Abstract
Level set methodology is crucially pertinent to tracking moving singular surfaces or thin fronts with steep gradients in the numerical solutions of partial differential equations governing complex flow fields. This methodology must be consistent with the basic solution technique for the partial differential equations. To this end, a discontinuous spectral element approach is developed for level set advection and reinitialization as these methods are becoming increasingly popular for the solution of the fluid dynamic problems. Example computations are provided, which demonstrate the high order accuracy of the method.
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Sussman, M., Hussaini, M.Y. A Discontinuous Spectral Element Method for the Level Set Equation. Journal of Scientific Computing 19, 479–500 (2003). https://doi.org/10.1023/A:1025328714359
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DOI: https://doi.org/10.1023/A:1025328714359