Event № 81
To compute wave propagation in unbounded domains, the domain is often truncated to a finite size, by introducing an artificial boundary at some, ideally not too large, distance. Boundary conditions are then needed on the artificial boundary, that render the boundary invisible to outgoing waves. In this work, we describe absorbing boundary treatment for the linearized water wave equation, governing incompressible, irrotational free surface flow. We use Fourier analysis to identify the structure of outgoing water waves and derive a one-way version of the equation, which we implement as an absorbing layer near the artificial boundary. Additional wave damping may also be incorporated and will be discussed.The one-way equation involves a fractional derivative operator corresponding to a half-derivative in space. The equation is viewed as a conservation law with a linear nonlocal flux involving a convolution with a singular integrable kernel. We construct high order numerical methods, based on local polynomial approximation of the solution followed by exact integration of the singular convolution. In this talk, we will discuss the water wave equation, its one-way counterparts, the numerical method, and present numerical results.