Commun. Comput. Phys., 8 (2010), pp. 265-288.


A Level Set Immersed Boundary Method for Water Entry and Exit

Yali Zhang 1*, Qingping Zou 1, Deborah Greaves 1, Dominic Reeve 1, Alison Hunt-Raby 1, David Graham 2, Phil James 2, Xin Lv 1

1 School of Marine Science and Engineering, University of Plymouth, United Kingdom, PL4 8AA.
2 School of Mathematics and Statistics, University of Plymouth, United Kingdom, PL4 8AA.

Received 6 July 2009; Accepted (in revised version) 6 January 2010
Available online 12 March 2010
doi:10.4208/cicp.060709.060110a

Abstract

The interaction between free surface flow and structure is investigated using a new level set immersed boundary method. The incorporation of an improved immersed boundary method with a free surface capture scheme implemented in a Navier-Stokes solver allows the interaction between fluid flow with free surface and moving body/bodies of almost arbitrary shape to be modelled. A new algorithm is proposed to locate exact forcing points near solid boundaries, which provides an accurate numerical solution. The discretized linear system of the Poisson pressure equation is solved using the Generalized Minimum Residual (GMRES) method with incomplete LU preconditioning. Uniform flow past a cylinder at Reynolds number Re=100 is modelled using the present model and results agree well with the experiment and numerical data in the literature. Water exit and entry of a cylinder at the prescribed velocity is also investigated. The predicted slamming coefficient is in good agreement with experimental data and previous numerical simulations using a ComFlow model. The vertical slamming force and pressure distribution for the free falling wedge is also studied by the present model and comparisons with available theoretical solutions and experimental data are made.

AMS subject classifications: 6D05, 76T10, 65B99, 65E05

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Key words: Level set method, immersed boundary method, slamming coefficient, water entry and exit, free surface, fluid-structure interaction.

*Corresponding author.
Email: yali.zhang@plymouth.ac.uk (Y. Zhang), qingping.zou@plymouth.ac.uk (Q. Zou), deborah.greaves@plymouth.ac.uk (D. Greaves), dominic.reeve@plymouth.ac.uk (D. Reeve), alison.hunt-raby@plymouth.ac.uk (A. Hunt-Raby), david.graham@plymouth.ac.uk (D. Graham), phil.james@plymouth.ac.uk (P. James), xin.lv@plymouth.ac.uk (X. Lv)
 

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