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%0 Thesis
%A Rangarajan, Ajay Mandyam
%T Metric based hp−adaptation using a continuous mesh model for higher order schemes
%I Rheinisch-Westfälische Technische Hochschule Aachen
%V Dissertation
%C Aachen
%M RWTH-2021-03746
%P 1 Online-Ressource : Illustrationen, Diagramme
%D 2021
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
%Z Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2021
%X Adaptive meshing has been considered as a significant bottleneck in the advancement of Computational Fluid Dynamics (CFD). It is important, in particular, for flows that exhibit strong features such as singularities and shocks. In parallel, the use of higher order methods that use piecewise polynomial approximation spaces on meshes, such as Discontinuous Galerkin (DG) and Flux Reconstruction, has been increasing. For these schemes, the size and shape of the mesh elements (h−adaptation) and the local polynomial order (p−adaptation) or both can be optimized (hp−adaptation). Accomplishing this optimization based on a Riemannian metric field has gained popularity in the last decade for lower-order schemes as well as recently for higher order schemes. In this context, the notion of a continuous mesh was introduced in Loseille2011 and Loseille2011a. Based on higher order error models derived in Dolejsi2014, the h−adaptation to minimize the L<sup>q</sup> norm of a scalar field using the Hybridized DG scheme has been done as part of previous work in Rangarajan2016 and Rangarajan2018. Here, the adaptation framework has been developed for any scheme that uses a piecewise-polynomial representation for the solution. Further, an hp−adaptation technique based on the continuous mesh model has been derived. Finally, a novel error model has been developed to construct a goal-oriented adaptation based on the consistency arguments of numerical fluxes. The error model inherits the properties of the continuous approach such as being scheme independent and parameter-free. The adaptation techniques has been validated in both two- and three-dimensions. The construction of near-optimal meshes has been demonstrated using different solvers and mesh generators for various types of flows, including turbulent aerodynamic cases.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2021-03746
%U https://publications.rwth-aachen.de/record/817176