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Title: Mesh adaptation for high-order flow simulations
Author: Marcon, Julian
ISNI:       0000 0004 9351 0228
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2020
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Mesh adaptation has only been considered for high-order flow simulations in recent years and many techniques are still to be made more robust and efficient with curvilinear meshes required by these high-order methods. This thesis covers the developments made to improve the mesh generation and adaptation capabilities of the open-source spectral/hp element framework Nektar++ and its dedicated mesh utility NekMesh. This thesis first covers the generation of quality initial meshes typically required before an iterative adaptation procedure can be used. For optimal performance of the spectral/hp element method, quadrilateral and hexahedral meshes are preferred and two methods are presented to achieve this, either entirely or partially. The first method, inspired from cross field methods, solves a Laplace problem to obtain a guiding field from which a valid two-dimensional quadrilateral block decomposition can be automatically obtained. In turn, naturally curved meshes are generated. The second method takes advantage of the medial axis to generate structured partitions in the boundary layer region of three-dimensional domains. The method proves to be robust in generating hybrid high-order meshes with boundary layer aligned prismatic elements near boundaries and tetrahedral elements elsewhere. The thesis goes on to explore the adaptation of high-order meshes for the simulation of flows using a spectral/hp element formulation. First a new approach to moving meshes, referred to here as r-adaptation, based on a variational framework, is described. This new r-adaptation module is then enhanced by p-adaptation for the simulation of compressible inviscid flows with shocks. Where the flow is smooth, p-adaptation is used to benefit from the spectral convergence of the spectral/hp element methods. Where the flow is discontinuous, e.g. at shock waves, r-adaptation clusters nodes together to better capture these field discontinuities. The benefits of this dual, rp-adaptation approach are demonstrated through two-dimensional benchmark test cases.
Supervisor: Peiró, Joaquim ; Sherwin, Spencer Sponsor: European Union
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral