水螅水母\textit{Aequorea victoria}流态数值模拟的任意拉格朗日-欧拉公式
An arbitrary Lagrangian-Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa \textit{Aequorea victoria}
摘要：
提出了一种新的几何守恒的任意拉格朗日-欧拉（ALE）格式，用于无旋柱坐标系中的动边界问题。控制方程乘以径向距离，并集成在任意移动拉格朗日-欧拉四边形元素。因此，连续性和几何守恒方程采取类似于笛卡尔坐标的非常简单的形式。在每个单元内精确地满足连续性方程，并特别注意在离散水平上满足几何守恒定律（GCL）。除了纳维-斯托克斯方程之外，还以完全耦合的形式求解变形体的运动方程。通过求解每个时间水平的线性弹性方程来实现网格变形，同时避免重新网格化以增强数值鲁棒性。使用PETSc库提供的ILU（k）预处理GMRES方法求解所得的代数线性系统。本文的ALE方法在圆柱管内定常和振荡绕流中得到了验证，并应用于自由游动的水螅水母\textit{Aequorea victoria}（水晶水母）的绕流流态研究。水螅水母的计算表明，相反的符号的涡环非常接近彼此和形成大的诱导速度沿线的相互作用，而环涡远离水螅水母的脱落。此外，自由游泳的水螅水母的推进效率的计算和它的值进行了比较，从文献中的几个其他物种的值。这里展示的流体动力学视频显示了自由游动的水螅\textit{Aequorea victoria}周围瞬时三维涡量等值面的时间变化。
英文摘要：
A new geometrically conservative arbitrary Lagrangian-Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian-Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier-Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc library. The present ALE method is validated for the steady and oscillatory flow around a sphere in a cylindrical tube and applied to the investigation of the flow patterns around a free-swimming hydromedusa \textit{Aequorea victoria} (crystal jellyfish). The calculations for the hydromedusa indicate the shed of the opposite signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction while the ring vortices moving away from the hydromedusa. In addition, the propulsion efficiency of the free-swimming hydromedusa is computed and its value is compared with values from the literature for several other species. The fluid dynamics video presented here shows the time variation of the instantaneous three-dimensional vorticity isosurfaces around a free-swimming hydromedusa \textit{Aequorea victoria}.
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