Preprint C45/2005
Modelagem de ondas não lineares através do operador Dirichlet-to-Neumann

Artiles Roqueta , William

**Keywords: **
Operator Dirichlet to Neumann Operator | Pseudodifferential Operator | Surface Waves | Boussinesq Equations

In this work, we model the weakly nonlinear finite amplitude water wave problem through the Dirichlet-to-Neumann operator and we also obtain an efficient numerical method for calculating the propagation of surface waves. We consider an inviscid and incompressible two-dimensional flow. Since the flow is irrotational potential theory is applied. Through a conformal mapping, the variable bottom problem is transformed to another problem with flat bottom. With the help of the Dirichlet-to-Neumann operator (DtN), a new system of evolution equations is obtained for the fully dispersive regime. These equations are generalizations of the Boussinesq equations. The DtN operator is represented as a pseudodifferential operator through a boundary integral formulation. We present a numerical model in which the method of boundary integration is coupled to an explicit time-stepping scheme. We also present a numerical calculation method for the conformal mapping, which allows the free surface coefficient to be calculated quickly and efficiently, independently of the topography of the problem.