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Local-Maximum-and-Minimum-Preserving Solution Remapping Technique to Accelerate Flow Convergence for Discontinuous Galerkin Methods in Shape Optimization Design

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Abstract

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.

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Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to acknowledge the support of National Numerical Wind Tunnel Project and the National Natural Science Foundation of China (No.U1730118 and No.91530325).

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  1. LMIB, School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Jufang Wang & Tiegang Liu

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  1. Jufang Wang
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Wang, J., Liu, T. Local-Maximum-and-Minimum-Preserving Solution Remapping Technique to Accelerate Flow Convergence for Discontinuous Galerkin Methods in Shape Optimization Design. J Sci Comput 87, 79 (2021). https://doi.org/10.1007/s10915-021-01499-8

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