点阵玻尔兹曼法结合浸入边界法模拟弹性杆的旋转不稳定性

IF 1.9 3区 数学 Q1 MATHEMATICS, APPLIED
Axioms Pub Date : 2023-10-26 DOI:10.3390/axioms12111011
Suresh Alapati, Wooseong Che, Sunkara Srinivasa Rao, Giang T. T. Phan
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引用次数: 0

摘要

近年来,生物启发系统的数学建模和分析一直是一个引人入胜的研究课题。在这项工作中,我们介绍了通过使用晶格玻尔兹曼方法(LBM)结合浸入边界方法(IBM)模拟粘性流体中弹性杆(模仿鞭毛轴突)旋转运动的结果。鞭毛轴突的有限元模型是由一组梁和桁架单元组成的,用于对鞭毛轴突进行离散,而流体流动则由著名的LBM求解。利用IBM进行了流体动力耦合,以保持流体与弹性杆之间的无滑移边界条件。该杆是由施加在其基础横截面上的扭矩驱动的,该扭矩作为轴突的驱动马达。我们模拟了电机在三种不同的旋转频率(低、中、高)下的杆的旋转动力学。为了与前人发表的结果进行比较,我们选择精子数Sp=L(4πμω)/(EI)1/4作为验证参数。我们发现,在低旋转频率f = 1.5 Hz时,杆在达到平衡状态后进行稳定的旋转运动(杆围绕其轴进行刚性旋转)。在中频f = 2.65 Hz时,连杆进行旋转运动,连杆尖端围绕驱动电机的中心旋转轴旋转。当频率进一步增大,即达到临界值fc≈2.7 Hz时,旋转运动变为过旋转,灯丝尖端落回底座,进行稳定的曲轴运动。旋转、旋转和过旋转三种旋转动力学以及旋转频率临界值均与前人的研究结果吻合较好。我们还观察到,我们目前的模拟技术在计算上比以前的工作更有效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simulation of an Elastic Rod Whirling Instabilities by Using the Lattice Boltzmann Method Combined with an Immersed Boundary Method
Mathematical modeling and analysis of biologically inspired systems has been a fascinating research topic in recent years. In this work, we present the results obtained from the simulation of an elastic rod (that mimics a flagellum axoneme) rotational motion in a viscous fluid by using the lattice Boltzmann method (LBM) combined with an immersed boundary method (IBM). A finite element model consists of a set of beam and truss elements used to discretize the flagellum axoneme while the fluid flow is solved by the well-known LBM. The hydrodynamic coupling to maintain the no-slip boundary condition between the fluid and the elastic rod is conducted with the IBM. The rod is actuated with a torque applied at its base cross-section that acts as a driving motor of the axoneme. We simulated the rotational dynamics of the rod for three different rotational frequencies (low, medium, and high) of the motor. To compare with previous publication results, we chose the sperm number Sp=L(4πμω)/(EI)1/4 as the validation parameter. We found that at the low rotational frequency, f = 1.5 Hz, the rod performs stable twirling motion after attaining an equilibrium state (the rod undergoes rigid rotation about its axis). At the medium frequency, f = 2.65 Hz, the rod undergoes whirling motion, where the tip of the rod rotates about the central rotational axis of the driving motor. When the frequency increases further, i.e., when it reaches the critical value, fc ≈ 2.7 Hz, the whirling motion becomes over-whirling, where the tip of the filament falls back to the base and performs a steady crank-shafting motion. All three rotational dynamics, twirling, whirling, and over-whirling, and the critical value of rotational frequency are in good agreement with the previously published results. We also observed that our present simulation technique is computationally more efficient than previous works.
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来源期刊
Axioms
Axioms Mathematics-Algebra and Number Theory
自引率
10.00%
发文量
604
审稿时长
11 weeks
期刊介绍: Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.
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