The numerical solution of 2D Boussinesq/Boussinesq models for internal waves with spectral methods
Provides rigorous numerical analysis for a class of wave models, but the contribution is incremental as it applies known spectral methods to a specific system.
The authors develop and analyze spectral Fourier-Galerkin methods for solving 2D Boussinesq systems modeling internal waves, proving well-posedness and deriving error estimates, with numerical experiments demonstrating the method's performance.
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of fluids with different densities and subjected to a Boussinesq physical regime in each layer. Well-posedness of the periodic initial-value problem (ivp) of the systems is first analized. Then, a discretization in space based on the spectral Fourier-Galerkin method is introduced and error estimates for the semidiscrete approximation are derived. Using an efficient time integrator, some numerical experiments to illustrate the performance of the discretization are presented.