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

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• 作者：C.F. Rowlatt ^{RowlattC@Cardiff.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; T.N. Phillips ; ^{PhillipsTN@cf.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65M70 ; 74F10
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：298
• 期：Complete
• 页码：29-57
• 全文大小：5544 K

文摘

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$L^2$ and H¹$H^1$ norms. The area conservation and convergence properties of the scheme are demonstrated on a series of benchmark problems.