Development Of Phase-Field & VOF Coupled Method For Study Of Limiting Waves

Wave breaking is one of the most significant dynamic progress in coastal zone,and is also supposed to be the difficulty in the experimental observation and numerical simulation.This paper desires to build a new numerical model to study the limiting wave.Then a study of the mechanism of the wave breaking is carried out,and the effect of surface tension on limiting wave is analyzed.A new surface-tracking method is proposed,which couples Phase-Field method and one of the VOF-kind method.Corresponding numerical model and a double-grid system are also completed.The new coupled model combines the advantages of the dispersive surface method and the abrupt surface method.A new algorithm to deal with the boundary condition is proposed to exchange the information between two gridsystem.The coupled model is solved with Finite Volume Method and PISO algorithm,which is supposed to be convenience and stable.The coupled model is proved to be able to compute complex surface problems with high-accuracy via some basic validations.Compared with the un-coupled model,coupled model improves the computational efficiency.The coupled model is applied to the study of limiting waves.For the examples of progressive waves,periodic boundary condition and moving-frame coordinate are used to limit the computational domain to one wave length.Progressive waves are generated by forced pressure,and the initial wave energy could be controlled by the amplitude of the pressure.Results show that with a precise grid system nappe appears on the crest of the limiting wave in all the cases,and finally touches the front face.The scale of the nappe and the duration of the water wave in its limiting form reduce as the initial wave energy decreases.And so does the drift velocity of the limiting wave.The maximum velocity of the particle within the wave crest exceeds the wave celerity calculated via the linear wave theory,which agrees with the classical wave theory.For the problem of the standing waves,standing waves in two different oscillating modes and oscillating amplitudes are simulated.Numerical results show good agreements with the experiments.The coupled model overcomes the difficulty in accurately evaluating the normal of the interface and is then applied to study the effect of surface tension on the limiting wave.The influence of the relative strength between the inertial effect and the surface tension effect is discussed via the numerical results with different initial wave energies and different coefficients of surface tension.For the stronger plunging breakers,surface tension concentrates on the tip and the neck of the nappe,rounds the tip of the nappe,reduces the ejective angle and the ejective distance of the nappe and decreases the area surrounded by the nappe and the front face.For the weaker cases,the surface tension concentrates on the front face and the toe of the bulge and prevents the ejection of the nappe.The bulge on the crest enlarges to a certain extent and then glides along the front surface,which tends to form a spilling breaker.