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首页> 外文期刊>Journal of Computational Physics >A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes
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A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes

机译：二维非结构化网格的避免奇异移动最小二乘方案

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摘要

Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has specifically addressed this issue. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which singularities occur are identified. The theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner, while attempting to maintain stencil symmetry as closely as possible. Finally, the scheme is applied in a convection-diffusion equation solver and an incompressible Navier-Stokes solver, and the results are shown to compare favourably with known analytical solutions and previously published results.
机译：移动最小二乘插值方案被广泛用作对散乱数据进行数值分析的工具。特别是，它们在求解非结构化网格上的偏微分方程时经常使用，当定义域的几何形状复杂时，通常需要使用它们。众所周知，如果模板中的数据点碰巧处于某些特殊的几何排列中，则这些方案可能是奇异的，但是很少有研究专门针对此问题。本文提出了一种移动最小二乘方案，该方案是求解二维偏微分方程时的合适工具，并且可以确定发生奇异性的精确条件。该理论用于开发模板构建算法，该算法可自动检测奇异模板并以有效方式对其进行校正，同时尝试尽可能保持模板对称性。最后，该方案被应用于对流扩散方程求解器和不可压缩的Navier-Stokes求解器中，结果与已知的解析解和先前发表的结果进行了比较。

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