Simulation of free surface flows using the flux-difference splitting scheme on the hybrid Cartesian/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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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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