Semi-Lagrangian Methods for Level Set Equations
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Solving a system of 2D Burgers' equations using Semi-Lagrangian finite difference schemes
In this paper, we aim to generalize semi-Lagrangian finite difference schemes for a system of two-dimensional (2D) Burgers' equations. Our scheme is not limited by the Courant-Friedrichs-Lewy (CFL) condition and therefore we can apply larger step size for the time variable. Proposed schemes can be implemented in parallel very well and in fact, it is a local one-dimensional (LOD) scheme which o...
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1. Generalities about domain, or surface evolution problems 2 2. The Level Set Method for describing domain or interface evolution 3 2.1. Level Set framework and geometry 3 2.2. Surface evolution in the level set framework 4 2.3. A glimpse at the mathematical framework 5 2.4. Domain evolution as a boundary value problem: Eikonal equations 9 3. A model application of the level set framework 10 4...
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1. Generalities about domain, or surface evolution problems 2 2. The Level Set Method for describing domain or interface evolution 3 2.1. Level Set framework and geometry 3 2.2. Surface evolution in the level set framework 4 2.3. A glimpse at the mathematical framework 5 2.4. Domain evolution as a boundary value problem: Eikonal equations 8 3. A model application of the level set framework 10 4...
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Semi-Lagrangian schemes have been explored by several authors recently for transport problems, in particular for moving interfaces using the level set method. We incorporate the backward error compensation method developed in our paper from 2003 into semi-Lagrangian schemes with almost the same simplicity and three times the complexity of a first order semi-Lagrangian scheme but with improved o...
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Here a semi-implicit formulation of the gradient augmented level set method is presented. The method is a hybrid Lagrangian–Eulerian method that may be easily applied in two or three dimensions. By tracking both the level set function and the gradient of the level set function, highly accurate descriptions of a moving interface can be formed. Stability is enhanced by the addition of a smoothing...
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