Adjoint-Based Adaptive Isogeometric Discontinuous Galerkin Method for Euler Equations

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.