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

C.F. Rowlatt; T.N. Phillips

doi:10.1016/j.cma.2015.08.010

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

C.F. Rowlatt, T.N. Phillips

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	29-57
Number of pages	29
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	298
DOIs	https://doi.org/10.1016/j.cma.2015.08.010
Publication status	Published - 1 Jan 2016

Keywords

immersed boundary method
spectral element
fluid–structure interaction
Newtonian

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title = "A spectral element formulation of the immersed boundary method for Newtonian fluids",

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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T1 - A spectral element formulation of the immersed boundary method for Newtonian fluids

AU - Rowlatt, C.F.

AU - Phillips, T.N.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - immersed boundary method

KW - spectral element

KW - fluid–structure interaction

KW - Newtonian

U2 - 10.1016/j.cma.2015.08.010

DO - 10.1016/j.cma.2015.08.010

M3 - Article

SN - 0045-7825

VL - 298

SP - 29

EP - 57

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

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

Abstract

Keywords

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