Solution of Wave Equations Near Seawalls by Finite Element Method

A ۲D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve nonlinear wave equations. The finite element model includes the conventional method based on a variational principle. This model minimizes the relevant function of the problem. After calculating two independent variables (i.e.and) the pressure, forces, and moments acting on sea-walls can be computed. These values are compared with existing experimental and theoretical outputs. The standing wave behavior is well described by the model, e.g. we can get the envelope of breaking waves in curve designs, which are developed for non-breaking waves. Also we can estimate the effective depth of a certain wave. Therefore the model can be used to propose some design curves.

Keywords:

Finite element method , Wave Equation , Seawalls , Numerical method