A Semi-implicit Gradient Augmented Level Set Method

Abstract

Abstract. Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided, leading to highly accurate descriptions of a moving interface. The result is a hybrid LagrangianEulerian method that may be easily applied in two or three dimensions. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. In this work the algorithm, convergence and accuracy results are presented. Several numerical experiments in both two and three dimensions demonstrate the stability of the scheme.

Dynamics of three-dimensional vesicles in dc electric fields

“…This is done based on introducing a smoothing operator similar to the idea used in Refs. [28,29]. In the third step the center values are projected back to grid points and the jet of the solution including the gradients are updated; see Ref.…”

Electrohydrodynamics of Three-Dimensional Vesicles: A Numerical Approach

“…To ensure that surface quantities are smooth a semi-implicit level set advection scheme is utilized. The method used here is an improvement of the semi-implicit, gradient augmented level set [64], and is briefly described here.…”

“…The advection of the level set jet proceeds with the following three steps: 1) advection of cell-centers, 2) smoothing at cell-centers, and 3) projection onto grid points. Unlike the original semi-implicit, gradient-augmented level set method [64] this has the advantage of only requiring a single smoothing operation, as described below.…”

“…The advantage of this method over that of Ref. [64] is that only a single smoothing operation is required, versus one for the level set and three for the gradient fields. Work is currently underway investigating the full properties of this semi-implicit jet scheme.…”

An Immersed Interface Method for Axisymmetric Electrohydrodynamic Simulations in Stokes flow

“…This augmented variable is solved simultaneously in addition to solution of the elliptic equation. Recently AIIM has been applied to various problems [16,26], and various modifications have been made to solve the Navier-Stokes equations with piecewise constant fluid viscosity. The augmented method we use for the electric potential is based on [15], and here we extend it from two-dimensions to three-dimensions with axisymmetry.…”