A High-Order Level-Set Method with Enhanced Stability for Curvature Driven Flows and Surface Diffusion Motion

A high-order explicit level-set method based on the total variation diminishing Runge–Kutta method, a high-order scheme for distance computation and a smoothing scheme has been developed for simulating curvature driven flows and surface diffusion motion. This method overcomes the high-order CFL time restriction. The enhanced stability is achieved by utilizing several techniques, resulting in an accurate and smooth velocity field. In particular, the scheme for distance computation is used to reinitialize the level-set function and to extend the velocity from the zero level-set to the rest of the domain. As such, it greatly reduces the accumulated errors typically observed in the traditional PDE-based methods. The smoothing technique is used to remove the high-frequency oscillations produced by the high-order derivatives of the level-set function and is the key to the stability enhancement. A local treatment scheme was also developed which is crucial in the simulation of merging events. Results on several benchmark problems have demonstrated. Compared with some semi-implicit methods, the developed method is more accurate and has the same, if not better, stability.

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