@article { , title = {A stabilised immersed boundary method on hierarchical b-spline grids}, 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.}, doi = {10.1016/j.cma.2016.08.027}, issn = {0045-7825}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {415-437}, publicationstatus = {Published}, publisher = {Elsevier}, url = {http://researchrepository.napier.ac.uk/Output/2893875}, volume = {311}, keyword = {Immersed boundary method, Hierarchical b-splines, Nitsche’s method, Ghost penalty, Poisson equation, Navier–Stokes equations}, year = {2016}, author = {Dettmer, W.G. and Kadapa, C. and Peri?, D.} }