On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization
Provides structure-preserving discretizations for wave propagation models, relevant for computational fluid dynamics and coastal engineering.
The authors develop geometric numerical schemes for Boussinesq-type systems modeling surface waves, preserving multi-symplectic and Hamiltonian structures. The method-of-lines approach is used to analyze spatial and time discretizations.
In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence of solitary-wave solutions) were previously analyzed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated.