## Simulation modelling of irregular waves for marine object dynamics programmes

The aim of the research reported in the thesis is to find and develop mathematical apparatus that allows to simulate ocean waves of arbitrary amplitudes mitigating assumptions of linear wave theory. Such mathematical models are typically used as an input in numerical simulation of ship motion, and, since the simulation is conducted for an extended period of time, the software implementation of the model must be efficient and its performance scalable to a large number of computer cluster nodes. Three-dimensional autoregressive moving average (ARMA) model, one-dimensional version of which is popular in statistics, allows to generate waves of arbitrary amplitudes, if ocean wavy surface auto-covariate function is used as an input. Wave pressures are computed by finding velocity potential field for resulting wavy surface, i.e. finding explicit solution to inverse problem of hydrodynamics for inviscid incompressible fluid. High-performance software implementation is done for both the model and the explicit formula, because the model does not use transcendental mathematical functions and integrals in explicit formula are computed via fast Fourier transform family of algorithms. Integral characteristics of the resulting wavy surface match the ones of real ocean waves, and the resulting velocity potential field match the one produced by the formulae from linear wavy theory for small-amplitude waves, and moves the region where the most energy is concentrated to the wave crest for large-amplitude waves. Software implementation uses master-slave approach for handling autoregressive dependencies and for dynamic load distribution between cluster nodes and processor cores. The usage of ARMA model and new pressure field finding method allows to increase quality of ship motion simulation programmes by providing higher model convergence rate, aperiodicity and an ability to generate large-amplitude waves. The model and the method form a basis for virtual testbed — a programme for marine objects dynamics studies.

Full text: arma-thesis.pdf