Level-Set-Based Deformation Methods for Adaptive Grids

Journal of Computational Physics

Volumn 159, Issue 1, 2000, Pages 103-122

  Liao, Guojun ^a   Liu, Feng ^b   De La Pena, Gary C ^a   Peng, Danping ^c   Osher, Stanley ^d  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

^b University of California at Irvine   (United States)

^c MSCI Barra Inc   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Adaptive grids; Deformation methods; Level set functions

Indexed keywords

DIFFERENTIAL EQUATIONS; DROP BREAKUP; ROTATIONAL FLOW; SET THEORY;

ADAPTIVE GRIDS; CARTESIAN COORDINATE; DEFORMATION METHOD; INTERSECTION POINTS; LEVEL SET; LEVEL SET EVOLUTION EQUATIONS; LEVEL-SET FUNCTION; MOVING GRID; PHYSICAL QUANTITIES; VELOCITY VECTORS;

NUMERICAL METHODS;

EID: 0001006735     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6432     Document Type: Article

References (32)

1. Brackbill J. U., Saltzman J. S. Adaptive zoning for singular problems in two dimensions. J. Comput. Phys. 46:1982;342.
2. Thompson J. F., Warsi Z. U. A., Mastin C. W. Numerical Grid Generation. 1985.
3. Zegeling Paul A. Moving Grid Methods. 1992.
4. Knupp P., Steinberg S. The Fundamentals of Grid Generation. 1994.
5. Carey G. Computational Grid Generation. 1997.
6. Liseikin V. Grid Generation Methods. 1999.
7. Castillo J., Steinberg S., Roache P. J. Mathematical aspects of variational grid generation. J. Comput. Appl. Math. 20:1987;127.
8. Anderson D. A. Grid cell volume control with an adaptive grid generator. Appl. Math. Comput. 35:1990;35.
9. K. Miller, Recent results on finite element methods with moving nodes, in, Accuracy Estimates and Adaptive Methods in Finite Element Computations, edited by, Babuska, Zienkiewicz, Gago, and Oliveira, Wiley, New York, 1986, p, 325.
10. Arney D., Flaherty J. ACM Trans. Math. Software. 16:1990;48.
11. Hawken D. F., Gottlieb J. J., Hansen J. S. Review of some adaptive node-movement techniques in finite-element and finite-Difference solutions of partial difference equations. J. Comput. Phys. 95:1991;254.
12. Huang W., Ren Y., Russell R. Moving mesh methods based on moving mesh partial differential equations. J. Comput. Phys. 113:1994;279.
13. Moser J. Volume elements of a Riemann manifold. Trans. AMS. 120:1965;286.
14. Dacorogna B., Moser J. On a PDE involving the Jacobian determinant. Ann. Inst. H. Poincaré 7:1990.
15. Liao G., Anderson D. A new approach to grid generation. Applicable Anal. 44:1992;285.
16. Liao G., Su J. A moving grid method for (1+1) dimension. Appl. Math. Lett. 8:1995;47.
17. Semper B., Liao G. A moving grid finite element method using grid deformation. Numer. Methods PDEs. 11:1995;603.
18. Bochev P., Liao G., dela Pena G. Analysis and computation of adaptive moving grids by deformation. Numer. Methods PDEs. 12:1996;489.
19. Liu F., Ji S., Liao G. An adaptive grid method with cell-volume control and its applications to Euler flow calculations. SIAM J. Sci. Comput. 20:1998;811.
20. Liu F., Jameson A. Multi-grid Navier-Stokes calculation for three-dimensional cascades. AIAA J. 31:1993;1785.
21. Liu F., Zheng. A strongly coupled time-marching method for solving the Navier-Stokes and turbulance model equations with multigrid. J. Comput. Phys. 128:1996;289.
22. Liao G. Proceedings of the 15th IAMCS World Congress. 2:August 1997;155.
23. G. Liao, and, G. dela Pena, A moving grid finite difference algorithm for PDEs, preprint.
24. Sethian J. A. Curvature flow and entropy conditions to grid generation. J. Comput. Phys. 115:1994;440.
25. D. Peng, B. Merriman, S. Osher, H. Zhao, and, M. Kang, A PDE based fast level set method, UCLA CAM Report 98-25 (1998).
26. Chen S., Merriman B., Osher S., Smereka P. A simple level set method for solving Stefan problems. J. Comput. Phys. 134:1997;236.
27. Osher S., Sethian J. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79:1988;12.
28. Chorin, Marsden. A Mathematical Introduction to Fluid Dynamics. 1993.
29. Meyer R. Introduction to Mathematical Fluid Dynamics. 1971.
30. Osher S., Shu C. W. High order essentially non-oscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28:1991;907.
31. Sussman M., Smereka P., Osher S. A level set method for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114:1994;146.
32. B. Merriman, R. Caflisch, and, S. Osher, Level set methods with an application to modelling the growth of thin films, Proc of 1997 Congress on Free Boundary Problems, Heraklion, Crete, Greece (1997), to appear.