Towards the efficient calculation of quantity of interest from steady Euler equations I: a dual-consistent DWR-based h-adaptive Newton-GMG solver
Abstract
The dual consistency is an important issue in developing stable DWR error estimation towards the goal-oriented mesh adaptivity. In this paper, such an issue is studied in depth based on a Newton-GMG framework for the steady Euler equations. Theoretically, the numerical framework is redescribed using the Petrov-Galerkin scheme, based on which the dual consistency is depicted. A boundary modification technique is discussed for preserving the dual consistency within the Newton-GMG framework. Numerically, a geometrical multigrid is proposed for solving the dual problem, and a regularization term is designed to guarantee the convergence of the iteration. The following features of our method can be observed from numerical experiments, i). a stable numerical convergence of the quantity of interest can be obtained smoothly for problems with different configurations, and ii). towards accurate calculation of quantity of interest, mesh grids can be saved significantly using the proposed dual-consistent DWR method, compared with the dual-inconsistent one.
Keywords
Cite
@article{arxiv.2302.14262,
title = {Towards the efficient calculation of quantity of interest from steady Euler equations I: a dual-consistent DWR-based h-adaptive Newton-GMG solver},
author = {Jingfeng Wang and Guanghui Hu},
journal= {arXiv preprint arXiv:2302.14262},
year = {2023}
}
Comments
In this work, we validated the dual consistency under the Newton-GMG framework. Based on the previous work, we further constructed the h-adaptivity method for the steady Euler equations in the AFVM4CFD package