Volume 13, Issue 4
Solution Remapping Technique to Accelerate Flow Convergence for Finite Volume Methods Applied to Shape Optimization Design

Jufang Wang, Zheng Wang & Tiegang Liu

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 863-880.

Published online: 2020-06

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  • Abstract

A solution remapping technique is applied to transonic airfoil optimization design to provide a fast flow steady state convergence of intermediate shapes for the finite volume schemes in solving the compressible Euler equations. Specifically, once the flow solution for the current shape is obtained, the flow state for the next shape is initialized by remapping the current solution with consideration of mesh deformation. Based on this strategy, the formula of deploying the initial value for the next shape is theoretically derived under the assumption of small mesh deformation. Numerical experiments show that the present technique of initial value deployment can attractively accelerate flow convergence of intermediate shapes and reduce computational time up to 70% in the optimization process.

  • Keywords

Solution remapping technique, airfoil shape optimization, finite volume scheme, initial value.

  • AMS Subject Headings

49Q10, 65M08, 65M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-13-863, author = {Jufang Wang , and Zheng Wang , and Tiegang Liu , }, title = {Solution Remapping Technique to Accelerate Flow Convergence for Finite Volume Methods Applied to Shape Optimization Design}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {863--880}, abstract = {

A solution remapping technique is applied to transonic airfoil optimization design to provide a fast flow steady state convergence of intermediate shapes for the finite volume schemes in solving the compressible Euler equations. Specifically, once the flow solution for the current shape is obtained, the flow state for the next shape is initialized by remapping the current solution with consideration of mesh deformation. Based on this strategy, the formula of deploying the initial value for the next shape is theoretically derived under the assumption of small mesh deformation. Numerical experiments show that the present technique of initial value deployment can attractively accelerate flow convergence of intermediate shapes and reduce computational time up to 70% in the optimization process.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0164}, url = {http://global-sci.org/intro/article_detail/nmtma/16957.html} }
TY - JOUR T1 - Solution Remapping Technique to Accelerate Flow Convergence for Finite Volume Methods Applied to Shape Optimization Design AU - Jufang Wang , AU - Zheng Wang , AU - Tiegang Liu , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 863 EP - 880 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0164 UR - https://global-sci.org/intro/article_detail/nmtma/16957.html KW - Solution remapping technique, airfoil shape optimization, finite volume scheme, initial value. AB -

A solution remapping technique is applied to transonic airfoil optimization design to provide a fast flow steady state convergence of intermediate shapes for the finite volume schemes in solving the compressible Euler equations. Specifically, once the flow solution for the current shape is obtained, the flow state for the next shape is initialized by remapping the current solution with consideration of mesh deformation. Based on this strategy, the formula of deploying the initial value for the next shape is theoretically derived under the assumption of small mesh deformation. Numerical experiments show that the present technique of initial value deployment can attractively accelerate flow convergence of intermediate shapes and reduce computational time up to 70% in the optimization process.

Jufang Wang, Zheng Wang & Tiegang Liu. (2020). Solution Remapping Technique to Accelerate Flow Convergence for Finite Volume Methods Applied to Shape Optimization Design. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 863-880. doi:10.4208/nmtma.OA-2019-0164
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