The Segment Projection Method for Interface Tracking

Communications on Pure and Applied Mathematics

Volumn 56, Issue 1, 2003, Pages 47-79

  Tornberg, Anna Karin ^a   Engquist, Björn ^b  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037211311     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.10052     Document Type: Article

References (23)

1. Benamou, J.-D. Big ray tracing: multivalued travel time field computation using viscosity solutions of the eikonal equation. J. Comput. Phys. 128 (1996), 463-474.
2. Brenner, S. C.; Scott, L. R. The mathematical theory of finite element methods. Texts in Applied Mathematics, 15. Springer, New York, 1994.
3. Caflisch, R. E.; E, W.; Gyure, M. F.; Merriman, B.; Ratsch, C. Kinetic model for a step edge in epitaxial growth. Phys. Rev. E 59 (1999), no. 6, 6879-6887.
4. Chen, S.; Merriman, B.; Kang, M.; Caflisch, R. E.; Ratsch, C.; Cheng, L.-T.; Gyure, M.; Fedkiw, R. P.; Anderson, C.; Osher, S. A level-set method for thin film epitaxial growth. J. Comput. Phys. 167 (2001), 475-500.
5. Chesshire, G.; Henshaw, W. D. Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90 (1990), no. 1, 1-64.
6. Choquet-Bruhat, Y.; DeWitt-Morette, C.; Dillard-Bleick, M. Analysis, manifolds and physics. North Holland, Amsterdam, 1977.
7. Crandall, M. G.; Lions, P.-L. Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983), no. 1, 1-42.
8. Engquist, B.; Runborg, O.; Tornberg, A.-K. High frequency wave propagation by the segment projection method. J. Comput. Phys. 178 (2002), no. 2, 373-390.
9. Glimm, J.; Grove, J. W.; Li, X. L.; Shyue, K.-M.; Zeng, Y.; Zhang, Q. Three-dimensional front tracking. SIAM J. Sci. Comput. 19 (1998), no. 3, 703-727.
10. Grayson, M. A. The heat equation shrinks embedded plane curves to round points. J. Differential Geom. 26 (1987), no. 2, 285-314.
11. Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S. R. Uniformly high-order accurate essentially nonoscillatory schemes. III. J. Comput. Phys. 71 (1987), no. 2, 231-303.
12. Keller, J. The geometrical theory of diffraction. J. Opt. Soc. Am. 52 (1962), 116-130.
13. Osher, S.; Sethian, J. A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1998), 12-49.
14. 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), 269-282.
15. Sethian, J. A. Level set methods and fast marching methods. Cambridge University, Cambridge, 1999.
16. Sussman, M.; Smereka, P.; Osher, S. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1994), September, 146-159.
17. Tornberg, A.-K. Interface tracking methods with applications to multiphase flows. Thesis, Royal Institute of Technology (KTH), Stockholm, Sweden, 2000. Available online at: http://www.nada.kth.se/~annak/research.html
18. Tornberg, A.-K. Multi-dimensional quadrature of singular and discontinuous functions. BIT 42 (2002), 644-669.
19. Tornberg, A.-K.; Engquist, B. Interface tracking in two-phase flows. Multifield problems, state of the art, 58-66. Springer, Berlin, 2000.
20. Tryggvason, G.; Brunner, B.; Esmaeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W.; Han, J.; Nas, S.; Jan, Y.-J. A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2001), 708-759.
21. Unverdi, S. O.; Tryggvason, G. A front tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1992), 25-37.
22. van Trier, J.; Symes, W. W. Upwind finite-difference calculation of traveltimes. Geophysics 56 (1991), no. 6, 812-821.
23. Vidale, J. E. Finite-difference calculation of traveltimes. Bull. Seism. Soc. Am. 78 (1988), no. 6, 2062-2076.