Cosserat运动方程的一般解析解
On the General Analytical Solution of the Kinematic Cosserat Equations
摘要：
基于Lie对称性分析，我们构造了描述弹性杆力学行为的Cosserat方程（偏微分）运动学部分的封闭形式解。该解依赖于两个任意的解析向量函数，并且除了自变量的某个域之外处处解析，其中任意向量函数之一满足一个简单的显式代数关系。作为我们的主要理论结果，除了解决方案的建设，我们证明了它的一般性。基于这一观察，高粘性双向耦合流体杆问题的混合半解析求解器的开发，它允许的鞭毛虫microswimmer作为一个结果的数值刚度大幅减少的交互式高保真模拟。
英文摘要：
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
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