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A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids

Chennakesava Kadapa Orcid Logo, Wulf Dettmer Orcid Logo, Djordje Peric Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 301, Pages: 1 - 27

Swansea University Authors: Chennakesava Kadapa Orcid Logo, Wulf Dettmer Orcid Logo, Djordje Peric Orcid Logo

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DOI (Published version): 10.1016/j.cma.2015.12.023

Abstract

We present a numerical scheme for fluid–structure interaction based on hierarchical B-Spline grids and fictitious domain/distributed Lagrange multipliers. The incompressible Navier–Stokes equations are solved over a Cartesian grid discretised with B-Splines. The fluid grid near the immersed solids i...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa26366
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spelling 2020-10-06T11:28:10.1783208 v2 26366 2016-02-17 A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids de01927f8c2c4ad9dcc034c327ac8de1 0000-0001-6092-9047 Chennakesava Kadapa Chennakesava Kadapa true false 30bb53ad906e7160e947fa01c16abf55 0000-0003-0799-4645 Wulf Dettmer Wulf Dettmer true false 9d35cb799b2542ad39140943a9a9da65 0000-0002-1112-301X Djordje Peric Djordje Peric true false 2016-02-17 SCS We present a numerical scheme for fluid–structure interaction based on hierarchical B-Spline grids and fictitious domain/distributed Lagrange multipliers. The incompressible Navier–Stokes equations are solved over a Cartesian grid discretised with B-Splines. The fluid grid near the immersed solids is refined locally using hierarchical B-Splines. The immersed solid is modelled as geometrically-exact beam discretised with standard linear Lagrange shape functions. The kinematic constraint at the fluid–solid interface is enforced with distributed Lagrange multipliers. The unconditionally-stable and second-order accurate generalised-α method is used for integration in time for both the fluid and solid domains. A fully-implicit and fully-coupled solution scheme is developed by using the Newton–Raphson method to solve the non-linear system of equations obtained with Galerkin weak formulation. First, the spatial and temporal convergence of the proposed scheme is assessed by studying steady and unsteady flow past a fixed cylinder. Then, the scheme is applied to several benchmark problems to demonstrate the efficiency and robustness of the proposed scheme. The results obtained with the present scheme are compared with the reference values. Journal Article Computer Methods in Applied Mechanics and Engineering 301 1 27 0045-7825 Fictitious domain methods, Immersed boundary methods, Fluid–structure interaction, Hierarchical B-Splines, Distributed Lagrange multipliers, Flow-induced vibrations 1 4 2016 2016-04-01 10.1016/j.cma.2015.12.023 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2020-10-06T11:28:10.1783208 2016-02-17T16:02:42.2715412 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Chennakesava Kadapa 0000-0001-6092-9047 1 Wulf Dettmer 0000-0003-0799-4645 2 Djordje Peric 0000-0002-1112-301X 3 0026366-17022016160425.pdf KadapaFictitiousDomainDistributedLagrange2015Postprint.pdf 2016-02-17T16:04:25.7470000 Output 1646663 application/pdf Accepted Manuscript true 2016-12-30T00:00:00.0000000 true
title A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
spellingShingle A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
Chennakesava Kadapa
Wulf Dettmer
Djordje Peric
title_short A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
title_full A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
title_fullStr A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
title_full_unstemmed A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
title_sort A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids
author_id_str_mv de01927f8c2c4ad9dcc034c327ac8de1
30bb53ad906e7160e947fa01c16abf55
9d35cb799b2542ad39140943a9a9da65
author_id_fullname_str_mv de01927f8c2c4ad9dcc034c327ac8de1_***_Chennakesava Kadapa
30bb53ad906e7160e947fa01c16abf55_***_Wulf Dettmer
9d35cb799b2542ad39140943a9a9da65_***_Djordje Peric
author Chennakesava Kadapa
Wulf Dettmer
Djordje Peric
author2 Chennakesava Kadapa
Wulf Dettmer
Djordje Peric
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 301
container_start_page 1
publishDate 2016
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2015.12.023
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description We present a numerical scheme for fluid–structure interaction based on hierarchical B-Spline grids and fictitious domain/distributed Lagrange multipliers. The incompressible Navier–Stokes equations are solved over a Cartesian grid discretised with B-Splines. The fluid grid near the immersed solids is refined locally using hierarchical B-Splines. The immersed solid is modelled as geometrically-exact beam discretised with standard linear Lagrange shape functions. The kinematic constraint at the fluid–solid interface is enforced with distributed Lagrange multipliers. The unconditionally-stable and second-order accurate generalised-α method is used for integration in time for both the fluid and solid domains. A fully-implicit and fully-coupled solution scheme is developed by using the Newton–Raphson method to solve the non-linear system of equations obtained with Galerkin weak formulation. First, the spatial and temporal convergence of the proposed scheme is assessed by studying steady and unsteady flow past a fixed cylinder. Then, the scheme is applied to several benchmark problems to demonstrate the efficiency and robustness of the proposed scheme. The results obtained with the present scheme are compared with the reference values.
published_date 2016-04-01T03:31:37Z
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score 11.017016

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