数据驱动的浸没边界速度重构方法

Data-driven velocity reconstruction for immersed boundary methods

  • 摘要: 浸没边界方法(immersed boundary method, IBM)广泛应用于复杂几何边界的不可压缩流动中,其中直接力法计算和编程简单,能很好地捕捉壁面流动,但在非定常不可压缩流中难以维持速度场的无散性。为此,本文提出了一种基于数据驱动的浸没边界速度重构方法(DATA-I),通过数据集构造和训练方法的改进,能够捕捉近壁面速度的非线性关系,从而在数值模拟中保持不可压缩流动的无散性。为验证该方法的有效性,本文对雷诺数20 ~ 500的二维圆柱绕流进行了数值模拟,并通过方柱和尖楔绕流算例测试了数据驱动模型的几何泛化能力。在定常圆柱绕流算例中,该方法相较于传统插值方法降低了44.7% ~ 70.4%的散度误差,非定常圆柱绕流的斯特劳哈尔数的误差控制在5%以内。该研究为 IBM 在不可压流动中壁面流动的精确模拟提供了新的解决思路。

     

    Abstract: The Immersed Boundary Method (IBM) is widely used for incompressible flows with complex geometric boundaries. Among its variants, the direct forcing method is computationally and programmatically straightforward and effectively captures near-wall flow behavior. However, it struggles to maintain the divergence-free condition of the velocity field in unsteady incompressible flows. To address this issue, this paper proposes a data-driven velocity reconstruction approach for the immersed boundary method (DATA-I). By improving dataset construction and training methodologies, the method captures the nonlinear relationships of near-wall velocities, thereby preserving the divergence-free property in numerical simulations of incompressible flows. To validate the effectiveness of the proposed method, numerical simulations of two-dimensional flow around a circular cylinder at Reynolds numbers ranging from 20 to 500 were conducted. Additionally, the geometric generalization capability of the data-driven model was tested using flow cases around a square cylinder and a sharp wedge. In the steady flow past a circular cylinder, the method reduced divergence errors by 44.7% to 70.4% compared to traditional interpolation approaches. For unsteady cylinder flow, the error in the Strouhal number was controlled within 5%. This study offers a novel solution for accurately simulating near-wall flows in incompressible fluid dynamics using the IBM.

     

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