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A stabilised immersed boundary method on hierarchical b-spline grids

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

Computer Methods in Applied Mechanics and Engineering, Volume: 311, Pages: 415 - 437

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

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DOI (Published version): 10.1016/j.cma.2016.08.027

Abstract

In this work, an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b-spline grid and employs the non-symmetric and penalty-free version of Nitsche’s method to enforce the boundary conditions. The strategy allows for h- and p-refinement and emplo...

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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/cronfa29743
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spelling 2020-10-06T11:49:47.2730918 v2 29743 2016-09-05 A stabilised immersed boundary method on hierarchical b-spline grids 30bb53ad906e7160e947fa01c16abf55 0000-0003-0799-4645 Wulf Dettmer Wulf Dettmer true false de01927f8c2c4ad9dcc034c327ac8de1 0000-0001-6092-9047 Chennakesava Kadapa Chennakesava Kadapa true false 9d35cb799b2542ad39140943a9a9da65 0000-0002-1112-301X Djordje Peric Djordje Peric true false 2016-09-05 AERO In this work, an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b-spline grid and employs the non-symmetric and penalty-free version of Nitsche’s method to enforce the boundary conditions. The strategy allows for h- and p-refinement and employs a so-called ghost penalty term to stabilise the cut cells. An effective procedure based on hierarchical subdivision and sub-cell merging, which avoids excessive numbers of quadrature points, is used for the integration of the cut cells. A basic Laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty-free Nitsche method as well as their impact on accuracy. The methodology is also applied to the incompressible Navier–Stokes equations, where the SUPG/PSPG stabilisation is employed. Simulations of the lid-driven cavity flow and the flow around a cylinder at low Reynolds number show the good performance of the methodology. Excessive ill-conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field. Journal Article Computer Methods in Applied Mechanics and Engineering 311 415 437 0045-7825 1 11 2016 2016-11-01 10.1016/j.cma.2016.08.027 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2020-10-06T11:49:47.2730918 2016-09-05T12:17:46.6263120 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Wulf Dettmer 0000-0003-0799-4645 1 Chennakesava Kadapa 0000-0001-6092-9047 2 Djordje Peric 0000-0002-1112-301X 3 0029743-972016104243AM.pdf dettmer2016v3.pdf 2016-09-07T10:42:43.9970000 Output 1895532 application/pdf Accepted Manuscript true 2017-09-06T00:00:00.0000000 true eng
title A stabilised immersed boundary method on hierarchical b-spline grids
spellingShingle A stabilised immersed boundary method on hierarchical b-spline grids
Wulf Dettmer
Chennakesava Kadapa
Djordje Peric
title_short A stabilised immersed boundary method on hierarchical b-spline grids
title_full A stabilised immersed boundary method on hierarchical b-spline grids
title_fullStr A stabilised immersed boundary method on hierarchical b-spline grids
title_full_unstemmed A stabilised immersed boundary method on hierarchical b-spline grids
title_sort A stabilised immersed boundary method on hierarchical b-spline grids
author_id_str_mv 30bb53ad906e7160e947fa01c16abf55
de01927f8c2c4ad9dcc034c327ac8de1
9d35cb799b2542ad39140943a9a9da65
author_id_fullname_str_mv 30bb53ad906e7160e947fa01c16abf55_***_Wulf Dettmer
de01927f8c2c4ad9dcc034c327ac8de1_***_Chennakesava Kadapa
9d35cb799b2542ad39140943a9a9da65_***_Djordje Peric
author Wulf Dettmer
Chennakesava Kadapa
Djordje Peric
author2 Wulf Dettmer
Chennakesava Kadapa
Djordje Peric
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 311
container_start_page 415
publishDate 2016
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2016.08.027
college_str Faculty of Science and Engineering
hierarchytype
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 In this work, an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b-spline grid and employs the non-symmetric and penalty-free version of Nitsche’s method to enforce the boundary conditions. The strategy allows for h- and p-refinement and employs a so-called ghost penalty term to stabilise the cut cells. An effective procedure based on hierarchical subdivision and sub-cell merging, which avoids excessive numbers of quadrature points, is used for the integration of the cut cells. A basic Laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty-free Nitsche method as well as their impact on accuracy. The methodology is also applied to the incompressible Navier–Stokes equations, where the SUPG/PSPG stabilisation is employed. Simulations of the lid-driven cavity flow and the flow around a cylinder at low Reynolds number show the good performance of the methodology. Excessive ill-conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field.
published_date 2016-11-01T03:36:13Z
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score 10.997843

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