Wave Transformation Modeling with Effective Higher-Order Finite Elements

This study introduces a finite element method using a higher-order interpolation function for effective simulations of wave transformation. Finite element methods with a higher-order interpolation function usually employ a Lagrangian interpolation function that gives accurate solutions with a lesser number of elements compared to lower order interpolation function. At the same time, it takes a lot of time to get a solution because the size of the local matrix increases resulting in the increase of band width of a global matrix as the order of the interpolation function increases. Mass lumping can reduce computation time by making the local matrix a diagonal form. However, the efficiency is not satisfactory because it requires more elements to get results. In this study, the Legendre cardinal interpolation function, a modified Lagrangian interpolation function, is used for efficient calculation. Diagonal matrix generation by applying direct numerical integration to the Legendre cardinal interpolation function like conducting mass lumping can reduce calculation time with favorable accuracy. Numerical simulations of regular, irregular and solitary waves using the Boussinesq equations through applying the interpolation approaches are carried out to compare the higher-order finite element models on wave transformation and examine the efficiency of calculation.

Keywords:

Boussinesq equations , Finite element method , Lagrangian interpolation function , Legendre cardinal interpolation function