A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations. (May 2018)

• Record Type: Journal Article
• Authors: Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef
• Is Part Of: Ocean modelling. Volume 125(2018)
• Page Start: 61
• Page End: 79
• Publication Date: 2018-05
• Subjects: Green–Naghdi equations -- Second-order Discontinuous Galerkin -- Well-balanced scheme with dispersive terms -- Nearshore wave processes; Oceanography -- Periodicals; Océanographie -- Périodiques; Oceanography; Periodicals; 551.46
• DOI: 10.1016/j.ocemod.2018.03.006
• Languages: English
• ISSNs: 1463-5003

Abstract

Highlights: RKDG2 method for modeling waves propagation and transformation over uneven bottom topography. Realistic features extended from a robust RKDG2 hydrodynamic solver to the Green–Naghdi (GN) equations. Dispersive effects treated as elliptic source terms, and locally switched off to enable treatment of wave breaking. Quantitative and qualitative assessments over a range of test cases. RKDG2-GN solver preserves stability, accuracy and conservation in modeling nearshore wave patterns. Abstract: 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 modeling 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.