Comparative study on the accuracy of solitary wave generations in an ISPH-based numerical wave flume

• Six solitary wave generations by different mathematical approximations are studied.
• Waves have dimensionless amplitudes ranging from 0.1 to 0.6.
• Methods are: Boussinesq, KdV, Temperville, Rayleigh, Grimshaw and Fenton.
• ISPH results show that Fenton procedure is more accurate in free surface capturing.
• ISPH results show that Rayleigh predicts the maximum runup accurately.

In the present study, six solitary wave generations by different mathematical approximations are investigated using a piston type wave maker at dimensionless amplitudes ranging from 0.1 to 0.6 and two water depths. Incompressible smoothed particle hydrodynamics is used to simulate solitary wave propagation along the fixed depth channel. The present numerical results are compared with analytical results and experimental data in terms of free surface displacements, fluid particle velocity, phase speed, paddle motion, etc. The present mesh-free numerical results of wave profile variations over time proved that “Rayleigh” has the lowest relative wave height variation. However, its solitary wave has notable phase lead, while “Third order” and “Ninth order” have the least wave lags. Furthermore, the record of present numerical free surface elevation at different distances and the loss of amplitude of the main pulse showed that regarding both of them, “Ninth order” has supremacy over five others. Considering the numerical velocity components of generated solitary wave, “Third order” and “Ninth order” trace analytical results more accurately than other four ones, whereas “Rayleigh” is the most accurate one in predicting the maximum runup. Finally, the paddle motion, its velocity, and displacement, as well as phase speed and outskirts decay coefficient are also compared and discussed intensely.