论文标题
通过有限生成曲线描述的毛细管表面的光谱方法
Spectral Methods for capillary surfaces described by bounded generating curves
论文作者
论文摘要
我们考虑通过有限的生成曲线构建的毛细管表面。这类表面包括径向对称和较低的尺寸流体流体界面。我们使用这些表面的微分方程的电弧长度表示，以允许沿生成曲线垂直点和拐点。这些考虑因素接受了环形管中的毛细管，无柄滴和液体以及其他例子。 我们提出了一种基于Chebyshev多项式插值的相关边界值问题的拟合解决方案的伪谱法。该方法比传统的拍摄方法观察到更稳定，并且在计算上既瘦”。该算法也具有自适应，但不使用Chebfun中的自适应自动化。
We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points along the generating curve. These considerations admit capillary tubes, sessile drops, and fluids in annular tubes as well as other examples. We present a pseudo-spectral method for approximating solutions to the associated boundary value problems based on interpolation by Chebyshev polynomials. This method is observably more stable than the traditional shooting method and it is computationally lean and fast. The algorithm is also adaptive, but does not use the adaptive automation in Chebfun.
