Volume preserving integrators for solenoidal fields on a grid
Volume preserving integrators for solenoidal fields on a grid
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DOI：
10.1063/1.1889156
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发表时间：
2005-04
影响因子：
2.2
通讯作者：
J. Finn;L. Chacón
中科院分区：
文献类型：
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作者：
J. Finn;L. Chacón
本文提出了一种新的求解网格上给定的螺线管绕流的积分方法。在三维中，该方法涉及将流动分成两个或可能三个二维和面积保持的流动，因此可以通过Crank-Nicolson或修改形式的蛙跳积分，这两种形式都精确地保持面积。该方法涉及到一个插值方案，确保螺线管性质的领域在整个域（上和下的网格）通过三次样条。结果表明，该方法很容易推广到任意曲线坐标系，也推广到高维。本文概述了一种在网格上积分三维压缩流的方法。
A novel method of integrating solenoidal flows given on a grid is developed. In three dimensions, the method involves splitting the flow into two or possibly three flows that are two dimensional and area preserving, and can therefore be integrated by Crank–Nicolson or a modified form of leapfrog, both of which exactly conserve area. The method involves an interpolation scheme which ensures the solenoidal nature of the field throughout the domain (on and off the grid) by means of tricubic splines. It is shown that the method is easily generalized to arbitrary curvilinear coordinates and also generalizes to higher dimensions. A method of integrating compressional three-dimensional flows given on a grid is outlined.