On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization
Abstract
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.
Domains
Fluid mechanics [physics.class-ph] Fluid Dynamics [physics.flu-dyn] Analysis of PDEs [math.AP] Numerical Analysis [math.NA] Atmospheric and Oceanic Physics [physics.ao-ph] Computational Physics [physics.comp-ph] Pattern Formation and Solitons [nlin.PS] Exactly Solvable and Integrable Systems [nlin.SI]Origin | Files produced by the author(s) |
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