# 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