The distortion of the level set gradient under advection

JOURNAL OF COMPUTATIONAL PHYSICS

卷:334

Article

Trujillo, Mario E.¹  Anumolu, Lakshman²  Ryddner, Doug² 

[1] Dept Mech Engn, 1513 Univ Ave, Madison, WI 53706 USA

[2] Dept Engn Phys, 1513 Univ Ave, Madison, WI 53706 USA

关键词: Level set;    Reinitialization;    Gradient Augmented Level Set method;    Interfacial flows;   

DOI  :  10.1016/j.jcp.2016.11.050

来源: Elsevier

【 摘 要 】

The practice of periodically reinitializing the level set function is well established in twophase flow applications as a way of controlling the growth of anomalies and/or numerical errors. In the present work, the underlying roots of this anomalous growth are studied, where it is established that the augmentation of the magnitude of the level set gradient (vertical bar del phi) is directly connected to the nature of the flow field; hence, it is not necessarily the result of some type of numerical error. More specifically, for a general flow field advecting the level set function, it is shown that the eigenpairs of the strain rate tensor are responsible for the rate of change of IVOI along a fluid particle trajectory. This straining action not only affects the magnitude of IV0I, but the general character of 0, and consequently contributes to the growth in numerical error. These numerical consequences are examined by adopting the Gradient Augmented Level Set method. Specifically, it is shown that the local error for 0 is directly connected to the size of V and to the magnitude of the second and fourth order derivatives of 0. These analytical findings are subsequently supported by various examples. The role of reinitialization is discussed, where it is shown that in cases where the zero level set contour has a local radius of curvature that is below the local grid resolution, reinitialization exacerbates rather than diminishes the degree of error. For other cases, where the interface is well resolved, reinitialization helps stabilize the error as intended. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free