EI、Scopus 收录
中文核心期刊

基于稳定L2投影的有限元–浸没界面耦合方法

FINITE ELEMENT–IMMERSED INTERFACE COUPLING METHOD BASED ON STABILIZED L2 PROJECTION

  • 摘要: 有限元-浸没界面耦合方法(finite element- immersed interface method, FE-IIM)是一类结合有限元离散与浸没界面法边界间断特征的流固耦合模拟方法,旨在实现固体界面处物理量变化的精确解析,但是较差的稳定性限制了该方法的实际应用。本文提出一种基于稳定L2投影的FE-IIM耦合方法,要求固体边界满足C0连续性条件,在边界单元上引入有限元形函数,使得界面处的物理量能够在基函数空间中实现连续、可控的表达。通过稳定L2投影策略,重构固体C0连续边界上的间断条件,建立流场物理量延拓至固体界面的插值方案,有效抑制随着雷诺数增大界面物理量演化过程中易出现的非物理震荡。在间断条件处理中,本文在界面基函数空间内引入一阶导数的间断条件,提升界面物理量的计算准确性。通过分析Re=200-50000条件下的典型数值案例,结果展现了本文方法能够准确捕捉主要流动结构,有效解析边界上物理量的细致变化。稳定投影FE-IIM耦合方法为需要精确捕捉界面压力等物理量分布特征的流固耦合模拟提供理论参考。

     

    Abstract: The finite element–immersed interface method (FE-IIM) is a numerical method for fluid–structure interaction (FSI) that combines finite element discretization with the interface jump treatment of IIM. It aims to achieve accurate resolution of physical quantity variations at the structure interface, but its practical application has been limited by poor numerical stability. In this study, a stabilized L2 projection-based FE-IIM coupling method is proposed. This method requires the structure interface to satisfy the C0 continuity condition and introduces finite element shape functions on the boundary elements, yielding continuous and controllable representations of interfacial physical quantities within the basis function space. Through the stabilized L2 projection strategy, the jump conditions of IIM across the C0-continuous interface are reconstructed, and an interpolation scheme is developed to project flow field variables onto the interfacial basis function space, effectively suppressing non-physical oscillations that tend to arise at high Reynolds numbers. In treating interfacial discontinuities, first-order derivative jump conditions are introduced into the interfacial basis function space, enhancing the computational accuracy of interfacial variables. Numerical tests with Reynolds numbers ranging from 200 to 50,000 demonstrate that the proposed method can accurately capture the major flow structures and resolve fine-scale variations of physical quantities at the interface. The stabilized projection-based FE-IIM coupling approach provides a promising theoretical framework for simulating FSI problems that require high-fidelity resolution of interface quantities such as pressure.

     

/

返回文章
返回