Download or read book An Optimization-based Approach to Mesh-polynomial Adaptation of High-order Discretizations written by Nicolas Ringue and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Computational Fluid Dynamics (CFD) is an essential tool for scientists and engineers to understand and quantify aerodynamic flow. Numerous challenges however remain in order to improve computational efficiency, robustness and reliability of CFD methods. Mesh generation is one of the most time-consuming aspects of industrial CFD simulations since their accuracy heavily depends on mesh quality. In this context, mesh adaptation appears as one of the most promising approaches to improve CFD simulations. Since only an initial coarse grid is required, adaptive CFD algorithms enable a significant reduction in the amount of time spent on mesh generation as well as in the dependence of the accuracy of flow predictions on user input.This thesis presents a novel framework for hp-adaptation of high-order discontinuous finite element discretizations for compressible flow simulation. Using the sensitivities of a local adjoint-based error indicator, our method seeks element size, shape, and polynomial degree distributions which minimize a global error estimate for a specified number of degreesof freedom. This approach results in an optimized hp-mesh tailored to yield the most accurate prediction of an output quantity of interest, such as aerodynamic lift or drag coefficients, at a given computational cost. The proposed method features a reduced dependence on userdefined parameters compared to established fixed-fraction adjoint-based adaptive methods.It provides a unifying framework where adaptation decisions such as isotropic/anisotropic hp-refinement/coarsening do not only rely on local arbitrary measures of solution anisotropy and smoothness, but rather where a globally optimal distribution of degrees of freedom is sought to minimize the error in the chosen quantity of interest"--