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Harmonic Balance method for nonlinear and viscous free surface flows

The Harmonic Balance method applied to fully nonlinear, viscous, temporally periodic free surface flows is presented in this paper. The Harmonic Balance approach is used to project a transient periodic two phase flow into multiple coupled steady-state problems discretising the periodic time interval. The numerical framework is based on Finite Volume method for Computational Fluid Dynamics in the open--source software foam-extend. The disability of the Harmonic Balance method to simulate flows with zero or close to zero mean velocity is overcome by coupling the Harmonic Balance steady-state equations mplicitly, presenting a novelty in the field. Von Neumann stability analysis is performed for the governing Harmonic Balance equations to mathematically prove that zero mean velocity can be simulated using the proposed implicit coupling. The method is validated and verified on a periodic free surface flow over a ramp and regular surface wave propagation with current, both including grid convergence studies and spectral resolution sensitivity studies. All results are compared to fully transient computations. A detailed study is performed for wave propagation without current, confirming that convergence of free surface elevation can be achieved without mean velocity. The approach proved accurate and applicable for two–phase flows, opening a new research field.

Periodic ; Free surface flows ; CFD ; Harmonic Balance ; Naval hydrodynamics ; Foam – extend

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