Calculation of ship motions in steep waves with restoring and Froude-Krylov forces on an adaptive panel mesh with Gauss and analytic integration methods

Abstract

The impulse response method is a frequently used method to calculate ship seakeeping behavior. In this paper, the restoring and Froude-Krylov calculation is conducted with constant evaluation of panel pressures as well as Gauss quadrature and an analytical integration. The applied panel grid is coarsened by an adaptive algorithm which is based on a normal vector condition. The comparison of methods is based on grid convergence studies which are followed by a verification of forces with computational fluid dynamics (CFD) results on the fixed duisburg test case in waves. Validations with experimental results in head, oblique and following waves show that all integration methods are accurate. The exact integration is numerically sensitive in some cases. Gauss quadrature is highly accurate; however, the additional effort is not beneficial since the geometrical accuracy has-stronger influence on the force amplitudes than the integration method. Adaptive grid coarsening reduces the simulation time and is accurate up to a level, where the panel length comes close the wavelength. The added resistance at the investigated Froude number of 0.05 shows higher uncertainty levels, this applies to the results of both the numerical methods and model tests.