Discretization of Laplacian Velocity Potential Equation for Curtainwall-Pile Breakwater (CPB) and Pile Breakwater (PB) Under Regular Wave by Using Finite Difference Method (FDM)

In this study, the governing equation and the boundary conditions of the interaction between sea waves and pile breakwater (PB) and curtainwall-pile breakwater (CPB) are discretized by finite difference method (FDM) in order to obtain wave velocity potential in defined domain and prepare the equations for future numerical modeling. For this purpose the Laplacian velocity potential equation was used as the governing equation and the Summerfeld, sea bed, free surface, pile zone, and coastal side equations were used as the boundary conditions. Also, the equations for special points with mixed two or three boundary conditions were edited and all of the equations transferred in to time independency. Then, the difference between CPB and PB kinds of breakwaters was shown using the previous researchers suggested equations. Finally, by using the governing equation, the discretized equations were obtained in all normal, pile zones, and mixed boundary conditions and it was concluded that the interaction between the airy waves and the both types of mentioned breakwaters can be modeled by the obtained equations by using the finite difference numerical model method.

کلیدواژه ها:

Laplacian Velocity Potential Equation ، Finite Difference Method ، Curtain-Pile Breakwater ، Pile Breakwater ، Numerical Model