Abstract

The level set method, introduced by Osher and Sethian in 1988, is a powerful numerical approach for analyzing and computing interface motion. In this paper, we extend the level set method to two-dimensional unstructured adaptive Cartesian grid to further improve the solution accuracy and efficiency. A quadtree-based grid generator is developed for 2D adaptive Cartesian mesh generation. Following ideas from the finite volume method for hyperbolic conservation laws, we have developed a level-set numerical algorithm for the adaptive Cartesian grid. Some two-dimensional numerical examples are given to illustrate the capability of the developed algorithm. Secondorder accuracy in smooth regions, good stability and convergence to viscosity solutions are demonstrated.

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