Boundary element and spectral methods for water wave simulation

wave025_16_9268Philippe Guyenne gave a review of two classes of numerical methods for time-dependent simulations.  The first was the Boundary Element Method (BEM) for simulation of 3D waves.  The free surface and walls of the “numerical wave tank” are tiled with quadrilaterals.  Time integration includes evolving particles using Lagrangian displacements, and second-order explicit time stepping.  The time step is restricted by a CFL condition.  Examples of the method include modelling and simulation of tsunamis (particularly the 1998 Papua New Guinea tsunami) and overturning and spreading of 3D waves.  References and further examples can be found here. The second part of the talk was on spectral methods and the surface formulation using the Hamiltonian structure and the dirichlet-neumann operator (DNO).  This method involved Fourier pseudospectral in space, with splitting of the linear and nonlinear parts, and time integration with a fourth order RK method.  Examples of simulations using this method include solitary wave collision, hexagonal waves (including comparison with Hammack & Henderson experiments), and crescent waves (including comparison with Su’s experiments).  Extensions to variable bottom, two-layer flow (involving computation of two DNO operators, surface tension, and hydroelasticity.

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