A spectral element formulation of the immersed boundary method for Newtonian fluids

Rowlatt, C.F. and Phillips, T.N. (2016) A spectral element formulation of the immersed boundary method for Newtonian fluids. Computer Methods in Applied Mechanics and Engineering, 298. pp. 29-57. ISSN 0045-7825 (https://doi.org/10.1016/j.cma.2015.08.010)

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Abstract

A spectral element formulation of the immersed boundary method (IBM) is presented. The spectral element formulation (SE-IBM) is a generalisation of the finite element immersed boundary method (FE-IBM) based on high-order approximations of the fluid variables. Several schemes for tracking the movement of the immersed boundary are considered and a semi-implicit Euler scheme is shown to offer advantages in terms of accuracy and efficiency. High-order spectral element approximations provide improved area conservation properties of the IBM due to the incompressibility constraint being more accurately satisfied. Superior orders of convergence are obtained for SE-IBM compared with FE-IBM in both L2 and H1 norms. The area conservation and convergence properties of the scheme are demonstrated on a series of benchmark problems.

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