprint.
20. Tiwari S. A LSQ-SPH approach for compressible viscous flows. In: Freistuehler H., and Warnecke G. (Eds). International Series of Numerical Mathematics vol. 141 (2000), Birkhaueser, Basel
21. Tiwari S., and Kuhnert J. Finite pointset method based on the projection method for simulations of the incompressible Navier-Stokes equations. Springer Lecture Notes in Computational Science and Engineering: Meshfree Methods for Partial Differential Equations I vol. 26 (2002), Springer, Berlin
22. S. Tiwari, J. Kuhnert, A Meshfree Method for Incompressible Fluid Flows with Incorporated Surface Tension, revue aurope'enne des elements finis, vol. 11-n, 7-8/2002 (Meshfree and Particle Based Approaches in Computational Mechanics).
23. S. Tiwari, J. Kuhnert, Particle method for simulations of free surface flows, Proceedings of Hyp2002, 2003.
24. Tiwari S., and Kuhnert J. Grid free method for solving Poisson equation. Wavelet Analysis and Applications (2004), New Age International Publishers 151-166
25. Tiwari S., and Kuhnert J. A numerical scheme for solving incompressible and low Mach number flows by finite pointset method. Springer Lecture Notes in Computational Science and Engineering: Meshfree Methods for Partial Differential Equations II vol. 43 (2005), Springer, Berlin
26. S. Tiwari, S. Manservisi, Modeling incompressible Navier-Stokes flows by LSQ-SPH, Nepal Mathematical Sciences Report, vol. 20, Nos. 1, 2, 2003.