高阶DLM-ALE离散化方法与稳健操作符预处理用于流体-刚体相互作用
High-order DLM-ALE discretizations with robust operator preconditioning for fluid-rigid-body interaction
AI总结：
本文提出高阶DLM-ALE离散化方法与稳健操作符预处理，用于高精度模拟流体-刚体相互作用。
摘要：
受确定性横向位移（DLD）微流体设备设计的启发，我们开发了一种高阶数值框架，用于在适配移动网格上处理流体-刚体相互作用。刚体运动通过分布式拉格朗日乘数（DLM）公式强制执行，而移动流体域则通过任意拉格朗日-欧拉（ALE）映射进行处理。在空间上，我们使用等参数泰勒-霍德元素以实现高阶精度，并表示弯曲边界和流体-粒子界面。在时间上，我们采用高阶分区龙格-库塔策略，在其中网格运动被显式推进，而耦合的物理场被隐式推进，从而为粒子轨迹提供高阶精度。完全耦合系统被线性化为一个带有分布式约束的广义斯托克斯问题，这些约束包括不可压缩性和刚体运动。我们建立了该广义斯托克斯公式的连续和离散层面的适定性，为稳健于关键物理和离散化参数的操作符预处理提供了稳定性基础。数值实验在代表性基准上进行，包括DLD案例，展示了流体解和刚体动力学的高阶收敛性，以及所提出预处理程序的稳健迭代收敛性。
英文摘要：
Motivated by the design of deterministic lateral displacement (DLD) microfluidic devices, we develop a high-order numerical framework for fluid-rigid-body interaction on fitted moving meshes. Rigid-body motion is enforced by a distributed Lagrange multiplier (DLM) formulation, while the moving fluid domain is treated by an arbitrary Lagrangian-Eulerian (ALE) mapping. In space, we use isoparametric Taylor-Hood elements to achieve high-order accuracy and to represent curved boundaries and the fluid-particle interface. In time, we employ a high-order partitioned Runge-Kutta strategy in which the mesh motion is advanced explicitly and the coupled physical fields are advanced implicitly, yielding high-order accuracy for the particle trajectory. The fully coupled system is linearized into a generalized Stokes problem subject to distributed constraints of incompressibility and rigid-body motion. We establish well-posedness of this generalized Stokes formulation at both the continuous and discrete levels, providing the stability foundation for operator preconditioning that is robust with respect to key physical and discretization parameters. Numerical experiments on representative benchmarks, including a DLD case, demonstrate high-order convergence for the fluid solution and rigid-body dynamics, as well as robust iterative convergence of the proposed preconditioners.
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