论文标题
通过共形变量在有限域中的$ 2 $ d流体的动力学
Dynamics of $2$D fluid in bounded domain via conformal variables
论文作者
论文摘要
在目前的工作中，我们计算在存在表面张力的情况下，在$ 2 $ d的理想液体边界上的不分化方程的数值解。我们发现，具有多个裂片的溶液倾向于接近许多裂片极限的毛细管波。随着它们变得更加非线性，带有一些裂片的解决方案变得延长。目前尚不清楚是否存在少量裂片及其特性的限制解决方案。通过通过牛顿 - 偶联物残差方法求解非线性伪差方程来发现溶液。我们使用傅立叶基础将解决方案与最高$ n = 65536 $的傅立叶模式的数量近似。
In the present work we compute numerical solutions of an integro-differential equation for traveling waves on the boundary of a $2$D blob of an ideal fluid in the presence of surface tension. We find that solutions with multiple lobes tend to approach Crapper capillary waves in the limit of many lobes. Solutions with a few lobes become elongated as they become more nonlinear. It is unclear whether there is a limiting solution for small number of lobes, and what are its properties. Solutions are found from solving a nonlinear pseudo--differential equation by means of the Newton-Conjugate Residual method. We use Fourier basis to approximate the solution with the number of Fourier modes up to $N = 65536$.
