论文标题
通过虚拟元素方法对沉浸式刚性传单的平衡分析
Equilibrium analysis of an immersed rigid leaflet by the virtual element method
论文作者
论文摘要
我们从理论和数字上研究了带有附着的旋转弹簧的铰链刚性小叶的平衡，并浸入刚性通道内的固定不可压缩的流体中。通过仔细研究功能的特性，描述了流体在传单上施加的角动量（这既取决于小叶角位置及其厚度），我们确定了在春季僵硬功能（和唯一性）平衡位置的春季僵硬功能上的足够条件。我们提出了一种数值技术，该技术利用虚拟元素方法（VEM）的网格灵活性。通过切割固定的背景网格与传单几何形状来生成A（多边形）计算网格，然后使用稳定的VEM Stokes元素$ 1 $ $ 1 $和2 $结合结合双分配算法来解决问题。我们提出了大量的数值实验，以记录提出方法学的变性几何形状的准确性和鲁棒性。
We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the properties of the functional describing the angular momentum exerted by the fluid on the leaflet (which depends on both the leaflet angular position and its thickness), we identify sufficient conditions on the spring stiffness function for the existence (and uniqueness) of equilibrium positions. We propose a numerical technique that exploits the mesh flexibility of the Virtual Element Method (VEM). A (polygonal) computational mesh is generated by cutting a fixed background grid with the leaflet geometry, and the problem is then solved with stable VEM Stokes elements of degrees $1$ and $2$ combined with a bisection algorithm. We present a large array of numerical experiments to document the accuracy and robustness with respect to degenerate geometry of the proposed methodology.
