Staggered grid implementation of 1D Boussinesq model for simulating dispersive wave (original) (raw)

2018

In this paper, a numerical implementation of 1D Variational Boussinesq (VB) wave model in a staggered grid scheme is discussed. The staggered grid scheme that is used is based on the idea proposed by Stelling & Duinmeijer (2003) who implemented the scheme in a nondispersive Shallow Water Equations in a conservative form. Here, we extend the idea of the staggered scheme to be applied for VB wave model. To test the accuracy of the implementation, we test the numerical implementation of VB wave model for simulating propagation of solitary wave against analytical solution. Moreover, to test dispersiveness of the model, we simulate a standing wave against analytical solution. Results of simulations show a good agreement with analytical solutions.

Boussinesq-Peregrine water wave models and their numerical approximation

2020

© 2020 Elsevier Inc. In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive terms are compared. A detailed study of the convergence properties of the standard Galerkin method, using various finite element spaces on unstructured triangular grids, is presented. Along with the study of the Peregrine system, a new Boussinesq system of BBM-BBM type is derived. The new system has the same structure in its momentum equation but differs slightly in the mass conservation equation compared to the Peregrine system. Further, the finite element method applied to the new system has better convergence properties, when used for its numerical approximation. Due to the lack of analytical formulas for solitary wave solutions for the systems under consideration, a Galerkin finite element method combined with the Pe...

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