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Parallel Mesh Deformation Method Using Support Vector Regression for Aerodynamics

机译：支持向量回归的空气动力学并行网格变形方法

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Mesh deformation technique is widely applied in unsteady aerodynamic simulation involving moving boundaries like fluid-structure coupling and shape optimization. This kind of method redistributes the position of grid points in accordance with the movement of the computational domain without changing their connectivity relations. In this paper, we regard the dynamic mesh problem as a nonlinear distribution problem, and present an efficient parallel mesh deformation method based on the support vector regression (SVR). In each time step, the proposed method first trains three SVRs using the coordinates of the boundary points and their known displacements in each direction as training data, and then predicts the displacements of the internal points of the mesh using the SVRs. After deforming the mesh, a dual-time step flow solver is used to solve the governing equations. Two kinds of parallel strategies are applied for different types of movement. For pre-known moving boundary cases, only a special CPU process is assigned to train the SVRs one time step earlier than the flow computing, so that the training cost will be hidden. For unpredictable moving boundary case, to ensure the consistency of the method running in parallel, the training part of the method is executed with all global boundary points in each decomposed domain. Therefore, each CPU needs to maintain a copy of the entire boundary points via a point-to-point communication. The internal evaluation of the method is predicted separately in each decomposed domain without any data dependency. An oscillatory and transient pitching airfoil case is simulated to demonstrate the applicability of the proposed mesh deformation method, and its parallel efficiency for the second strategy is over 60% with 64 cores.
机译：网格变形技术已广泛应用于涉及流动边界的非定常空气动力学模拟，例如流固耦合和形状优化。这种方法根据计算域的移动来重新分配网格点的位置，而不会更改它们的连接关系。在本文中，我们将动态网格问题视为非线性分布问题，并提出了一种基于支持向量回归（SVR）的有效并行网格变形方法。在每个时间步中，所提出的方法首先使用边界点的坐标及其在每个方向上的已知位移作为训练数据来训练三个SVR，然后使用SVR预测网格内部点的位移。网格变形后，使用双时间步流求解器求解控制方程。两种并行策略适用于不同类型的运动。对于已知的移动边界情况，仅分配一个特殊的CPU进程来比流计算提前一个时间步来训练SVR，因此将隐藏训练成本。对于无法预测的移动边界情况，为了确保方法并行运行的一致性，将对方法的训练部分执行每个分解域中的所有全局边界点。因此，每个CPU需要通过点对点通信维护整个边界点的副本。该方法的内部评估是在每个分解域中单独预测的，没有任何数据依赖性。模拟了一个振荡和瞬变俯仰翼型的情况，以证明所提出的网格变形方法的适用性，其第二种策略的并行效率在使用64个芯子的情况下超过60％。

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