Discontinuous Galerkin methods for solving Boussinesq-Green-Naghdi equations in resolving non-linear and dispersive surface water waves

作者：Panda Nishant^*; Dawson Clint; Zhang Yao; Kennedy Andrew B; Westerink Joannes J; Donahue Aaron S

来源：Journal of Computational Physics, 2014, 273: 572-588.

DOI：10.1016/j.jcp.2014.05.035

• Rotational Boussinesq-Green-Naghdi
• Discontinuous Galerkin
• Mixed space-time derivatives
• Unstructured mesh
• Surf-zone
• Non-conservative

A local discontinuous Galerkin method for Boussinesq-Green-Naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal. Currently Green-Naghdi equations have many variants. In this paper a numerical method in one dimension is presented for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations for both the analytical problem and the numerical method. Verification is done against a linearized standing wave problem in flat bathymetry and h, p (denoted by K in this paper) error rates are plotted. Validation plots show good agreement of the numerical results with the experimental ones.

• 出版日期2014-9-15