Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model

This work reports on the application and experimental validation, for idealized geometries, of a multiple-fluid Navier–Stokes model of waves generated by rigid and deforming slides, with the purpose of improving predictive simulations of landslide tsunamis. In such simulations, the computational domain is divided into water, air, and slide regions, all treated as Newtonian fluids. For rigid slides, a penalty method allows for parts of the fluid domain to behave as a solid. With the latter method, the coupling between a rigid slide and water is implicitly computed (rather than specifying a known slide kinematics). Two different Volume of Fluid algorithms are tested for tracking interfaces between actual fluid regions. The simulated kinematics of a semi-elliptical block, moving down a water covered plane slope, is first compared to an earlier analytical solution. Results for the vertical fall of a rectangular block in water are then compared to earlier experimental results. Finally, more realistic simulations of two- and three-dimensional wedges sliding down an incline are compared to earlier experiments. Overall, in all cases, solid block velocities and free surface deformations are accurately reproduced in the model, provided that a sufficiently resolved discretization is used. The potential of the model is then illustrated on more complex scenarios involving waves caused by multi-block or deformable slides.     

A higher-order non-hydrostatic σ model for simulating non-linear refraction–diffraction of water waves

A higher-order non-hydrostatic σ model is developed to simulate non-linear refraction–diffraction of water waves. To capture non-linear (or steep) waves, a 4th-order spatial discretization is utilized to approximate the large horizontal pressure gradient. A higher-order top-layer pressure treatment is further implemented to resolve wave propagation. The model's characteristics including linear wave dispersion and non-linearity are carefully examined. The accuracy of the present model using only two vertical layers is validated by laboratory data and the available results predicted by the non-linear Schrödinger equation, Boussinesq-type equations, the non-linear mild slope equation, and the Laplace equation. Features of harmonic generation as well as the influences of dispersion and non-linearity on wave energy transfer processes are discussed.