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A unified approach for a posteriori high-order curved mesh generation using solid mechanics / Roman Poya; Ruben Sevilla; Antonio J. Gil

Computational Mechanics, Volume: 58, Issue: 3, Pages: 457 - 490

Swansea University Author: Sevilla, Ruben

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Abstract

The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticit...

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Published in: Computational Mechanics
ISSN: 0178-7675 1432-0924
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa28844
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Abstract: The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
Item Description: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Keywords: High-order mesh generation, Solid mechanics analogy, Curved elements, Isoparametric finite elements
College: College of Engineering
Issue: 3
Start Page: 457
End Page: 490