Gradient Augmented Level Set Method

With R. Rosales and B. Seibold

Introduction

We propose a new method for the advection of interfaces. Our method is based on a level set representation of the imbedded curve or surface and relies on using both function values and gradients. The advection is treated using a characteristic method (e.g. CIR). To guaranty consistency between gradients and function value we use a projection step. The main benefits are that sub-grid structures can be captured accurately, the method is compact (cell based), no reinitialization is required, and we achieve a 3^rd order global truncation error on function values, and 2^nd order globally on gradients.

This work is supported until 2011by NSF grant DMS-0813648, “Capturing subgrid structures with level set methods”, with Ruben Rosales and Benjamin Seibold

Standard Tests

[Click on the pictures below for movies in DIVX format]

3D Zalesak’s Circle – WENO/RK3TVD (left) vs. Present method (right)

Resolution = 50x50x50

3D deformation field – WENO/RK3TVD (left) vs. Present method (right)

Resolution = 50x50x50

2D “vortex in a box” flow – WENO/RK3TVD (blue) vs. Present method (red)

Resolution = 64x64

2D Zalesak’s circle test – Initial conditions (left) - WENO/RK3TVD (center) vs. Present method (right)

Convergence Results

Global truncation error (Linf Norm) for the level set function – 2D ‘vortex in a box’ test

Global truncation error (Linf Norm) for the gradients – 2D ‘vortex in a box’ test

Relevant Publications:

J.C. Nave, R.R. Rosales, B. Seibold, “A gradient-augmented level set method with an optimally local, coherent advection scheme”, submitted to J. Comp. Phys., preprint: arXiv:0905.3409

Last Modified by Jean-Christophe Nave – July 2009