RT info:eu-repo/semantics/article
T1 On the numerical approximation of Boussinesq/Boussinesq systems for internal waves
A1 Dougalis, Vassilios A.
A1 Saridaki, Leetha
A1 Durán Martín, Ángel
K1 Boussinesq/Boussinesq systems
K1 error estimates
K1 internal waves
K1 solitary waves
K1 spectral methods
AB The present paper is concerned with the numerical approximation of a three-parameter family of Boussinesq systems. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer system of fluids with rigid-lid condition for the upper layer and under a Boussinesq regime for the flow in both layers. We first present some theoretical properties of the systems on well-posedness, conservation laws, Hamiltonian structure, and solitary-wave solutions, using the results for analogous models for surface wave propagation. Then the corresponding periodic initial-value problem is discretized in space by the spectral Fourier Galerkin method and for each system, error estimates for the semidiscrete approximation are proved. The spectral semidiscretizations are numerically integrated in time by a fourth-order Runge–Kutta-composition method based on the implicit midpoint rule. Numerical experiments illustrate the accuracy of the fully discrete scheme, in particular its ability to simulate accurately solitary-wave solutions of the systems.
PB Wiley
SN 0749-159X
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/62407
UL https://uvadoc.uva.es/handle/10324/62407
LA eng
NO Numerical Methods for Partial Differential Equations, 2023, 39(5), pp. 3677-3704
NO Producción Científica
DS UVaDOC
RD 11-jul-2024