A fast and accurate semi-Lagrangian particle level set method
A fast and accurate semi-Lagrangian particle level set method
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DOI：
10.1016/j.compstruc.2004.04.024
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发表时间：
2005-02-01
影响因子：
4.7
通讯作者：
Fedkiw, R
中科院分区：
文献类型：
--
作者：
Enright, D;Losasso, F;Fedkiw, R
本文提出了一种有效的基于半拉格朗日的粒子水平集方法来准确捕捉界面。该方法保持了Level Set方法的强健拓扑性质，没有数值耗散的不利影响。Level Set方法和粒子Level Set方法通常在时间和空间上使用高精度的数值离散，例如TVD Runge-Kutta和HJ-WENO格式。我们证明了这些计算代价高昂的方案是不必要的。相反，快速、低阶精度的数值格式就足够了。也就是说，在Level Set方法中加入粒子不仅消除了与数值扩散相关的困难，而且还减少了对计算昂贵的高阶精度格式的需求。我们使用一种有效的一阶精度半拉格朗日平流。方案结合一阶精确快速行进方法来演化水平集函数。为了准确地跟踪底层流动特性，粒子采用二阶精确方法进行演化。由于我们避免了复杂的高阶精度数值方法，将算法扩展到任意数据结构变得更加可行，并给出了基于八叉树的自适应网格的初步结果。(C)2004爱思唯尔有限公司。保留所有权利。
In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method with- out the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD Runge-Kutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the level set method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semi-Lagrangian advection. scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh. (C) 2004 Elsevier Ltd. All rights reserved.