320
Coastal Engineering: Theory and Practice
along with the boundary conditions are transformed to prescribe within
each element and then the overall solution is obtained after assembling the
éléments with the continuity requirements between the éléments. The finite
element System of équations within each element is derived either using
weighted residual technique or variational formulation. Due to its flexibility
of this approach, this method has been widely adopted to prescribe the flow.
The following sections explain the various numerical modelling schemes
being carried out in Coastal applications.
10.5 Numerical Wave Modelling
A numerical wave model is arrived at by a combination of the mathematical
form which describes the physical wave problem and numerical approximation of the mathematical équations. It differs from theoretical modelling in
terms of the method instrumental in reaching the solution of the governing
équations. The foundation of numerical wave modelling is laid by the existing wave équations resulting from theoretical studies. Many a times, the
same condition of wave propagation may be represented by means of more
than one équation, the choice of which depending on the levels of approximation desired. Likewise, a wave model may be applicable to different cases
of wave motion provided, the fundamental assumptions hold good.
There are two approaches in defining numerical wave models: the first
approach is the résultant of the vertical intégration of the time-dependent
mass and momentum balance équations that leads to phase-resolving models and the second one is the phase-averaged approach by including the
required physical processes into the energy or action balance équation.
Appropriate numerical techniques need to be employed to solve équations
from either approach.
The phase-resolving models can be applied over relatively small régions
of the order of tens of kilométré and the temporal resolution dictâtes the
need for 10 ~ 100 time steps for each wave period. In these models the sea
surface élévation is resolved with a grid laid on the free surface. However,
the phase averaged models can be used to cover much larger régions and
only, the statistics of the sea surface élévation is computed, i.e., in the
frequency domain.
10.5.1 Wave spectral models
Best suited to model large scale wave propagation, the wave energy spectral model is formulated based on the assumption that an irregular sea
Coastal Engineering: Theory and Practice
along with the boundary conditions are transformed to prescribe within
each element and then the overall solution is obtained after assembling the
éléments with the continuity requirements between the éléments. The finite
element System of équations within each element is derived either using
weighted residual technique or variational formulation. Due to its flexibility
of this approach, this method has been widely adopted to prescribe the flow.
The following sections explain the various numerical modelling schemes
being carried out in Coastal applications.
10.5 Numerical Wave Modelling
A numerical wave model is arrived at by a combination of the mathematical
form which describes the physical wave problem and numerical approximation of the mathematical équations. It differs from theoretical modelling in
terms of the method instrumental in reaching the solution of the governing
équations. The foundation of numerical wave modelling is laid by the existing wave équations resulting from theoretical studies. Many a times, the
same condition of wave propagation may be represented by means of more
than one équation, the choice of which depending on the levels of approximation desired. Likewise, a wave model may be applicable to different cases
of wave motion provided, the fundamental assumptions hold good.
There are two approaches in defining numerical wave models: the first
approach is the résultant of the vertical intégration of the time-dependent
mass and momentum balance équations that leads to phase-resolving models and the second one is the phase-averaged approach by including the
required physical processes into the energy or action balance équation.
Appropriate numerical techniques need to be employed to solve équations
from either approach.
The phase-resolving models can be applied over relatively small régions
of the order of tens of kilométré and the temporal resolution dictâtes the
need for 10 ~ 100 time steps for each wave period. In these models the sea
surface élévation is resolved with a grid laid on the free surface. However,
the phase averaged models can be used to cover much larger régions and
only, the statistics of the sea surface élévation is computed, i.e., in the
frequency domain.
10.5.1 Wave spectral models
Best suited to model large scale wave propagation, the wave energy spectral model is formulated based on the assumption that an irregular sea