In this work, a solution remapping technique is developed to accelerate the flow convergence for the intermediate shapes when a high-order discontinuous Galerkin (DG) method is employed as a compressible Euler flow solver in the airfoil design problems. Once the shape is updated, the proposed technique is applied to initialize the flow simulation for the new shape via a solution remapping formula and a maximum-and-minimum-preserving limiter. First, the solution remapping formula is used to remap the solution of the current shape into a piecewise polynomial on the mesh of the new shape. Then the piecewise polynomial is constrained with the maximum-and-minimum-preserving limiter. The modified piecewise polynomial is used as the initial value for the new shape. Numerical experiments show that the proposed technique can attractively accelerate flow convergence and significantly reduce up to 80% of the computational time in the airfoil design problems with a high-order DG solver.

在这项工作中，开发了一种解决方案重新映射技术，以在机翼设计问题中采用高阶不连续Galerkin（DG）方法作为可压缩的Euler流动求解器时，加快中间形状的流动收敛。形状更新后，将通过溶液重映射公式和最大最小保留限制器将提出的技术应用于新形状的流动模拟初始化。首先，使用解重新映射公式将当前形状的解重新映射为新形状的网格上的分段多项式。然后，分段多项式受最大和最小保留限制器约束。修改后的分段多项式用作新形状的初始值。