A strongly coupled immersed boundary method for fluid-structure interaction that mimics the efficiency of stationary body methods
A strongly coupled immersed boundary method for fluid-structure interaction that mimics the efficiency of stationary body methods
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DOI：
10.1016/j.jcp.2021.110897
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发表时间：
2021-03
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通讯作者：
Nirmal J. Nair;Andres Goza
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作者：
Nirmal J. Nair;Andres Goza
强耦合浸入边界（IB）方法同时求解非线性流体和结构运动方程，以加强对物体的无滑移约束。处理这个约束需要解决几个大的尺寸系统，规模的网格点的数量在流域中，即使非线性约束规模仅由用于表示流体-结构界面的少量的点。这些昂贵的大规模的操作，以确定只有少量的未知数的接口创建一个瓶颈，有效的时间推进强耦合IB方法。在这篇手稿中，我们提出了一个补救措施，这个瓶颈是由固定体IB方法中采用的有效策略，同时保持强耦合算法的良好稳定性，我们预先计算一个矩阵，封装的大尺寸系统，使禁止大规模的操作不需要在每一个时间步执行。这个预先计算过程产生一个修改后的系统的小维约束方程，解决了在最小的计算成本，同时时间推进的方程。我们还提出了一种可在多个处理器上顺利扩展的并行实现。我们的方法的精度，计算效率和可扩展性证明了几个二维流动问题。虽然演示问题包括刚性和扭转安装的机构的组合，配方推导出在一个更一般的设置，涉及任意数量的刚性，扭转安装，和连续变形的机构。
Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large dimensional systems that scale by the number of grid points in the flow domain even though the nonlinear constraints scale only by the small number of points used to represent the fluid-structure interface. These costly large scale operations for determining only a small number of unknowns at the interface creates a bottleneck to efficiently time-advancing strongly coupled IB methods. In this manuscript, we present a remedy for this bottleneck that is motivated by the efficient strategy employed in stationary-body IB methods while preserving the favorable stability properties of strongly coupled algorithms—we precompute a matrix that encapsulates the large dimensional system so that the prohibitive large scale operations need not be performed at every time step. This precomputation process yields a modified system of small-dimensional constraint equations that is solved at minimal computational cost while time advancing the equations. We also present a parallel implementation that scales favorably across multiple processors. The accuracy, computational efficiency and scalability of our approach are demonstrated on several two dimensional flow problems. Although the demonstration problems consist of a combination of rigid and torsionally mounted bodies, the formulation is derived in a more general setting involving an arbitrary number of rigid, torsionally mounted, and continuously deformable bodies.