## Usage of numerical modelsDimensionality (general)Boundaries of the grid (general) Discrete step sizes in the grid (general) Iterative processes (general) Nesting (general) Validation of the model (general) Dimensionality of a Swan model Choice of computational region and boundary conditions (Swan) Choice of step sizes (Swan) Iterative behaviour of Swan Nesting with SWAN Validation of SWAN results ## Numerical models in generalNumerical computations by nature always involve a finite number of values that can be computed; so the phenomenon that is to be simulated has to be schemetised to such extent that it is represented by a finite number of values (often a large number, e.g. many millions). Most numerical models therefore carry out computations on a grid in space, and if the phenomenon is time-dependent, also for a finite number of time steps. ## DimensionalitySometimes the number of grid points can be reduced drastically by reducing the number of dimensions. For instance a 2-dimensional problem can be reduced to a 1-dimensional problem if the gradients in one direction are much smaller than those in the direction perpendicular to it. Or, which is quite common in near-shore wave models, the conditions are considered to be stationary, so that it is not necessary to make computations over many time steps. Conditions in nature are never truly stationary, so criteria are needed to decide if the reduction is justified. Time-derivatives cannot be compared with space-derivatives because of their different physical dimensions, but for wave problem criteria are available to decide whether a stationary computation is applicable. Specifics for Swan are described below. ## Boundaries of the gridNumerical
simulation are carried out on a grid, usually a regular grid. The grid
necessarily covers a finite region, and the influence of the outside world is
taken into account by means of the boundary conditions on the boundary of the
grid. The partial differential equations underlying the model determine how
many boundary conditions are needed. The choice of the computational area is
one of the responsibilities of the model engineer (i.e. the SWAN user). Specifics for Swan are described below. ## Discrete steps in the gridThe mesh
sizes in the grid, and the time steps, have to chosen also by the model
engineer. In each case these steps must be such that relevant (length or time)
scales are resolved well, i.e. the steps must be small compared with these
characteristic lengths or time intervals; a good initial guess is 1/20 or 1/40
of such lengths or intervals. Specifics for Swan are described below. ## The need for IterationMany
numerical models employ iterative procedures. Some also have coefficients that
can speed-up the iteration, at the risk of making the model unstable. Specifics for Swan are described below. ## The need for NestingFrequently
the desired accuracy requires a dense grid in the area of interest, whereas at
the same time boundaries have to be chosen so far away from the area of
interest that the total number of grid points becomes infeasible, either
because of memory constraints or because of constraints on the simulation time.
Specifics for Swan are described below. ## Validation of the modelWhether the
quality of numerical computations allows valid conclusions to be drawn, can
never be taken for granted. Thus validation is necessary, by comparing
numerical results with observations, preferably in the area of interest. The
unfortunate thing with validation is that it is possible only for an existing
situation and for conditions that have actually occurred. Validation is
impossible for design situations, and/or for extreme (and therefore rare)
conditions. Thus conclusions have to be drawn with great care. Specifics for Swan are described below. ## Specifics of SWANIn this section the findings of the previous section are applied to the SWAN model. ## Dimensionality
In many places in the world gently curved beaches occur.
Such situations can usually be modeled as one-dimensional, also if the incident waves
are not perpendicular to the coast. Note that the requirement is that the alongshore gradients
of the wave field (and consequently also of the bottom) are much smaller
than the gradients in cross-shore direction.
The one-dimensional domain must be normal to the coast, NOT parallel to the (average) wave
direction.
General considerations on dimensionality are described above. ## Choice of computational region and boundary conditionsThe
spectral action balance equation requires boundary values for all incoming wave
components at the boundary. It is stressed here that outgoing components cannot
be prescribed by the SWAN user. General considerations on the choice of boundaries are described above. ## Step sizesSince
computations by SWAN are carried out in 5-dimensional space, in general 5 step
sizes have to be determined. For each of these the arguments in the previous
section have to be kept in mind. Note that time and space steps do NOT have to be small compared with the wave period or length. This is because the average properties of the wave field (which is what we compute when using a spectral model) vary over a period and length much larger than the wave period and length. Time and space steps must be small compared with the wave period or length in the case of phase-resolving models; this is the type of models used for wave penetration in harbours. General considerations on the choice of step sizes are described above. ## Iterative behaviourThe SWAN
model uses a four-sweep numerical integration technique. Since there are
interactions between the sweeps, due to refraction and to nonlinear source
terms, SWAN has to carry out a number of iterations. Experience shows that SWAN
is often slowly converging. This seems to be due mainly to the quadruplet
interaction term. Its value at the peak of the spectrum is relatively small,
but it still has a non-negligible effect on the final results of the
computation.
In SWAN you can control the
iteration by specifying a maximum allowed difference between subsequent values
of wave height and wave period, and the number of grid points where the
difference has to be smaller in order to stop the iteration process.
For investigating the iterative behaviour of SWAN there is the possibility of producing output of action density and source terms for a number of test points (see command TEST); the output can be in the form of a table of overall wave parameters, or in the form of 1-dimensional or 2-dimensional spectra. General considerations on iteration are described above. ## Nesting with SWAN
Nesting from a coarse model to a finer model is extremely simple in SWAN.
It is done by means of the combination of the commands
NGRID and NESTOUT.
In some cases it is done by means of the the combination of the commands
CURVE and SPECOUT.
This way is more complicated, but this is seldom necessary.
SWAN allows the user to
build nesting boundary conditions to more than one nested model from a
computation. Thus it is easy to find out whether it is possible to skip an
intermediate nesting level or not. The depth at the nesting boundary may be
different for the coarse and the fine model because the values are interpolated
from a different bathymetry in the two models. Since some of the source terms
depend strongly on the depth the nesting may cause a strong gradient near the
boundary of the finer grid. The model engineer can take precautions to
guarantee that the depth is continuous from the coarse to the fine model.
General considerations on nesting are described above. ## Validation of SWAN resultsIn
near-shore applications of SWAN the bathymetry is crucial to the results. It
must be determined accurately in a SWAN validation. A problem with design
situations is that sandy bottom may be very dynamic so that the bathymetry may
be variable during the period for which the design is intended. General considerations on validation are described above. |

## Swan Course |