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A stabilised immersed boundary method on hierarchical b-spline grids

Dettmer, W.G.; Kadapa, C.; Peri?, D.


W.G. Dettmer

D. Peri?


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 - and -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.


Dettmer, W., Kadapa, C., & Perić, D. (2016). A stabilised immersed boundary method on hierarchical b-spline grids. Computer Methods in Applied Mechanics and Engineering, 311, 415-437.

Journal Article Type Article
Acceptance Date Aug 28, 2016
Online Publication Date Sep 6, 2016
Publication Date 2016-11
Deposit Date Aug 29, 2022
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 311
Pages 415-437
Keywords Immersed boundary method, Hierarchical b-splines, Nitsche’s method, Ghost penalty, Poisson equation, Navier–Stokes equations
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