Boundary conditions for limited area models based on the shallow water equations. (English) Zbl 1373.35232
Summary: A new set of boundary conditions has been derived by rigorous methods for the shallow water equations in a limited domain. The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions. The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain. The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
86A05 | Hydrology, hydrography, oceanography |
86A10 | Meteorology and atmospheric physics |