English

On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization

Numerical Analysis 2020-02-20 v1 Classical Physics Fluid Dynamics

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.

Keywords

Cite

@article{arxiv.1905.06019,
  title  = {On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization},
  author = {Angel Durán and Denys Dutykh and Dimitrios Mitsotakis},
  journal= {arXiv preprint arXiv:1905.06019},
  year   = {2020}
}

Comments

38 pages, 4 figures, 33 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/