Imposing jump conditions on nonconforming interfaces for the Correction Function Method: A least squares approach
Imposing jump conditions on nonconforming interfaces for the Correction Function Method: A least squares approach
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在校正函数方法的不合格接口上施加跳跃条件：最小二乘法
DOI：
10.1016/j.jcp.2019.108869
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发表时间：
2019
影响因子：
4.1
通讯作者：
Rosales, Rodolfo Ruben
中科院分区：
文献类型：
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作者：
Marques, Alexandre Noll;Nave, Jean-Christophe;Rosales, Rodolfo Ruben
在修正函数方法(CFM)的背景下，我们介绍了一种技术，它简化了在不与计算网格对齐的界面上施加跳跃条件的问题。CFM提供了一个求解泊松方程的通用框架，在存在高精度间断的情况下，同时使用紧凑的离散化模板。CFM背后的一个关键概念是在最小二乘意义上执行跳跃条件。这个概念需要在界面的各个部分上计算积分，当只有界面的隐式表示可用时(例如，水平集函数的零轮廓)，这在3-D中是一个挑战。这里介绍的技术是基于最小二乘法的一种新的公式，该公式仅依赖于在局部坐标变换后服从简单求积的区域上的积分。我们将这种技术引入CFM的四阶精确实现中，并给出了在二维和三维中计算的带有附加跳跃条件的泊松方程的解的例子。
We introduce a technique that simplifies the problem of imposing jump conditions on interfaces that are not aligned with a computational grid in the context of theCorrection Function Method(CFM). The CFM offers a general framework to solve Poisson's equation in the presence of discontinuities to high order of accuracy, while using a compact discretization stencil. A key concept behind the CFM is enforcing the jump conditions in a least squares sense. This concept requires computing integrals over sections of the interface, which is a challenge in 3-D when only an implicit representation of the interface is available (e.g., the zero contour of a level set function). The technique introduced here is based on a new formulation of the least squares procedure that relies only on integrals over domains that are amenable to simple quadrature after local coordinate transformations. We incorporate this technique into a fourth order accurate implementation of the CFM, and show examples of solutions to Poisson's equation with imposed jump conditions computed in 2-D and 3-D.
利用散度定理生成高精度嵌入式边界网格
DOI：
--
发表时间：
2015
期刊：
影响因子：
--
作者：
P. Schwartz;J. Percelay;T. Ligocki;H. Johansen;D. Graves;D. Devendran;P. Colella;E. Ateljevich
通讯作者：
E. Ateljevich