Year: 2018
Author: Shengjiao Yu, Renzhong Feng, Huiqiang Yue, Zheng Wang, Tiegang Liu
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 652–672
Abstract
In this work, an adjoint-based adaptive isogeometric discontinuous Galerkin method is developed for Euler equations. Firstly, the solution space used in DG on each cell is constructed with the locally owned geometric representation by the isogeometric concept. Then the local $h$-refinement is applied directly through Bézier decomposition, without the restrictions of tensor product nature or basis function support. Furthermore, the adjoint-based error estimator is employed to enhance the estimation of practical engineering outputs. With the isogeometric concept, a novel and natural adjoint space is proposed for the associated discrete adjoint problem. Several numerical examples are selected to demonstrate its ability of handling curved geometry, capturing shocks as well as efficiency in reducing the computational cost in comparison to uniform mesh refinement.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0046
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 652–672
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Discontinuous Galerkin isogeometric analysis adjoint-based error estimation adaptive refinement Euler equations.
Author Details
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