Numerical prediction of two fluid systems with sharp interfaces

Numerical simulation of breaking waves by a multi-scale turbulence model

A two-fluid solver has been developed for flow problems with both moving solid bodies and free surfaces. The underlying scheme is based on the solution of the incompressible Navier–Stokes equations for a variable density fluid system with a free surface. The cut cell method is used for tracking moving solid boundaries across a stationary background Cartesian grid. The computational domain encompasses fully both fluid regions and the fluid interface is treated as a contact discontinuity in the density field, which is captured automatically without special provision as part of the numerical solution using a time-accurate artificial compressibility method and high resolution Godunov-type scheme. A pressure-splitting algorithm is proposed for the accurate treatment of the normal pressure gradient at the interface in the presence of a gravity term. The Cartesian cut cell technique provides a highly efficient and fully automated process for generating body fitted meshes, which is particularly useful for moving boundary problems. Several test cases have been calculated using the present approach including a moving paddle as a wave generator and the initial stages of entry into still water of rigid wedges. The results compare well with other theoretical results and experimental data. Finally, test cases involving the entry into water and subsequent total immersion of a two-dimensional rigid wedge-shaped body as well as the inverse problem of wedge egress have been calculated to demonstrate the ability of the current method to tackle more general two fluid flows with interface break-up, reconnection, entrapment of one fluid into the other, as well as handling moving bodies of complex geometry.

A free-surface capturing method for two fluid flows with moving bodies

[1] An experimental and numerical study of the effects of a gravel slope on wave shoaling and breaking is presented herein. In the laboratory experiments, fluid velocities, pressure and water surface elevations were measured. Experiments were conducted for both spilling and plunging breakers and for gravel slopes with different gravel sizes. Since gravel slopes caused additional energy dissipation, wave heights in the shoaling zone as well as at the breaking point were reduced. On the other hand, the mean free surface setup inside the surf zone increased. It was also observed that the gravel slope had a stronger influence on the vertical profile of undertow under spilling breaker than on that under a plunging breaker. Moreover, the undertow became weaker over a gravel slope with a larger gravel size. Outside the surf zone, turbulent velocities near the gravel slope were relatively high because of the bottom roughness and percolation. Inside the surf zone, turbulence generated by wave breaking dominated over the gravel bed generated turbulence. The vertical flow induced by the gravel slope changed the turbulence pattern only at cross sections very close to the shoreline. Numerical simulations of the wave breaking processes over a gravel slope were performed. The numerical model was tested by comparing numerical results with experimental data. The model accurately simulated the mean flow quantities. The magnitude of turbulence and turbulence characteristics were also simulated reasonably well.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005JC003374

Breaking waves over a mild gravel slope: Experimental and numerical analysis

Plunging solitary wave and its interaction with a slender cylinder on a sloping beach

A simple technique is presented for the numerical solution of two-dimensional time-dependent flows, either laminar or turbulent, involving multiple free surfaces of arbitrary configuration The governing equations are the Reynolds equations for incompressible fluids with Boussinesq closure, the k- and ϵ-equations and an additional equation describing the fluid configuration This technique can potentially describe the propagation, deformation and overturning of pre-breaking waves and the mean flow, surface configuration and turbulence field after breaking The properties of the method are illustrated by several calculational examples The main parts of the algorithm are optimized for vector processing in a form suitable for installation in supercomputer facilities

A simple numerical technique for turbulent flows with free surfaces

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A simple numerical technique for turbulent flows with free surfaces