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Level set question

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Hello, I"ve read about the level set method to evolve a surface along a velocity field. I've understood the basics of the level set method and have implemented most of it, but I don't know hoe to discretize the evolution formula \phi_t + U * \nabla phi = 0 I've read that higher-order upwind schemes have to be used for this as simple finite differences are not accurate enough (I've already tried this), but I have no idea how this higher-order schemes works. If anybody could show me a way on how to discretize this formula accurately I would be really grateful.. Thanks, Icebraker

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Two good books on the topic:

Level Set Methods and Fast Marching Methods, J.A. Sethian, Cambridge University Press. Chapter 5 (on Hyperbolic Conservation Laws) has some discussion about higher-order upwind schemes.

Level Set Methods and Dynamic Implicit Surfaces, S. Osher and R. Fedkiw, Springer-Verlag. Section 3.3 (Hamilton-Jacobi ENO) is a discussion on improving the derivative approximations (higher-order methods).

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