Nonlinear wave transmission and pressure on the fixed truncated breakwater using NURBS numerical wave tank

Fully nonlinear wave interaction with a fixed breakwater is investigated in a numerical wave tank (NWT). The potential theory and high-order boundary element method are used to solve the boundary value problem. Time domain simulation by a mixed Eulerian-Lagrangian (MEL) formulation and high-order boundary integral method based on non uniform rational B-spline (NURBS) formulation is employed to solve the equations. At each time step, Laplace equation is solved in Eulerian frame and fully non-linear free-surface conditions are updated in Lagrangian manner through material node approach and fourth order Runge-Kutta time integration scheme. Incident wave is fed by specifying the normal flux of appropriate wave potential on the fixed inflow boundary. To ensure the open water condition and to reduce the reflected wave energy into the computational domain, two damping zones are provided on both ends of the numerical wave tank. The convergence and stability of the presented numerical procedure are examined and compared with the analytical solutions. Wave reflection and transmission of nonlinear waves with different steepness are investigated. Also, the calculation of wave load on the breakwater is evaluated by first and second order time derivatives of the potential