An Efficient Numerical Scheme for Simulating Unidirectional Irregular Waves Based on a Hybrid Wave Model

The Unidirectional Hybrid Wave Model (UHWM) predicts irregular wave kinematics and pressure accurately in comparison with its linear counterpart and modification, especially near the free surface. Hence, in using the Morrison equation it has been employed in the computation of wave loads on a moored floating structure, such as Spar or TLP (Tension Leg Platform), which can be approximated by a slender body or a number of slender components. Dr. Jun Zhang, with his former and current graduate students, have developed a numerical code, known as COUPLE, over the past two decades, simulating 6 Degree Of Freedom (DOF) motions of a moored floating structures interacting with waves, current and wind. COUPLE employs UHWM as a module for computing wave loads on a floating structure. However, when the duration of simulating the wave-structure interaction is long, say 3 hours (typically required by the offshore industry for extreme storm cases), the computation time of using UHWM increases significantly in comparisons with the counterpart based upon linear wave theory.

This study is to develop a numerical scheme which may significantly reduce the CPU time in the use of UHWM and COUPLE. In simulating irregular (or random) waves following a JONSWAP spectrum of a given cut off frequency, the number of free wave components in general grows linearly with the increase of the simulation duration. The CPU time for using a linear spectral method to simulate irregular waves is roughly proportion to N2, where N is the number of free wave components used in simulating irregular waves, while that for using a nonlinear wave model, such as UHWM, it is roughly proportional to N3. Therefore, to reduce the CPU time, the total simulation duration is divided into a number of segments. However, due to the nature of Fast Fourier Transform (FFT), the connection between the two neighboring surface elevations segments is likely discontinuous. To avoid the discontinuity, an overlapped duration between the two neighboring segments is adopted. For demonstration, a free-wave spectrum is input to COUPLE for simulating the 6 DOF motions of a floating 5-MW wind turbine installed on an OC3 moored Spar and tensions in the mooring lines. It is shown that the CPU time for the above simulation for duration of 2048 seconds is reduced from more than16 hours when the irregular wave elevation and kinematics are calculated without dividing into segments to less than three hours when those are calculated by dividing into five segments.