二维合并Voronoi-Delaunay网格上的算子差分逼近
Operator-difference approximations on two-dimensional merged Voronoi-Delaunay grids
AI总结：
本文针对不规则区域多维偏微分方程的求解，提出在二维合并Voronoi-Delaunay网格上构造梯度、散度和旋度算子的一致逼近，并以此建立了典型稳态标量与向量问题的算子差分逼近方法。
摘要：
用向量（张量）分析的不变算子来表述多维偏微分方程的边值问题十分方便。近似解的计算算法基于构造向量分析算子的网格模拟。当网格节点与单元顶点重合或为单元中心时，通过将计算域划分为矩形单元最容易实现这一点。不规则区域的向量分析网格算子是使用Delaunay三角剖分或Voronoi划分构造的。本文使用二维合并Voronoi-Delaunay网格将网格单元表示为正交对角四边形。提出了梯度、散度和旋度算子的一致逼近。在此基础上，构造了典型稳态标量和向量问题的算子差分逼近。
英文摘要：
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing grid analogs of vector analysis operators. This is most easily done by dividing the computational domain into rectangular cells when the grid nodes coincide with the cell vertices or are the cell centers. Grid operators of vector analysis for irregular regions are constructed using Delaunay triangulations or Voronoi partitions. This paper uses two-dimensional merged Voronoi-Delaunay grids to represent the grid cells as orthodiagonal quadrilaterals. Consistent approximations of the gradient, divergence, and rotor operators are proposed. On their basis, operator-difference approximations for typical stationary scalar and vector problems are constructed.
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