移动边界问题的谱元法求解
Solution of moving-boundary problems by the spectral element method
AI总结：
提出一种基于谱元法和动网格技术的数值模型，用于求解自由表面流或流固耦合等移动边界问题，并通过二维和三维模拟验证其精度和鲁棒性。
摘要：
本文描述了一种新颖的数值模型，旨在求解移动边界问题，如自由表面流或流固耦合。该模型使用动网格技术求解以任意拉格朗日-欧拉运动学表达的纳维-斯托克斯方程。空间离散基于谱元法。流体方程和动网格方程的耦合主要通过移动边界上的条件实现。给出了二维和三维模拟：流体中圆柱体的平移和旋转，以及矩形水箱中的大幅晃动。研究并讨论了本数值模型的精度和鲁棒性。
英文摘要：
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in the arbitrary Lagrangian--Eulerian kinematics. The discretization in space is based on the spectral element method. The coupling of the fluid equations and the moving-grid equations is essentially done through the conditions on the moving boundaries. Two- and three-dimensional simulations are presented: translation and rotation of a cylinder in a fluid, and large-amplitude sloshing in a rectangular tank. The accuracy and robustness of the present numerical model is studied and discussed.
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