A Discrete-Forcing Immersed Boundary Method for Moving Bodies in Air–Water Two-Phase Flows

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.

A New Wall Model for Large Eddy Simulation of Separated Flows

The aim of this work is to propose a new wall model for separated flows which is combined with large eddy simulation (LES) of the flow field in the whole domain. The model is designed to give reasonably good results for engineering applications where the grid resolution is generally coarse. Since in practical applications a geometry can share body fitted and immersed boundaries, two different methodologies are introduced, one for body fitted grids, and one designed for immersed boundaries. The starting point of the models is the well known equilibrium stress model. The model for body fitted grid uses the dynamic evaluation of the von Kármán constant κ of Cabot and Moin (Flow, Turbulence and Combustion, 2000, 63, pp. 269–291) in a new fashion to modify the computation of shear velocity which is needed for evaluation of the wall shear stress and the near-wall velocity gradients based on the law of the wall to obtain strain rate tensors. The wall layer model for immersed boundaries is an extension of the work of Roman et al. (Physics of Fluids, 2009, 21, p. 101701) and uses a criteria based on the sign of the pressure gradient, instead of one based on the friction velocity at the projection point, to construct the velocity under an adverse pressure gradient and where the near-wall computational node is in the log region, in order to capture flow separation. The performance of the models is tested over two well-studied geometries, the isolated two-dimensional hill and the periodic two-dimensional hill, respectively. Sensitivity analysis of the models is also performed. Overall, the models are able to predict the first and second order statistics in a reasonable way, including the position and extension of the downward separation region.