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基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

AN IMMERSED BOUNDARY LATTICE BOLTZMANN METHOD BASED ON IMPLICIT DIFFUSE DIRECT-FORCING SCHEME

  • 摘要: 采用浸没边界格子Boltzmann (immersed boundary-lattice Boltzmann, IB-LB)模型执行动边界绕流数值模拟时, 信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率. 基于隐式扩散界面, 一种改进的直接力格式IB-LB模型被提出. 边界力表达式基于欧拉/拉格朗日变量同一性准则推导, 转换矩阵描述的信息交互界面耦合了拉格朗日节点间的非同步运动. 采用Richardson迭代数值求解关联边界力与无滑移速度约束的线性方程组, 不仅克服了传统速度修正格式中矩阵求逆引起的计算效率问题, 而且摆脱了算法稳定性对拉格朗日点分布的依赖. 根据解析解已知的Taylor-Green涡流评估本文模型的数值模拟精度, 结果表明改进的IB模型能够完整保留背景LB模型的二阶数值精度. 静止圆柱和振荡圆柱绕流数值实验结果表明, 当前模型在涉及复杂外形和运动界面的流动模拟中能够提供可靠的数值预测, 满足力同一性的IB-LB模型能够有效抑制非定常流体力的伪物理震荡. 波动翼型绕流模拟验证了当前模型的实用性, 可在大变形柔性体流固耦合动力学问题中进一步推广.

     

    Abstract: When the immersed boundary-lattice Boltzmann (IB-LB) model with the direct-forcing scheme is used to analyze the viscous fluid dynamics of the flow around a moving boundary, the interaction interface and the boundary force format directly affect the numerical accuracy and computational efficiency of the flow solver. Based on the implicit diffuse interface, an improved IB-LB model with the direct-forcing scheme was presented. The boundary force expression is derived based on Eulerian/Lagrangian variable identities. The interaction interface described by the transfer matrix couples the asynchronous movement between Lagrangian points. Use Richardson iteration to numerically solve the linear equations related to the boundary force and the non-slip velocity constraint. It not only overcomes the calculation efficiency problem caused by matrix inversion in the traditional velocity correction scheme, but also gets rid of the dependence of algorithm stability and Lagrangian point distribution. According to the Taylor-Green flow with analytical solution, the numerical accuracy of the present model is evaluated. The results show that the improved IB model can retain the second-order numerical accuracy of the background LB model. The numerical results of the flow over a stationary cylinder and an oscillating cylinder show that the model can provide reliable numerical predictions in the flow simulation involving complex geometries and moving interfaces. The IB-LB model yielded the force identity can effectively suppress the non-physical oscillation of the predicted hydrodynamic forces. The simulation of the flow around the undulating airfoil verifies the practicability of the current model, and can be further popularized in the fluid-structure coupling simulation of large-deformation flexible bodies.

     

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