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首页> 外文期刊>Journal of Computational Physics >Differential equation based constrained reinitialization for level set methods
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Differential equation based constrained reinitialization for level set methods

机译：水平集方法的基于微分方程的约束重新初始化

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A partial differential equation based reinitialization method is presented in the framework of a localized level set method. Two formulations of the new reinitialization scheme are derived. These formulations are modifications of the partial differential equation introduced by Sussman et al. [M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146-159] and, in particular, improvements of the second-order accurate modification proposed by Russo and Smereka [G. Russo, P. Smereka, A remark on computing distance functions, J. Comput. Phys. 163 (2000) 51-67]. The first formulation uses the least-squares method to explicitly minimize the displacement of the zero level set within the reinitialization. The overdetermined problem, which is solved in the first formulation of the new reinitialization scheme, is reduced to a determined problem in another formulation such that the location of the interface is locally preserved within the reinitialization. The second formulation is derived by systematically minimizing the number of constraints imposed on the reinitialization scheme. For both systems, the resulting algorithms are formulated in a three-dimensional frame of reference and are remarkably simple and efficient. The new formulations are second-order accurate at the interface when the reinitialization equation is solved with a first-order upwind scheme and do not diminish the accuracy of high-order discretizations of the level set equation. The computational work required for all components of the localized level set method scales with O(N). Detailed analyses of numerical solutions obtained with different discretization schemes evidence the enhanced accuracy and the stability of the proposed method, which can be used for localized and global level set methods. (C) 2008 Elsevier Inc. All rights reserved.
机译：在局部水平集方法的框架内，提出了一种基于偏微分方程的重新初始化方法。推导了新的重新初始化方案的两种公式。这些公式是Sussman等人引入的偏微分方程的修正。 [M. Sussman，P。Smereka，S。Osher，一种计算不可压缩两相流解决方案的水平集方法，J。Comput。物理114（1994）146-159]，尤其是Russo和Smereka提出的对二阶精确修改的改进[G. Russo，P。Smereka，关于计算距离函数的评论，J。Comput。物理163（2000）51-67]。第一个公式使用最小二乘法来显式最小化重新初始化内设置的零电平的位移。在新的重新初始化方案的第一个公式中解决的超定问题在另一个公式中被简化为确定的问题，从而使接口的位置局部保留在重新初始化中。第二种表述是通过系统地最小化施加在重新初始化方案上的约束数量而得出的。对于这两个系统，生成的算法都以三维参考框架表示，并且非常简单有效。当用一阶迎风方案求解重新初始化方程时，新公式在界面处具有二阶精度，并且不会降低水平集方程的高阶离散化的精度。本地化水平集方法的所有组件所需的计算工作均以O（N）进行缩放。对采用不同离散化方案获得的数值解进行的详细分析表明，该方法具有更高的准确性和稳定性，可用于局部和全局水平集方法。 （C）2008 Elsevier Inc.保留所有权利。

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