A General Finite Difference Method for Arbitrary Meshes
A General Finite Difference Method for Arbitrary Meshes
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DOI：
10.1016/0045-7949(75)90018-8
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发表时间：
1975-04
影响因子：
4.7
通讯作者：
N. Perrone;R. Kao
中科院分区：
文献类型：
--
作者：
N. Perrone;R. Kao
一个二维的不规则网格的有限差分技术制定的衍生物的二阶。给定中心点附近的域被分成八个45度饼形段，并记录每个段中距中心点最近的有限差分点。通过利用泰勒级数展开的中心点的一个独特的平均过程中的四个对角线段的点，良好的逼近的所有衍生物，直到二阶，包括混合衍生物。对于正方形网格，所确定的任意网格的一般导数表达式归结为通常的有限差分公式。在一个示例问题中，针对不规则网格求解泊松方程。在第二个例子中，第一次的几何非线性问题，即大挠度响应的平膜，解决了不规则网格。该解决方案与以前获得的结果相比非常有利。讨论了确定二阶以上有限差分导数的可能方法。
A two-dimensional finite-difference technique for irregular meshes is formulated for derivatives up to the second order. The domain in the vicinity of a given central point is broken into eight 45 degree pie shaped segments and the closest finite-difference point in each segment to the center point is noted. By utilizing Taylor series expansions about a central point with a unique averaging process for the points in the four diagonal segments, good approximations to all derivatives up to the second order and including the mixed derivatives are obtained. For square meshes the general derivative expressions for arbitrary meshes which were determined reduce to the usual finite difference formulae. In one example problem the Poisson equation is solved for an irregular mesh. In a second example for the first time a problem with a geometric nonlinearity, namely large deflection response of a flat membrane, is solved with an irregular mesh. The solutions compare very favorably with results obtained previously. Some discussion is given on possible approaches for determination of finite difference derivatives higher than the second.