Assessment and modification of sub-cell-fix method for re-initialization of level-set distance function

✍ Scribed by M. B. Sun; Z. G. Wang; X. S. Bai

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 888 KB
• Volume: 62
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.2204

✦ Synopsis

Abstract

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.