کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
522129 | 867812 | 2007 | 22 صفحه PDF | دانلود رایگان |
We present a level set method on non-graded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells is not constrained. We use quadtree and octree data structures to represent the grid and a simple algorithm to generate a mesh with the finest resolution at the interface. In particular, we present (1) a locally third order accurate reinitialization scheme that transforms an arbitrary level set function into a signed distance function, (2) a second order accurate semi-Lagrangian methods to evolve the linear level set advection equation under an externally generated velocity field, (3) a second order accurate upwind method to evolve the non-linear level set equation under a normal velocity as well as to extrapolate scalar quantities across an interface in the normal direction, and (4) a semi-implicit scheme to evolve the interface under mean curvature. Combined, we obtain a level set method on adaptive Cartesian grids with a negligible amount of mass loss. We propose numerical examples in two and three spatial dimensions to demonstrate the accuracy of the method.
Journal: Journal of Computational Physics - Volume 225, Issue 1, 1 July 2007, Pages 300–321