Simulation of Standing and Propagating Sea Waves . . .
271
The experiment, in which velocity fields produced numerically by different formulae
were compared, shows that velocity fields produced by formulae (19) and (3) correspond to each other for small-amplitude waves. Two ocean wavy surface realisations
were made by AR model: one containing small-amplitude waves, other containing
large-amplitude waves. Integration in formula (19) was done over wave numbers
range extracted from the generated wavy surface. For small-amplitude waves both
formulae showed comparable results (the difference in the velocity is attributed to
the stochastic nature of AR model), whereas for large-amplitude waves stable velocity field was produced only by formula (19) (Fig. 5). So, generic formula (19) gives
satisfactory results without restriction on wave amplitudes.
High-Performance Software Implementation
for Heterogeneous Platforms
White Noise Generation
In order to eliminate periodicity from generated wavy surface, it is imperative to
use PRNG with sufficiently large period to generate white noise. Parallel Mersenne
Twister [22] with a period of 2
19937
− 1 is used as a generator in this work. It allows to
produce aperiodic ocean wavy surface realisations in any practical usage scenarios.
There is no guarantee that multiple Mersenne Twisters executed in parallel threads
with distinct initial states produce uncorrelated pseudo-random number sequences,
however, algorithm of dynamic creation of Mersenne Twisters [23] may be used
to provide such a guarantee. The essence of the algorithm is to find matrices of
initial generator states, that give maximally uncorrelated pseudo-random number
sequences when Mersenne Twisters are executed in parallel with these initial states.
Since finding such initial states consumes considerable amount of processor time,
vector of initial states is created preliminary with knowingly larger number of parallel threads and saved to a file, which is then read before starting white noise generation.
Wavy Surface Generation
In ARMA model value of wavy surface elevation at a particular point depends on previous in space and time points, as a result the so called ramp-up interval (see Fig. 6),
in which realisation does not correspond to specified ACF, forms at the beginning
of the realisation. There are several solutions to this problem which depend on the
simulation context.
If the realisation is used in the context of ship stability simulation without manoeuvring, ramp-up interval will not affect results of the simulation, because it is located
271
The experiment, in which velocity fields produced numerically by different formulae
were compared, shows that velocity fields produced by formulae (19) and (3) correspond to each other for small-amplitude waves. Two ocean wavy surface realisations
were made by AR model: one containing small-amplitude waves, other containing
large-amplitude waves. Integration in formula (19) was done over wave numbers
range extracted from the generated wavy surface. For small-amplitude waves both
formulae showed comparable results (the difference in the velocity is attributed to
the stochastic nature of AR model), whereas for large-amplitude waves stable velocity field was produced only by formula (19) (Fig. 5). So, generic formula (19) gives
satisfactory results without restriction on wave amplitudes.
High-Performance Software Implementation
for Heterogeneous Platforms
White Noise Generation
In order to eliminate periodicity from generated wavy surface, it is imperative to
use PRNG with sufficiently large period to generate white noise. Parallel Mersenne
Twister [22] with a period of 2
19937
− 1 is used as a generator in this work. It allows to
produce aperiodic ocean wavy surface realisations in any practical usage scenarios.
There is no guarantee that multiple Mersenne Twisters executed in parallel threads
with distinct initial states produce uncorrelated pseudo-random number sequences,
however, algorithm of dynamic creation of Mersenne Twisters [23] may be used
to provide such a guarantee. The essence of the algorithm is to find matrices of
initial generator states, that give maximally uncorrelated pseudo-random number
sequences when Mersenne Twisters are executed in parallel with these initial states.
Since finding such initial states consumes considerable amount of processor time,
vector of initial states is created preliminary with knowingly larger number of parallel threads and saved to a file, which is then read before starting white noise generation.
Wavy Surface Generation
In ARMA model value of wavy surface elevation at a particular point depends on previous in space and time points, as a result the so called ramp-up interval (see Fig. 6),
in which realisation does not correspond to specified ACF, forms at the beginning
of the realisation. There are several solutions to this problem which depend on the
simulation context.
If the realisation is used in the context of ship stability simulation without manoeuvring, ramp-up interval will not affect results of the simulation, because it is located