2026-05-05T11:34:30Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/624072023-10-27T19:00:36Zcom_10324_1176com_10324_931com_10324_894col_10324_1359

Dougalis, Vassilios A. Saridaki, Leetha Durán Martín, Ángel 2023-10-27T06:48:32Z 2023-10-27T06:48:32Z 2023 Numerical Methods for Partial Differential Equations, 2023, 39(5), pp. 3677-3704 0749-159X https://uvadoc.uva.es/handle/10324/62407 10.1002/num.23021 3677 5 3704 Numerical Methods for Partial Differential Equations 39 1098-2426 Producción Científica 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. PID2020-113554GB-I00/AEI/10.13039/501100011033 Ministerio de Ciencia e Innovación. VA193P20 Junta de Castilla y León application/pdf eng Wiley info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional Boussinesq/Boussinesq systems error estimates internal waves solitary waves spectral methods On the numerical approximation of Boussinesq/Boussinesq systems for internal waves info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion https://onlinelibrary.wiley.com/doi/10.1002/num.23021 SI