A cubic spline approximation for problems in fluid mechanics
A cubic spline approximation for problems in fluid mechanics
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发表时间：
1975-10
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通讯作者：
S. Rubin;R. A. Graves
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作者：
S. Rubin;R. A. Graves
提出了一种适用于多种流体力学问题的三次样条法。这一过程提供了很高的精度，即使在网格不均匀的情况下也是如此，并导致了对导数边界条件的精确处理。给出了几种隐式和显式积分格式的截断误差和稳定性极限。对于二维流，采用了一种样条交替方向隐式方法。对样条法进行了评价，并给出了一维非线性Burgers型方程、二维扩散方程和描述驱动腔内粘性流动的涡度-流函数系统的结果。与前两个问题的解析解和空腔流动的有限差分计算进行了比较。
A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.