An LDG numerical approach for Boussinesq type modelling

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modelling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

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A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

Sharifian

Kesserwani

Hassanzadeh

2018

Ocean Modelling

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An LDG numerical approach for Boussinesq type modelling

Cited by 1 publication

References 45 publications

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

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