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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 (|∇φ|) 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 |∇φ| along a fluid particle trajectory. This straining action not only affects the magnitude of |∇φ|, but the general character of φ, 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 φ is directly connected to the size of |∇φ| and to the magnitude of the second and fourth order derivatives of φ. 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.

SUMMARYA hybrid scheme for reinitializing the level set function and its gradient within the frame work of the augmented level set method is presented. It is based on first dividing the domain into an interfacial region (i.e. nodes close to the interface) and its complement. Within the interfacial region, the level set and its gradient are updated explicitly through a modified version of Newton's method (Chopp, 2001, SIAM J. Sci. Comput. 23 230‐244) and is implemented here within the context of Hermite polynomials. In the region away from the interface, the solution pertains to a semi‐Lagrangian implementation of the reinitialization equations, which are solved based on Hermite polynomials and are time marched with a single step and a multipoint scheme. It is shown that for various exercises, the present method predicts the signed distance function and its gradient to 4th and 3rd order (in space), respectively with regards to the L1, L2, and L ∞  norms, provided the level set field is sufficiently smooth. A range of test cases are also considered from the literature, where the present method is compared with existing methods and shown to be generally more accurate. Moreover, the well‐known issue of volume loss due to reinitialization is addressed successfully with the current implementation, even for objects that are of the size of one grid cell, and whose local radius of curvature falls below the local grid size. For both time marching schemes, it is shown that the L2 and L ∞  errors decay to negligible levels, are smooth in space, and do not exhibit temporal oscillations. Finally the performance of the hybrid scheme is evaluated by applying it on various kinematic test cases. For solid body rotation problems (zero deformation flow field), the benefit stemming from hybrid reinitialization is marginal. When applied to kinematic cases involving severe deformation, such as the standard vortex flow, the reinitialization strategy helps maintain a smooth level set field, which prevents serious numerical errors from developing.Copyright © 2013 John Wiley & Sons, Ltd.

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