2009/07/28 by Dougalis, Vassilios, Dimitrios Mitsotakis, Mitsotakis, Dimitrios +2
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Ocean Waves and Remote Sensing
paper · doi:10.48550/arxiv.0907.4918
openalex publication_date 2009/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show that various initial-boundary-value problems for these systems, posed on a bounded plane domain are well posed locally in time. In the case of reflective boundary conditions, the systems are discretized by a modified Galerkin method which is proved to converge in L2 at an optimal rate. Numerical experiments are presented with the aim of simulating two-dimensional surface waves in complex plane domains with a variety of initial and boundary conditions, and comparing numerical solutions of Bona-Smith systems with analogous solutions of the BBM-BBM system.