Viscous numerical wave tank for Bragg resonance by cnoidal and Stokes waves

Abstract

In this study, a quadtreeadaptive viscous numerical wave tank in which the free surface is resolved by the volume of fluid method is established to solve Bragg resonance caused by Stokes and cnoidal waves. Numerical wavemakers of third-order cnoidal and fifth-order Stokes waves are implemented. Additionally, a numerical damping zone is implemented such that the numerical grid in that area is automatically coarsened under a prescribed low resolution in which the time-matching is more efficient without an excessively small time-step. Furthermore, the areas with intense vorticity, boundary layers, and free surfaces are automatically refined to prescribed high resolutions. The model is shown as stable even when multiple adaptation () criteria are implemented in the computation. With respect to the simulation of Bragg resonance caused by Stokes waves, the obtained reflection and transmission coefficients, velocity in the boundary layers as well as velocity and vorticity fields are compared with other results obtained by extant studies. The model is then applied for solving Bragg resonance caused by cnoidal waves which show stronger scouring on the lee side of the submerged obstacles. The numerical results exhibit higher resolution for examining the secondary eddies compared with the conventional numerical methods. In addition, the computing time of the model with an adaptive grid is at least six times faster than that with a semi-uniform grid while their results are in a good agreement.

Keywords

• Computational fluid dynamics
• quadtree–adaption
• volume of fluid
• numerical damping zone
• Stokes Bragg resonance
• cnoidal Bragg resonance