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Assessment and modification of sub‐cell‐fix method for re‐initialization of level‐set distance function
Author(s) -
Sun M. B.,
Wang Z. G.,
Bai X. S.
Publication year - 2009
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2204
Subject(s) - initialization , level set (data structures) , set (abstract data type) , zero (linguistics) , algorithm , signed distance function , mathematics , level set method , function (biology) , curvature , computer science , geometry , artificial intelligence , philosophy , linguistics , segmentation , evolutionary biology , image segmentation , biology , programming language
Sub‐cell‐fix re‐initialization method was proposed by Russo and Smereka ( J. Comput. Phys. 2000; 163 : 51–67) as a modification to the re‐distancing algorithm of Sussman et al . ( J. Comput. Phys. 1994; 114 : 146–159) that determines the distance function from an interface known as the zero level‐set. The principal goal of sub‐cell‐fix method is to compute the distance function of the cells adjacent to the zero level‐set without disturbing the original zero level‐set. Following the original work of Russo and Smereka, several improved sub‐cell‐fix schemes were reported in the literature. In this paper, we show that in certain situations almost all the previous sub‐cell‐fix schemes can disturb the zero level‐set, and the accuracy would not improve when the CFL numbers are decreased. Based on the scheme of Hartmann et al . ( J. Comput. Phys. 2008; 227 :6821–6845), we propose an improved sub‐cell‐fix scheme that can significantly increase the accuracy of sub‐cell‐fix method on problems that are challenging. The scheme makes use of a combination of the points adjacent to zero level‐set surfaces and preserves the interface in a second‐order accuracy. The new sub‐cell‐fix scheme is capable of handling large local curvature, and as a result it demonstrates satisfactory performance on several challenging test cases. Limitations of the schemes on highly stretched grids are illustrated. Copyright © 2009 John Wiley & Sons, Ltd.