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On the General Analytical Solution of the Kinematic Cosserat Equations

机译:运动Cosserat方程的一般解析解

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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.
机译:基于Lie对称性分析,我们为描述弹性杆的机械行为的(偏微分)Cosserat方程的运动学部分构造了一个封闭形式的解决方案。该解决方案取决于两个任意解析矢量函数,并且除自变量的某个特定域外都可以解析,在该域中,任意矢量函数之一满足一个简单的,明确给出的代数关系。作为我们的主要理论结果,除了构造解决方案之外,我们还证明了其普遍性。基于此观察结果,开发了一种用于高粘性双向流体杆问题的混合半解析求解器,该方法可对鞭毛微游泳器进行交互式高保真模拟,从而大大降低了数值刚度。

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