Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Modeling free surface flow pass solid obstructions by Immersed Boundary Method (IBM)Pengxuan Luo1, Jingxin Zhang1,2

1. School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University.
Shanghai, China.
2. MOE Key Laboratory of Hydrodynamics, Shanghai Jiao Tong University.
Shanghai, China.

ABSTRACTAt the same time, complex terrain and submerged structures are also
typical in ocean engineering. Immersed boundary method (IBM)(Peskin, 1972) is an effective numerical method to simulate the fluidstructure interaction whit complex boundaries. Peskin (1972) proposed
to replace the actual physical boundary by setting virtual boundaries
with virtual boundary forces which can simplify the complexity of thecomputational domain.

Immersed Boundary Method (IBM) is used to numerically model
boundaries with complex geometry and moving boundaries in the fixed
grid system. The core idea of this method is to add virtual force terms
into momentum equations to replace physical boundaries in thecomputational domain. The virtual force term is used to meet theboundary conditions in a body non-fitted grid system. In this paper, anumerical model combined IBM for free surface flow has beendeveloped. The main algorithm is based on the framework of codes inhouse. The model is used to simulate the fluid-structure interaction withthe uniform flow and solitary wave in the present work. In the first part,the fundamental governing equations and numerical method of IBM
model are briefly introduced. The core algorithm of immersedboundary identification and interpolation method is described in detailin this part. In the second part, a classical numerical case of flow
around a cylinder under Re = 40 is used to validate this model. And a
study case with experimental results of solitary wave interacting withvertical cylinders is designed to prove the practicability of the model.
The free surface elevations recorded at eight wave gauges were used tovalidate the simulations. The numerical cases show that the modelachieves good results with enough stability and accuracy.

Tseng et al. (2003) improved this method by other ways named ghost
cell method, which simulates the virtual boundary by the virtual
elements in the grid system and calculates virtual force term by velocity
interpolation. The linear interpolation of ghost cells is used to meet noslip boundary conditions in this model. Mittal et al. (2008) usedtrilinear interpolation with the three-dimensional domain and provedthat linear interpolation had obtained a good accuracy in most cases. Haet al. (2014) used IBM to simulate the impact of solitary waves on thecoast. The virtual force term was added to the two-step projection
method to solve the problem directly, and the results are well-validated.
Zhang et al. (2019) used the distance interpolation function to deal withthe boundary of the rigid body. Yousefzadeh et al. (2019) used ahigher-order interpolation method which obtained a solution with thirdorder accuracy. However, it was much more challenging to locate theinterpolation points. Ai et al. (2019) combined IBM with coordinatetransformation to solve problems with wave-structure interaction. Liuet al. (2020) proposed a wall function method to deal with the flow
field near the boundary, which improves the calculation accuracy of theimmersed boundary method at a high Reynolds number.

KEY WORDS: Immersed boundary method; Free surface flow;
Solitary wave; Fluid structure coupling

INTRODUCTION
In the ocean and coastal engineering, wave and flow interacting withstructures are common research issues. The study on issues ofinteraction between water flow and structures provides guidance forcoastal structure design and prevention of natural disasters such as
tsunamis. In order to establish the proper numerical model for theseproblems, two aspects need to be paid attention to. Natural water
environments such as oceans, rivers and lakes have a common featureof a free surface. Lin et al. (2002) used vertical σ-coordinatetransformation to establish a three-dimensional numerical model forwave propagation pass obstructions, which solve the problem of freesurface flow interacting with solid bodies. The model of σ-coordinatetransformation is based on the assumption that the free surface is asingle value function of horizontal coordinates.

In this paper, based on the framework of codes in-house (Zhang et al.
2017), a numerical model of immersed boundary method with freesurface flow has been developed. The numerical method and algorithm
design of this model will be introduced at first. Then, some numericalcases are used to validate the model in the present work. At last, brief
conclusions and results are presented.
NUMERICAL METHODS
Governing Equations
A vertical σ-coordinate transformation has been used to fit the free2492