descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2020Embargo end date: 01 Jan 2020 English Publisher:Elsevier BVJournal:Computer Methods in Applied Mechanics and Engineering, volume 372, page 113,397 (issn: 0045-7825,

Authors: Sevilla Cárdenas, Rubén; Borchini, Luca; Giacomini, Matteo; Huerta, Antonio;

doi: 10.1016/j.cma.2020.113397 , 10.48550/arxiv.2006.11846

arXiv: 2006.11846

handle: 2117/328743

Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows

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Abstract

This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an off-line solution for a given set of geometric parameters. The generalised solution contains the information for all the geometric parameters in a user-defined range and it can be used to compute sensitivities. The proposed approach circumvents many of the weaknesses of other approaches based on the proper generalised decomposition for computing generalised solutions of geometrically parametrised problems. Four numerical examples show the optimal approximation properties of the proposed method and demonstrate its applicability in two and three dimensions.

51 pages, 30 figures

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Keywords

FOS: Computer and information sciences, FOS: Physical sciences, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical analysis--Simulation methods, Investigació operativa, Stokes and related (Oseen, etc.) flows, 510, :Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC], Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science, Classificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry, Computational Engineering, Finance, and Science (cs.CE), 65M60, 76D07, 76M10, :90 Operations research, mathematical programming::90B Operations research and management science [Classificació AMS], :65 Numerical analysis::65D Numerical approximation and computational geometry [Classificació AMS], FOS: Mathematics, geometry parametrisation, reduced order model, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, hybridisable discontinuous Galerkin (HDG), Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Simulació, Anàlisi numèrica, Classificació AMS::90 Operations research, Reduced order model, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, Geometry parametrisation, proper generalised decomposition (PGD), Numerical Analysis (math.NA), Proper generalised decomposition (PGD), Computational Physics (physics.comp-ph), :Matemàtiques i estadística::Investigació operativa::Simulació [Àrees temàtiques de la UPC], mathematical programming::90B Operations research and management science, Hybridisable discontinuous Galerkin (HDG), Physics - Computational Physics, Finite element methods applied to problems in fluid mechanics, Numerical analysis

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