Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid
Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid
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DOI：
10.1142/s1758825115500453
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发表时间：
2015-06
影响因子：
3.5
通讯作者：
Lihua Wang;Z. Zhong
中科院分区：
文献类型：
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作者：
Lihua Wang;Z. Zhong
提出了一种结合显式和隐式时间积分方案的无网格径向基配置方法（RBCM），研究了含变系数偏微分方程（PDE）的旋转柔性管输送流体的耦合动力学问题。进行了色散研究，结果表明，与传统有限元法和基于galerkin的无网格方法相比，该方法具有非常小的色散误差。通过数值算例分析了流体初始流速、离散化和形状参数对离散误差的影响。临界时间步长由冯·诺依曼稳定性分析得到。对于特征问题，提出了hermite型RBCM构造方阵，并通过特征值分析给出了系统的频率。随后，研究了流体角速度、流速和时间变化对基频的影响。虽然该方案是为研究旋转柔性管输送流体的动力学问题而提出的，但也适用于其他具有类似变系数偏微分方程的动力学问题。
A Meshfree Radial Basis Collocation Method (RBCM) associated with explicit and implicit time integration scheme is formulated to study the coupling dynamics of a rotating flexible tube conveying fluid, which involves a partial differential equation (PDE) with variable coefficients. Dispersion studies are performed and they indicate that the proposed RBCM has a very small dispersion error compared with conventional FEM and Galerkin-based meshfree methods. Numerical examples are conducted for the influence of initial flow rate of the fluid, discretization and shape parameter on the dispersion error. The critical time step is obtained from a Von Neumann stability analysis. For the eigenproblem, Hermite-type RBCM is proposed in order to construct square matrices and eigenvalue analysis gives the frequencies of the system. Subsequently, the influence of angular velocity, flow rate of the fluid and the time variation on the fundamental frequencies is studied. Though proposed for studying the dynamics of a rotating flexible tube conveying fluid, this solution scheme is applicable to other dynamical problems which have similar PDEs with variable coefficients.