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Adaptive grid based on geometric conservation law level set method for time dependent PDE
Author(s) -
Soheili Ali R.,
Ameri Maryam A.
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20360
Subject(s) - mathematics , conservation law , partial differential equation , fast marching method , intersection (aeronautics) , jacobian matrix and determinant , level set (data structures) , level set method , cartesian coordinate system , transformation (genetics) , grid , set (abstract data type) , partial derivative , mathematical analysis , geometry , algorithm , image (mathematics) , computer science , biochemistry , chemistry , artificial intelligence , engineering , image segmentation , gene , programming language , aerospace engineering
A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103–122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75–98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118–142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009