E
0.06
0.04
0.02
0.00
0
3.7 Numerical Integration of the Source Function
77
50000
100000
150000
t, s
200000
Fig. 3.8. Energy time variation obtained using different integration methods. Designations are the same as in Fig. 3.7
This difference is probably connected with the use of the Euler integration
method (3.40), whose result is rough enough at the first fractional integration
step (3.58). The numerical error can be significantly reduced if the more
precise explicit (3.41) or semi-implicit (3.47) integration methods are used.
In conclusion it should be noted that the performed tests reveal the high
efficiency of the splitting method for integrating the wave energy balance
equation with the non-linear energy transfer function. An additional problem consists in substantiating the source function with energy wind input and
dissipation, which allows a precise analytical solution (3.53) . The problem of
the optimal choice of the source function is discussed in the next chapter. It
should be noted that the adopted dissipation function contains a number of
free parameters. Their adjustment allows the model to be adapted to a number of functions describing the non-linear mechanism of wind wave energy
dissipation.
Adjustment of integration of the source function with the wave
energy propagation scheme. The aforementioned wave time evolution
calculations were made for one spatial point and a uniform wind field. And,
naturally, the question arises about the validity of the application method
for a more complicated case of wave calculation in a specific area, with the
wind field being non-uniform and non-stationary. It should also be noted that
0.06
0.04
0.02
0.00
0
3.7 Numerical Integration of the Source Function
77
50000
100000
150000
t, s
200000
Fig. 3.8. Energy time variation obtained using different integration methods. Designations are the same as in Fig. 3.7
This difference is probably connected with the use of the Euler integration
method (3.40), whose result is rough enough at the first fractional integration
step (3.58). The numerical error can be significantly reduced if the more
precise explicit (3.41) or semi-implicit (3.47) integration methods are used.
In conclusion it should be noted that the performed tests reveal the high
efficiency of the splitting method for integrating the wave energy balance
equation with the non-linear energy transfer function. An additional problem consists in substantiating the source function with energy wind input and
dissipation, which allows a precise analytical solution (3.53) . The problem of
the optimal choice of the source function is discussed in the next chapter. It
should be noted that the adopted dissipation function contains a number of
free parameters. Their adjustment allows the model to be adapted to a number of functions describing the non-linear mechanism of wind wave energy
dissipation.
Adjustment of integration of the source function with the wave
energy propagation scheme. The aforementioned wave time evolution
calculations were made for one spatial point and a uniform wind field. And,
naturally, the question arises about the validity of the application method
for a more complicated case of wave calculation in a specific area, with the
wind field being non-uniform and non-stationary. It should also be noted that