A Lagrangian particle level set method

Journal of Computational Physics

Volumn 210, Issue 1, 2005, Pages 342-367

  Hieber, Simone E ^a   Koumoutsakos, Petros ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Interface capturing; Lagrangian particle methods; Level set method

Indexed keywords

DROP BREAKUP; LAGRANGE MULTIPLIERS; LEVEL MEASUREMENT; NUMERICAL METHODS;

INTERFACE-CAPTURING; LAGRANGIAN FRAMES; LAGRANGIAN PARTICLE METHOD; LAGRANGIAN PARTICLES; LEVEL SET METHOD; LEVEL-SET EQUATION; PARTICLE LEVEL SET; REGULARISATION; REMESHING;

ADVECTION;

EID: 23044469964     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.04.013     Document Type: Article

References (49)

1. C.W. Hirt B.D. Nichols Volume of fluid (Vof) method for the dynamics of free boundaries J. Comput. Phys. 39 1 1981 201-225
2. S. Osher J.A. Sethian Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation J. Comput. Phys. 79 1 1988 12-49
3. J.A. Sethian A fast marching level set method for monotonically advancing fronts Proc. Natl. Acad. Sci. USA 93 4 1996 1591-1595
4. R. Scardovelli S. Zaleski Direct numerical simulation of free-surface and interfacial flow Annu. Rev. Fluid Mech. 31 1999 567-603
5. J.A. Sethian Evolution, implementation, and application of level set and fast marching methods for advancing fronts J. Comput. Phys. 169 2 2001 503-555
6. S. Osher R. Fedkiw The Level Set Method and Dynamics Implicit Surfaces 2002 Springer-Verlag New York
7. J.A. Sethian Level Set Methods and Fast Marching Methods 1999 Cambridge University Press Cambridge, UK
8. S. Osher R.P. Fedkiw Level set methods: An overview and some recent results J. Comput. Phys. 169 2 2001 463-502
9. F. Gibou R. Fedkiw R. Caflisch S. Osher A level set approach for the numerical simulation of dendritic growth J. Sci. Comput. 19 1-3 2003 183-199
10. J.A. Sethian P. Smereka Level set methods for fluid interfaces Annu. Rev. Fluid Mech. 35 2003 341-372
11. S. Bryson D. Levy High-order central WENO schemes for multidimensional Hamilton-Jacobi equations SIAM J. Numer. Anal. 41 4 2003 1339-1369
12. W.J. Rider D.B. Kothe Reconstructing volume tracking J. Comput. Phys. 141 1998 112-152
13. J. Strain A fast semi-lagrangian contouring method for moving interfaces J. Comput. Phys. 161 2 2001 512-536
14. D. Enright R. Fedkiw J. Ferziger I. Mitchell A hybrid particle level set method for improved interface capturing J. Comput. Phys. 183 1 2002 83-116
15. L. Rosenhead The formation of vortices from a surface of discontinuity Proc. R. Soc. Lond. A 134 1931 170-192
16. A.J. Chorin Numerical study of slightly viscous flow J. Fluid Mech. 57 4 1973 785-796
17. N. Zabusky M. Hughes K. Roberts Contour dynamics for the Euler equations in two dimensions J. Comput. Phys. 30 1979 96-106
18. G.-H. Cottet P. Koumoutsakos Vortex Methods - Theory and Practice 2000 Cambridge University Press New York
19. P. Koumoutsakos A. Leonard High-resolution simulation of the flow around an impulsively started cylinder using vortex methods J. Fluid Mech. 296 1995 1-38
20. M. Sussman P. Smereka S. Osher A level set approach for computing solutions to incompressible 2-phase flow J. Comput. Phys. 114 1 1994 146-159
21. J.A. Sethian Fast marching methods SIAM Rev. 41 2 1999 199-235
22. J.P. Morris Simulating surface tension with smoothed particle hydrodynamics Int. J. Numer. Methods Fluids 33 3 2000 333-353
23. O.H. Hald Convergence of vortex methods for Euler's equations III SIAM J. Numer. Anal. 24 3 1987 538-582
24. J.T. Beale A convergent 3-D vortex method with grid-free stretching Math. Comput. 46 1986 401-424
25. J.J. Monaghan Smoothed particle hydrodynamics Annu. Rev. Astron. Astrophys. 30 1992 543-574
26. J.D. Eldredge A. Leonard T. Colonius A general deterministic treatment of derivatives in particle methods J. Comput. Phys. 180 2 2002 686-709
27. P. Degond S. Mas-Gallic The weighted particle method for convection-diffusion equations. Part 1: The case of an isotropic viscosity Math. Comput. 53 188 1989 485-507
28. G.-H. Cottet B. Michaux S. Ossia G. VanderLinden A comparison of spectral and vortex methods in three-dimensional incompressible flows J. Comput. Phys. 175 2002 702-712
29. G.-H. Cottet Artificial viscosity models for vortex and particle methods J. Comput. Phys. 127 1996 299-308
30. P. Koumoutsakos Vorticity flux control in a turbulent channel flow Phys. Fluids 11 2 1999 248-250
31. D.L. Chopp Computing minimal-surfaces via level set curvature flow J. Comput. Phys. 106 1 1993 77-91
32. M. Sussman E. Fatemi An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow SIAM J. Sci. Comput. 20 4 1999 1165-1191
33. G.-H. Cottet, E. Maitre, A level-set formulation for fluid-structure interactions with immersed surfaces, Math. Models and Methods in Appl. Sciences, accepted.
34. B. Engquist A.-K. Tornberg R. Tsai Discretization of Dirac delta functions in level set methods J. Comput. Phys. 207 1 2004
35. D. Adalsteinsson J.A. Sethian A fast level set method for propagating interfaces J. Comput. Phys. 118 2 1995 269-277
36. R.W. Hockney J.W. Eastwood Computer Simulation Using Particles second ed. 1988 IOP
37. L. Verlet Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules Phys. Rev. 159 1 1967 98-103
38. H.-Z. Tang T. Tang P. Zhang An adaptive mesh redistribution method for nonlinear Hamiltion-Jacobi equations in two- and three-dimensions J. Comput. Phys. 188 2003 543-572
39. D. Chopp J. Sethian Flow under curvature: Singularity formation, minimal surfaces, and geodesics Exp. Math. 2 4 1993 235-255
40. J. Sethian Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservations laws J. Differential Geometry 31 1990 131-161
41. S.T. Zalesak Fully multidimensional flux-corrected transport algorithms for fluids J. Comput. Phys. 31 3 1979 335-362
42. J.B. Bell P. Colella H.M. Glaz A 2nd-order projection method for the incompressible Navier-Stokes equations J. Comput. Phys. 85 2 1989 257-283
43. R.J. LeVeque High-resolution conservative algorithms for advection in incompressible flow SIAM J. Numer. Anal. 33 2 1996 627-665
44. J. Sethian J. Strain Crystal growth and dendritic solidification J. Comput. Phys. 98 1992 231-253
45. M. Grayson The heat equation shrinks embedded plane curves to round points J. Diff. Geom. 26 1987 555-558
46. M. Grayson A short note on the evolution of surfaces via mean curvatures J. Diff. Geom. 58 1989 285-314
47. B. Heidelberger M. Teschner M. Gross Real-time volumetric intersections of deforming objects Vision Modeling and Visualization 2003 IOS Press pp. 461-468
48. M. Bergdorf, G.-H. Cottet, P. Koumoutsakos, Multilevel adaptive particle methods for convection-diffusion equations, SIAM Multiscale Model. Simulat., in press.
49. P. Koumoutsakos Multiscale flow simulations using particles Annu. Rev. Fluid Mech. 37 2005 457-487