An inflow-boundary-based Navier-Stokes wave tank: verification and validation for waves propagating over flat and inclined bottoms

Abstract: Development of mass-source function based numerical wave tank (NWT) algorithms in the Navier-Stokes (NSE) framework is impeded by multiple design issues such as: (a) optimization of a number of variables characterizing the source region, (b) wave-vorticity interactions and (c) a mandatory requirement of modeling the domain on both sides of the wavemaker. In this paper, we circumvent these hurdles by proposing a volume-preserving inflow-boundary based Navier-Stokes wave tank. Wave generation and propagation is modeled in a two-phase PLIC-VOF set-up. Near-exact volume preservation is achieved (at arbitrarily large steepness) using kinematic stretching that is aimed towards balancing the streamwise momentum between points lying above and below the still water level. Numerical damping of steep waves is prevented by using blended third-order and limiter schemes for momentum advection. In addition, a mesh stair-stepping strategy has been adopted for modeling non-Cartesian immersed boundaries on a staggered variable arrangement. The proposed NWT model is rigorously benchmarked against various wave-propagation scenarios. These include the simulation of: (a) monochromatic waves of various steepnesses, (b) monochromatic waves superimposed with free harmonics, (c) irregular waves in deep water and (d) wave transformation occurring over a submerged trapezoidal bar. Excellent agreement with analytical, numerical and experimental data is reported with both validation as well as verification of the proposed NWT model being established.