AI 中文总结
该研究提出采用Mortar单元法的无矩阵有限元框架，结合高阶方法模拟旋转混合设备，通过多算例验证其稳健性、准确性与高效性，适配旋转几何流场模拟。
AI 中文摘要
我们提出了一种有限元框架，用于采用Mortar单元法作为区域分解策略来模拟旋转混合设备。该模型在采用高阶连续Galerkin方法的无矩阵Navier-Stokes框架中实现，离散化的区域被细分为转子和定子部分。任意拉格朗日-欧拉方法用于处理转子与定子的相对运动，通过流线迎风/Petrov-Galerkin方法和压力稳定Petrov-Galerkin方法确保稳定性。转子与定子区域通过由Mortar单元组成的界面连接，以间断Galerkin方式通过考虑转子-定子界面的边界积分来弱强制连续性。二维稳态和瞬态算例的收敛阶验证显示达到最优速率，转子旋转在Mortar界面处产生的几何非一致性不会给解引入显著误差。三维算例用于研究模型的可扩展性，对大问题实现了理想的强缩放。二维Rushton叶轮算例采用扭矩分析展示网格收敛性，对应的速度剖面与现有数值结果一致。在三维斜桨涡轮机案例中，功率数曲线（Np vs Re）在雷诺数1至2000范围内与实验数据吻合良好。能量平衡分析显示，Re=200时数值耗散为1%，Re=2000时为10%。通过无矩阵方法利用现代硬件能力，所提模型是一种适用于旋转几何流场模拟的稳健、准确且高效的框架。
英文摘要
We present a finite element framework to simulate rotating mixing devices using the Mortar Element Method as a domain decomposition strategy. The model is implemented within a matrix-free Navier-Stokes framework which uses a high-order Continuous Galerkin method. The discretized domain is subdivided into rotor and stator parts. An Arbitrary Lagrangian-Eulerian approach accounts for the relative rotor-stator motion, and stabilization is ensured through the Streamline-Upwind/Petrov-Galerkin and Pressure-Stabilizing Petrov-Galerkin methods. The rotor-stator domains are connected by an interface composed of mortar cells, and continuity is weakly enforced in a Discontinuous Galerkin fashion by accounting for boundary integrals at the rotor-stator interface. Verifications of the convergence order in two-dimensional steady and transient examples report optimal rates. The geometric non-conformity created at the mortar interface due to rotor rotation does not introduce significant error in the solution. A three-dimensional example is used to investigate the model's scalability, which yields ideal strong scaling for large problems. A two-dimensional Rushton impeller example uses a torque analysis to showcase the mesh convergence, and the corresponding velocity profile is in agreement with existing numerical results. In a three-dimensional pitched blade turbine case, the power number curve (Np vs Re) shows good agreement with experimental data for Reynolds number values from 1 to 2000. An energy balance analysis reports a numerical dissipation of 1% for Re=200 and of 10% for Re=2000. By exploiting modern hardware capabilities through matrix-free methods, the proposed model is a robust, accurate, and efficient framework suitable for simulating flows with rotating geometries.
