Flux-based level set method: A finite volume method for evolving interfaces

Applied Numerical Mathematics

Volumn 57, Issue 4, 2007, Pages 436-454

  Frolkovič, Peter ^a   Mikula, Karol ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

Author keywords

Evolving interfaces; Finite volume method; Level set method

Indexed keywords

COMPUTATIONAL METHODS; FINITE VOLUME METHOD; NUMERICAL METHODS; PROBLEM SOLVING;

3D INTERFACE MOTIONS; EVOLVING INTERFACES; LEVEL SET METHOD; SEMI-IMPLICIT TREATMENT;

INTERFACES (MATERIALS);

EID: 33847309228     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.06.002     Document Type: Article

References (35)

1. Beneš M. Mathematical and computational aspects of solidification of pure crystallic materials. Acta Math. Univ. Comenian. 70 (2001) 123-151
2. Cai Z. On the finite volume element method. Numer. Math. 58 (1991) 713-735
3. Caselles V., Kimmel R., and Sapiro G. Geodesic active contours. Internat. J. Comput. Vision 22 (1997) 61-79
4. D.A. Di Pietro, S. Lo Forte, N. Parolini, Mass preserving finite element implementations of the level set method, Appl. Numer. Math. (2006), in press
5. Evans L.C., and Spruck J. Motion of level sets by mean curvature I. J. Differential Geometry 33 (1991) 635-681
6. Eymard R., Gallouet T., and Herbin R. The finite volume method. In: Ciarlet Ph., and Lions J.L. (Eds). Handbook for Numerical Analysis vol. 7 (2000), Elsevier, Amsterdam
7. Falcone M., Giorgi T., and Loreti P. Level sets of viscosity solutions: some applications to fronts and randez-vous problems. SIAM J. Appl. Math. 54 (1994) 1335-1354
8. 3 F-ein Programmpaket zur Modellierung von Dichteströmungen. GRS vol. 139 (1999), GRS, Braunschweig. http://www.iwr.uni-heidelberg.de/~Peter.Frolkovic Also available at:
9. Frolkovič P. Flux-based method of characteristics for contaminant transport in flowing groundwater. Comput. Visualization Sci. 5 2 (2002) 73-83
10. P. Frolkovič, K. Mikula, High-resolution flux-based level set method, Preprint 2005-12, Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, 2005
11. Ginzburg I., and Wittum G. Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolants. J. Comput. Phys. 166 (2001) 302-335
12. Handlovičová A., Mikula K., and Sgallari F. Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution. Numer. Math. 93 (2003) 675-695
13. Jiang G.S., and Peng D. Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21 (2000) 2126-2143
14. Kossioris G., Makridakis Ch., and Souganidis P.E. Finite volume schemes for Hamilton-Jacobi equations. Numer. Math. 83 (1999) 427-442
15. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics (2002), Cambridge University Press, Cambridge
16. Luo X.Y., Ni M.J., Ying A., and Abdou M.A. Numerical modeling for multiphase incompressible flow with phase change. Numer. Heat Transfer, Part B: Fund. 48 (2005) 425-444
17. Mikula K., and Kačur J. Evolution of convex plane curves describing anisotropic motions of phase interfaces. SIAM J. Sci. Comput. 17 (1996) 1302-1327
18. Mikula K., and Ramarosy N. Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Numer. Math. 89 3 (2001) 561-590
19. Mikula K., and Ševčovič D. Evolution of plane curves driven by a nonlinear function of curvature and anisotropy. SIAM J. Appl. Math. 61 (2001) 1473-1501
20. Mikula K., and Ševčovič D. Computational and qualitative aspects of evolution of curves driven by curvature and external force. Comput. Visualization Sci. 6 4 (2004) 211-225
21. Oberman A.M. A convergent monotone difference scheme for motion of level sets by mean curvature. Numer. Math. 99 (2004) 365-379
22. Olsson E., and Kreiss G. A conservative level set method for two phase flow. J. Comput. Phys. 210 (2005) 225-246
23. Osher S., and Sethian J. Fronts propagating with curvature dependent speed: algorithm based on Hamilton-Jacobi formulation. J. Comput. Phys. 79 (1988) 12-49
24. Osher S., and Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces (2003), Springer, Berlin
25. Peng D., Merriman B., Osher S., Zhao H.K., and Kang M. A PDE based fast local level set method. J. Comput. Phys. 155 (1999) 410-438
26. Rouy E., and Tourin A. A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29 (1992) 867-884
27. Russell T.F., and Celia M.A. An overview of research on Eulerian-Lagrangian localized adjoint methods (ELLAM). Adv. Water Resourc. 25 (2002) 1215-1231
28. Sapiro G. Geometric Partial Differential Equations and Image Analysis (2001), Cambridge University Press, Cambridge
29. Schmidt A. Computation of three-dimensional dendrites with finite elements. J. Comput. Phys. 125 (1996) 293-312
30. Shu C.W., and Osher S. Efficient implementation of essentially nonoscillatory shock capturing schemes. J. Comput. Phys. 77 (1988) 439-471
31. Sarti A., Malladi R., and Sethian J.A. Subjective surfaces: A method for completing missing boundaries. Proc. National Acad. Sci. USA 12 97 (2000) 6258-6263
32. Sethian J.A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science (1999), Cambridge University Press, New York
33. Strain J. Semi-Lagrangian methods for level set equations. J. Comput. Phys. 151 (1999) 498-533
34. Tornberg A.-K., and Engquist B. A finite element based level set method for multiphase flow applications. Comput. Visualization Sci. 3 (2000) 93-101
35. Walkington N.J. Algorithms for computing motion by mean curvature. SIAM J. Numer. Anal. 33 6 (1996) 2215-2238