Development of a conservative 3D free surface code

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Abstract
The paper describes the salient features of a three-dimensional finite difference code at present under development for Large Eddy Simulation of free-surface turbulence. It is essential in this application that the numerical approximations conserve mass, momentum, and kinetic + potential energy while allowing for large movements of the free surface and these are presented in detail for cells cut by the surface. The surface advancement is by a combined Volume-of-Fluid and height function method which conserves mass exactly over finite time steps, but does not permit breaking waves. Momentum is advanced by control volume techniques, and the potential singularity caused by very small surface cells is avoided by a new split-merge technique which is numerically stable. Results are presented for a two-dimensional inviscid large amplitude wave in a periodic box.

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