Coupling of Two Absorbing Boundary Conditions for 2D Time-Domain Simulations of Free Surface Gravity Waves
✍ Scribed by A. Clément
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 664 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
The numerical simulation of nonlinear gravity waves propagating at the surface of a perfect fluid is now usually solved by totally For this kind of equations in unbounded domains, exact nonlinear time-domain numerical models in two dimensions, and absorbing boundary conditions nonlocal in both space and this approach is being extended to three dimensions. The original time [3], or partially nonlocal [4, 5] has been developed initial boundary value problem is posed in an unbounded region, for FEM solvers. Following Engquist and Majda [6], some extending horizontally up to infinity to model the sea. Its numerical authors have devised higher order approximate local solution requires truncating the domain at a finite distance. Unfortunately, no exact nonreflecting boundary condition on the truncating NRBC, in order to improve the results obtained with the surface exists in this time-domain formulation. The proposed stratclassical first-order Sommerfeld condition [7-9]. Using egy is based on the coupling of two previously known methods in similar techniques, Bayliss et al. [10] derived high order order to benefit from their different, and complementary, band-NRBC for time independent elliptic problems in extewidth: the numerical ''beach,'' very efficient in the high frequency rior region. range; and a piston-like Neumann condition, asymptotically ideal for low frequencies. The coupling method gives excellent results
The mathematical modelling of the propagation of in the whole range of frequencies of interest and is as easy to free surface gravity waves leads to an initial boundary implement in nonlinear as in linear versions. One of its major advanvalue problem (IBVP) posed in a domain bounded by tages is that it does not require any spectral knowledge of the a moving unknown free surface on which a nonlinear incident waves.