Fully nonlinear propagation of waves in a uniform current using NURBS numerical wave tank

A two-dimensional Numerical Wave Tank (NWT) is developed to simulate in the time domain fully nonlinear propagation of ocean waves in uniform currents. Fully nonlinear free surface motion is modeled using Mixed Eulerian-Lagrangian (MEL) scheme and Non-Uniform Rational B-Spline (NURBS) formulation. The potential theory and Laplace equation are solved in the Eulerian frame using a high-order formulation of Boundary Elements Method (BEM) at each time step. The distribution of boundary values is defined based on NURBS to discretize the boundary integral equation. The spatial derivatives of the boundary values are computed precisely based on NURBS. Material node approach and fourth-order Runge-Kutta time integration are employed to update the free surface boundary conditions. Propagation of robust nonlinear wave is simulated to examine the accuracy and convergence of the present fully nonlinear numerical procedure. Propagation the nonlinear regular waves in the uniform flows are also studied and the solutions are compared with the theoretical results. Propagation of the irregular nonlinear waves is studied to compare with the analytical solutions. Furthermore, fully nonlinear irregular wave in the uniform currents is simulated.