A stabilised immersed boundary method on hierarchical b-spline grids

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

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.

Citation

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. https://doi.org/10.1016/j.cma.2016.08.027

• 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