Parallel Mesh Deformation Method Using Support Vector Regression for Aerodynamics

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.