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A stabilised immersed boundary method on hierarchical b-spline grids

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

Authors

W.G. Dettmer

D. Peri?



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 - 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.

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
DOI https://doi.org/10.1016/j.cma.2016.08.027
Keywords Immersed boundary method, Hierarchical b-splines, Nitsche’s method, Ghost penalty, Poisson equation, Navier–Stokes equations
Public URL http://researchrepository.napier.ac.uk/Output/2893875