Practical Implementation of the Polynomial Representation of Potential Damping in Time Domain Simulations

Time domain simulations are required when analyzing nonlinear vessel behaviour. The usual approach conducting time domain simulations is to transform a complex valued function of frequency dependent damping and added mass to a convolution integral in the time domain. Evaluating the integrals during time domain simulations is computational expensive and the accuracy of the calculation of the limit value of added mass in diffraction calculations is dependent on the panel size of the model. In this paper, an alternative approach based on a polynomial model for damping proposed by K.E. Kaasen et al is extended from a single degree of freedom to a 6 degrees of freedom model of a heavy lift barge. Polynomials for contributions of velocity to the damping force are constructed generically using a least square curve fitting method. The polynomials then are transformed to the time domain counterpart using a state space representation. The quality of the fits of the damping function has a large influence on the resulting damping force in time domain. Furthermore, the higher the order of the differential equation, the larger the number of variables to integrate during a time domain simulation. Consequently, the presented method is not necessarily more efficient in simulations than the traditional retardation functions.