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Analysis of Essentially Non-oscillatory Numerical Techniques for the Computation of the Level Set Method

Abstract:

In this paper, we analyze the Upwind Differencing and the Essentially Non-Oscillatory (ENO) schemes for the level set method during the evolution of interfaces. Our evolution experiments use different vector fields to test the behavior of the interface in different aspects. The experiments presented in this work are: evolution of a circle in a rotating field, shrinking and expanding of a square, Zalesak’s disk revolution, and single-vortex evolution. Each one of them provides a different view of the strengths and weaknesses of the method. The experiments use the percentage of area loss, the L1 error, and the order of convergence as accuracy metrics. We compare the different techniques, report our results, and provide conclusions.