Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation

摘要

We introduce a new stabilized high-order and unstructured numericalmodel for modeling fully nonlinear and dispersive water waves. Themodel is based on a nodal spectral element method of arbitrary order inspace and a -transformed formulation due to Cai, Langtangen, Nielsenand Tveito (1998). In the present paper we use a single layer ofquadratic (in 2D) and prismatic (in 3D) elements. The model has beenstabilized through a combination of over-integration of the Galerkinprojections and a mild modal filter. We present numerical tests ofnonlinear waves serving as a proof-of-concept validation for this newhigh-order model. The model is shown to exhibit exponentialconvergence even for very steep waves and there is a good agreementto analytic and experimental data.