Another Look at Velocity Extensions in the Level Set Method
نویسنده
چکیده
The level set method [8] has become a widely used numerical method for moving interfaces, e.g. see the many examples in [11, 7]. For many applications, the velocity of the interface is known only on the interface, while the level set method requires information about the interface speed at least in a neighborhood of grid points near the interface. To address this issue, velocity extensions are used to map the velocity information on the interface into the rest of the computational domain [2]. This allows the level set method to proceed. The velocity extension method presented in [2] uses the fast marching method [12, 13], and is only a first order approximation for the velocity field near the interface. Furthermore, it can lead to unexpected behavior in some cases. This is primarily due to the strictly local solution for the characteristics of the flow near the interface. In this paper, we look more closely at the characteristics near the interface, and then present a modified velocity extension method, also based on the fast marching method, which handles the characteristcs more accurately. In turn, this new method will lead to some interesting new possibilities for the fast marching method.
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عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 31 شماره
صفحات -
تاریخ انتشار 2009