Numerical Calculation of Free-surface Flow using Immersed Boundary Method

For numerical simulations of ship and offshore hydrodynamic problems, it is challenging to model the interaction between the free surface and moving complex geometries. This paper proposes a discrete-forcing immersed boundary method (IBM) to efficiently simulate moving solid boundaries in incompressible air–water two-phase flows. In the present work, the air–water two-phase flows are modeled using the Volume-of-Fluid (VoF) method. The present IBM is suitable for unstructured meshes. It can be used combined with body-fitted wall boundaries to model the relative motions between solid walls, which makes it flexible to use in practical applications. A field extension method is used to model the interaction between the air–water interface and the immersed boundaries. The accuracy of the method is demonstrated through validation cases, including the three-dimensional dam-break problem with an obstacle, the water exit of a circular cylinder, and a ship model advancing with a rotating semi-balanced rudder. The flow field, free-surface profile and force on the immersed boundaries (IBs) are in good agreement with experimental data and other numerical results.

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A weighted Shifted Boundary Method for free surface flow problems

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109837 ◽

2021 ◽

Vol 424 ◽

pp. 109837

Author(s):

Oriol Colomés ◽

Alex Main ◽

Léo Nouveau ◽

Guglielmo Scovazzi

Keyword(s):

Free Surface ◽

Free Surface Flow ◽

Surface Flow ◽

Flow Problems ◽

Boundary Method

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An immersed boundary method with iterative symmetric interpolation for irregular surface topography in seismic wavefield modelling

Journal of Geophysics and Engineering ◽

10.1093/jge/gxaa019 ◽

2020 ◽

Author(s):

Xiang Li ◽

Gang Yao ◽

Fenglin Niu ◽

Di Wu

Keyword(s):

Free Surface ◽

Finite Difference ◽

Surface Topography ◽

Immersed Boundary Method ◽

Acoustic Waves ◽

Interpolation Method ◽

Immersed Boundary ◽

Boundary Method ◽

Wavefield Simulation ◽

Irregular Free Surface

Abstract The irregular free surface topography has a significant impact on simulations of seismic wave propagation. Therefore, an accurate representation of the irregular free surface is required for an accurate wavefield simulation. We propose an immersed boundary method used in fluid dynamics calculation to simulate acoustic waves with finite-difference in media with irregular surfaces. First, we set the number of ghost layers to half the length of the finite-difference stencil. Then, we define mirror points by orthogonally projecting the ghost points to fractional points below the free surface. We calculate the wavefield at these mirror points using an iterative symmetric interpolation method. Finally, we set the wavefield at the ghost points to the negative value of the wavefield of their corresponding mirror points. The proposed iterative symmetric interpolation method allows computing the wavefield at the mirror points more accurately and stably than the conventional immersed boundary methods. Numerical examples validate the accuracy and stability of this method in seismic forward modelling with strongly varying topography.

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STUDY ON WATER ENTRY PROBLEM USING A LEVEL-SET IMMERSED BOUNDARY METHOD

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194514603767 ◽

2014 ◽

Vol 34 ◽

pp. 1460376

Author(s):

WEI BAI ◽

CHENGZHONG HUO

Keyword(s):

Free Surface ◽

Level Set ◽

Immersed Boundary Method ◽

Surface Profile ◽

Water Entry ◽

Navier Stokes ◽

Immersed Boundary ◽

Interface Evolution ◽

Boundary Method ◽

Moving Bodies

Water entry of a solid through the free surface is a persisting field of research in ship hydrodynamics applications. Indeed, the knowledge of pressure forces acting on structures is necessary to ensure the verification of safety criteria in the design and operation. However, in water entry problems, jets can be generated, thus an effective numerical model is needed to capture this complicated breaking water surface. In this paper, the level set method is adopted, which has been shown to be capable of capturing interface evolution when the topological change of shape is extremely large, or merging, breaking and pinching occur. Moreover, the incorporation of an immersed boundary method with this free surface capture scheme implemented in a Navier-Stokes solver allows the interaction between fluid flow with free surface and moving bodies of almost arbitrary shape to be modeled. The developed Level-Set Immersed Boundary Method is applied to simulate the water entry of a rectangular body with different velocities into the still water. The complicated surface profile, velocity field and pressure are obtained. The simulation is also carried out for the same body exiting the water, and some preliminary results are presented.

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Detached Eddy Simulation of Free-Surface Flow Around a Submerged Submarine Fairwater

Journal of Fluids Engineering ◽

10.1115/1.4006321 ◽

2012 ◽

Vol 134 (6) ◽

Cited By ~ 5

Author(s):

Z. Ikram ◽

E. J. Avital ◽

J. J. R. Williams

Keyword(s):

Free Surface ◽

Free Surface Flow ◽

Significant Rise ◽

Surface Flow ◽

Tip Vortex ◽

Immersed Boundary ◽

Wake Region ◽

Detached Eddy Simulation ◽

Eddy Simulation ◽

Submergence Depth

The effects of reducing submergence depth around a submerged submarine fairwater without its associated appendages is numerically studied using detached eddy simulation. The submerged body is modeled using the ghost-cell immersed boundary method, while the free-surface is accounted for by using a moving mesh. The numerical simulations are performed at a Reynolds number of 11 × 106 for a submergence ratio in the range of 0.44–0.32 and for Froude numbers <1. This paper examines the effect of depth variation on the statistical and structural behavior of the flow around a fully submerged fairwater. The results include profiles of the time averaged velocity, turbulent intensities, turbulent kinetic energy spectra and budget. These have all shown that the major part of the turbulence is confined to the near wake region of the fairwater. Vortical structures are found to show no significant rise or interaction with the free-surface, while in the wake region, the results show that vorticity is present for over 50% of the total monitored period. Reducing the submergence depth is found to influence the tip vortex shedding. Additionally, time averaged forces, force variations, and shedding frequency are also examined. In all cases, the surface waves generated by the submerged fairwater are of a Kelvin kind.

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Numerical Simulation of Wave Propagation Over Submerged Composite Breakwaters Using the Immersed Boundary Method

Volume 8B: Ocean Engineering ◽

10.1115/omae2014-24055 ◽

2014 ◽

Author(s):

Theofano I. Koutrouveli ◽

Athanassios A. Dimas

Keyword(s):

Free Surface ◽

Numerical Model ◽

Immersed Boundary Method ◽

Stokes Equations ◽

Splitting Method ◽

Staggered Grid ◽

Immersed Boundary ◽

Two Phase ◽

Boundary Method ◽

Two Dimensional Flow

The two-dimensional flow induced by waves over submerged breakwaters of two different shapes is studied by means of a two-phase (water and air) Navier-Stokes equations solver. A time-splitting method is used for the temporal discretization, while the spatial discretization is based on the use of finite differences in a Cartesian staggered grid. The implementation of the boundary conditions at solid surfaces, as well as the treatment of the free surface is performed using the immersed boundary method where the breakwater, the seabed and the free surface are boundaries immersed in the numerical grid. The numerical model was applied on the propagation and breaking over a constant slope beach, as well as on the propagation and nonlinear transformation of waves over two types of submerged breakwaters, i.e., trapezoidal and composite (with berm in the up-slope side). The results of the numerical model reveal that the presence of the berm reduces the transmission coefficient and this reduction increases with the decrease of the berm depth of submergence.

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