Ricerc@Sapienza

An original integral formulation of the three-dimensional contravariant Navier-Stokes equations, devoid of the Christoffel symbols, in general time-dependent curvilinear coordinates is presented. The proposed integral form is obtained from the time derivative of the momentum of a material fluid volume and from the Leibniz rule of integration applied to a control volume that moves with a velocity which is different from the fluid velocity.

In this paper a new numerical model for the simulation of the wave breaking is proposed. In order to represent the complex geometry of coastal regions, the three-dimensional equations of motion are expressed in integral contravariant form and are solved on a curvilinear boundary conforming grid. A time-dependent transformation of the vertical coordinate that is a function of the oscillation of the turbulent wave boundary layer is proposed. New boundary condition bottom for the equations of motion expressed in contravariant form are proposed.

In this paper we propose a new numerical model for the simulation of the wave breaking. The three-dimensional equations of motion are expressed in integral contravariant form and are solved on a curvilinear boundary conforming grid that is able to represent the complex geometry of coastal regions. A time-dependent transformation of the vertical coordinate that is a function of the oscillation of the turbulent wave boundary layer is proposed. A new numerical scheme for the simulation of the resulting equations is proposed.