• 论文 •

### 非结构网格上针对间断有限元方法的初值重映流场收敛加速技术

1. LMIB, 北京航空航天大学数学科学学院, 北京 100191
• 收稿日期:2020-12-07 发布日期:2021-06-03
• 基金资助:
国家自然科学基金（U1730118，91530325）资助.

Wang Jufang, Liu Tiegang. SOLUTION REMAPPING TECHNIQUE TO ACCELERATE FLOW CONVERGENCE FOR DISCONTINUOUS GALERKIN METHODS ON UNSTRUCTURED MESHES[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 169-182.

### SOLUTION REMAPPING TECHNIQUE TO ACCELERATE FLOW CONVERGENCE FOR DISCONTINUOUS GALERKIN METHODS ON UNSTRUCTURED MESHES

Wang Jufang, Liu Tiegang

1. LMIB, School of Mathematical Sciences, Beihang University, Beijing 100191, China
• Received:2020-12-07 Published:2021-06-03

A framework of the solution remapping technique on unstructured meshes is proposed to accelerate flow convergence for the discontinuous Galerkin (DG) methods in aerodynamic shape optimization. A local one-to-one correspondence between the meshes of different shapes is established by the one-to-one mappings from a given reference cell to each grid cell in the physical domain if the mesh topology is preserved in the optimization process. Then when the shape is updated, the solution of the current shape is remapped to the mesh of the new shape as the initial value to accelerate the convergence of the DG solver. The proposed framework is implemented in the airfoil design problem on triangular meshes. Numerical experiments show that more than 70% of the computational time can be saved with a third-order DG solver.

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