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Delft

TechnischeUniversiteitDelft

USER MANUAL FOR THE PROGRAM

DUCHESS

Delft University Computer program for 2-dimensional Horizontal

Estuary and Sea Surges

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USER MANUAL FOR THE PROGRAM

DUCHESS

Delft University Computer program

for 2-dimensional Horizontal

Estuary and Sea Surges

date of printing: March 1990

by N. Booij

Delft University of Technology Fac. of Civil Engineering

Group of Fluid Mechanics P.O. Box 5048

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DUCHESS User Manual 2

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CONTENTS 1. Introduetion 2. Methods of Computation

2.1. Partial Differential Equations 2.2. Discretization

2.3. Numerical Approximations

2.4.lnundation Procedure

3. System of units

4. Some practical advice

5. Descriptions of Commands

5.1. Format of the input 5.2. General commands

5.3. Commands for model description 5.4. Boundary conditions

5.5. Output requests

6. Error Messages

7. A sample problem

8. Modifications with respect to previous version

Appendix 1. Run instructions for the Personal Computer

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DUCHESS User Manual 3

1. INTRODUCTION

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DUCHESS is a computer program written in Fortran-77 intended to perform two-dimensional tidal and storm surge computations.

It is available on the central computer of the Delft University. The program is based on a finite difference approximation of the two-dimensional shallow water equations. The program uses water level and current (=depth

*

velocity) as unknown quantities.

The computational procedure is according to the Alternating Direction Implicit method.

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Among the facilities of the program are the following:

steady and unsteady boundary conditions in either water level or one of the current components. Dams in the computational region can be modeled by means of intemal boundary conditions.

nesting of modeis; boundary data for a model with a finer grid can be obtained from a coarser grid model.

steady or unsteady wind influence. The influence can be via wind shear stress of via air pressure, or both.

the program allows that parts of the computational region become dry or get inundated. The user does not have to take special precautions of this is expected to happen.

output: print of computed variables in a selected subregion, plot of iso-lines of water level, vector plots of either velocity or current.

Input to the program is in the form of user-friendly, easily readable commands.

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The program is divided into four main parts having the following tasks: assigning default values to a large number of variables,

reading and carrying out the user's commands, executing the surge computation proper,

printing and plotting the computational results.

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Sometimes DUCHESS detects errors in the user's input.

Chapter 6 provides some general information on error messages.

The appendix lists the Job Control statements by which a DUCHESS job can be submitted to the computer.

Since the program is stored in the computer in compiled form, the user will usually not see the souree text of the program.

Still it is necessary that he is familiar with the numerical approximations employed in the program. Chapter 2 gives a survey of the approximation.

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DUCHESS User Manual 5 2. METHODS OF COMPUTATION

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2.1. Partial Differential Equations

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The DUCHESS model is based on the 2-dimensional shallow water equations..

This is a model where the equations are integrated in vertical direction. The quantities appearing in the model thus are functions of the horizontal coordinates X and Y, and of the time T. The unknowns appearing in the equations are H, the water level with respect to a chosen datum, and Qx and Qy, which are the X- and Y-components of the velocity integrated over depth.

The quantities Qx and Qy will be designated in the sequel as the components of the current.

The current thus is the average velocity multiplied by the depth.

There are three equations in the model, one of them is the continuity equation, which follows from the conservation of mass:

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The other two equations are the equations of motion. We will write down here only the equation of motion in X-direction; the equation in Y-direction is analogous, apart from the Coriolis term, which is +Co *Qx in that case.

The equation of motion in X-direction reads:

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The terms present in the equation are the following: local acceleration term,

advective aceleration terms, viscosity terms, surface and pressure gradient terms, bottom friction term, Coriolis term (term due to the earth's rotation) and the wind

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shear stress component. Notations:

g = gravitational acceleration

H = water level with respect to a chosen datum Z = bottom level with respect to the same datum D = water depth (=H-Z)

Qx = depth integrated velocity (x-comp.), or x-current

Qy = depth integrated velocity (y-comp.), or y-current

IQI = Sqrt(Qx2+Q/)

E = (eddy) viscosity

P = air pressure, divided by gravitation and by water density,

Fr = friction coefficient Co = Coriolis coefficient W = Wind shear stress.

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DUCHESS User Manual 6

These quantities are normally expressed in S.l. units. Other possibilities exist; these are described in chapter 3.

2.2. Discretization

The main characteristics of the computational scheme are the following: - Altemating Direction Implicit Method,

- current vector and water level are calculated at altemating points.

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DUCHESS User Manual 7

Plan view of the grid:

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o - 0 - 0 - 0 - Qx-point o - 0 - 0 - 0 - Qy-point o - 0 - 0 - 0 - o H- I Z-point

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o - 0 0 0 --> X

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Q, is the current component in X-direction, and Qy is the current component in Y-direction. H is the water level, and Z the bottom level (both positive in upward direction). D, the depth, is equal to H-Z, and the velocity is found from:

U=QxfD, V=Q/D.

The place in the grid is indicated by two subscripts i and j (IX and IY in the program). This is done as follows:

Hij is H in (X, Y)

QXij is Qx in (X

+

sxn,

Y)

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DUCHESS User Manual 8

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Y Qx-connection Qy-connection OH-point, Z-point

o

o

---0

o

t..Y

o

- : 0

o

+---+---+---X >11

in this square the points share the indices land J Fig. 2.1. Computational scheme projected in the x-y-plane

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DUCHESS User Manual 9

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In the computational procedure new values for Qx , Qy and H are computed every half time step.

In the first half time step a computation along a line in X-direction takes place, and in the second half step a computation in Y-direction.

The values along one line in X- or Y-direction resp. are computed in an implicit manner.

In the computation in X-direction the derivatives with respect to X are treated implicitly, and the derivatives with respect to Y explicitly, and vice versa.

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in the first half time step for every line:

and for every line:

- 0 - 0 - 0 - 0 - 0 - Qx and H Qy

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0

second half time step Qy

and so on for every line 0 H then: Qx in Y-direction

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The water levels are advanced in time using the continuity equation, the currents using the equation of motion.

Both partial differential equations are approximated by means of a numerical scheme which is central in space and approximately central in time.

The user can increase the stability by making the scheme more implicit (see the coefficient THETA command NUM), thereby also making the scheme less accurate.

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The order of accuracy is second order in space, and first or second order in time depending on the value of THETA.

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2.3. Numerical Aru?roximations

In the following the numerical approximations of the terms appearing in the partial differential equation are developed.

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DUCHESS User Manual

Only a computation step in X-direction is described, since the computation in Y-direction is identical, apart from the swapping of the variables Qx and Qy. The superscript - indicates the (known) value at time T, the superscript

+

indicates the as yet unknown values at a time a half step ahead (T+loT/2).

In the first half time step (implicit in X-direction) the continuity equation (1) is approximated by the following expression:

H~ . - H~,J -:~,J. flt/2 (3A) Qxi,j - QXi-l,j +--=-fl":""x--"":""::'" (3B) + QYi,j - QYi-,j-l = 0 fly (3C)

The equation for the computation in the second half time step is found by swapping Qx and Qy and by substituting (i-l,j) by (i.j-I) etc.

Thus in the second half time step unknown values of Qy appear in equation.

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DUCHESS User Manual 11

The equation of motion in X-direction is approximated by:

(QXi~ - QxD)

At/2

(4A)

(4B)

(QxD + QXi~lj) (2 (QXi~+ QXi~lj) - (Qx;j + QXi~IJ))

4 Dij Ax

(4C)

EtJ D'J QX'++IJ Qy':J

- 2 ( - )

Ax2 (Di+IJ + Dt+2

)/2

(Dij + Di+I)12

(4D)

E D

o:

0,+

+ 2 t-lJ HJ ( ij _ t-IJ)

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DUCHESS User Manual

(4F)

(4G)

+ WXjJ = 0

(4H)

In the advective acceleration term (4C) the value of Qx is approximated by a higher order upstream method. This method is used in order to improve the stability. The coefficients shown above apply if Qy is positive. If Qy is negative, the values of Qx for (i,j-1) and (i,j-2) resp. disappear, and values for (i,j+2) and for (i,j + 1) appear; furthermore the coefficients are in the opposite order. Furthermore one notices that in the viscosity term (4D) the term (fQi

ax

2

appears with a factor 2, whereas the term éflQiay2 does not appear at all. This

is compensated by the fact that the first is absent from the equations employed in the next half time step, whereas the second appears there with factor 2. This way of treating the viscosity term will cause some oscillation, but it seems permissible since the viscosity term is usually small. The reason for this

procedure is computational efficiency, and an expected contribution to stability. In the computation which is implicit in X-direction the equation of motion in Y-direction is approximated by:

(5 A) + 2(QXD + QXD+l) (Qyt~ + Qyj~+l) (Dij + DjJ+l + Di+1J + Dj+1j+1) .t1x (5B) 12

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DUCHESS User Manual 13

2(Qxi~IJ + Qxi~IJ+I) (Qyi~lj + Qyi~lj+l)

(Di-IJ + Di-1J+1 + Djj + Djj+l) äx

(5C)

(0.375 QyD + 0.75Qy;J_t - 0.125Qy;j_~2

DjJ äx (5D) Qyi~lj ----''----) D.l' + D. l' 1 1- " 1-J+ (5E) (5F) (5G) (5H)

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DUCHESS User Manual 14

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where

Q;

is the average of the 4 surrounding Qx-points.

In term (5C) the same higher order upstream approximation is used. The version shown here, is valid if Qy

>

O.In the opposite case the term is modified in the same way as described previously regarding this method of approximation. Analogous equations are used for the computation implicit in Y-direction. The Qx- and Qy-values, as well as the X- and Y-coordinates are interchanged. Furthermore the sign in front of the Coriolis term changes.

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In the manner described above a set of linear equations is formed with Qy-values as unknowns. This system is solved efficiently by means of the Thomas algorithm, and new values for Qy result. This procedure is followed for every line in X-direction. Then the time is increased by a half time step, and the procedure is

applied in Y-direction, this time with H and Qy first and then Qx as unknowns.

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2.4. Inundation procedure

In regions where the depth becomes negative, points are taken out of the computation or as it is called here, made inactive. If dry points tend to become flooded again, they are made active again. This is the inundation procedure which is described in more detail below. The flooding and falling dry is visualized in different forms of output, such as the plot (of shorelines), and the Block output.

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If the water level is going down the H-points are checked to see whether the depth has become negative. In the current points the depth is taken equal to the average of the two neighbouring H-points, so these will never be the first to become dry. The following procedure is adopted: after each half time step all active H-points are checked for positive depth. If the depth in an H-point has become negative, it is made inactive, and also the surrounding current points are made inactive (if they were not inactive already); the current in these points is made O.

The flooding is carried out by checking for each inactive current point connecting an active H-point and an inactive H-point, whether the water level in the active H-point is above the bottom in the inactive H-point. If so, the current point is made

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DUCHESS User Manual 15 active, as well as the inactive H-point. Also inactive current points connecting two active H-points are made active.

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DUCHESS User Manual

3. SYSTEM OF UNITS

DUCHESS works by default with the S.l. units m (meter), kg (as unit of mass) and s (second). For instance the standard value of the gravitational acceleration is 9.81 (m/s2) . Other consistent unit systems can be used; the rules for consistency are shown in the table below. Different units can be used for length and depth. In the general unit system the units of length, depth, time and concentration can be chosen arbitrarily, and the other units follow from the table shown below.

The units will be printed in the output. The command UNITS is used if one wishes to modify any names of units. It is stressed that modification of unit names itself does not cause any change in the computed numbers. It is the responsibility of the user to introduce a consistent unit system.

table of units

physical quantity general example length, hor. coordinate u) 1000 m depth, water level Uh 1 m time ~ 1000 s velocity u/Ut 1 mts current Uh*u/~ 1 m2/s grav. acceleration (U)2)/Uh*~2 1 m/s2 friction coeff. f (= g/C2) Uh/U) 0.001 wind stress ') UhU/(~2) 0.001 m2/s2 atmospheric pressure ') Uh 1m

Wind stress ') means the true physical wind stress divided by the density of the water. What is called wind stress here, can be any extemal force in the horizontal plane, such as wave driven forces etc.. Atmospheric pressure ') is the true pressure divided by the density and gravitational acceleration.

The standard system of units that is used in DUCHESS, consists of the simple S.l. units: uh=l m, u)=l m, ~=1 s.

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DUCHESS User Manual 17

4. SOME PRACTICAL ADVICE

4.1. Choice of the axes

Impermeable walls (such as dams) are schemetised as straight lines parallel to either the x- or the y-axis. Thus a wall not exactly parallel to one of the axes is schemetised as a line with corners.

These corners may disturb the velocity pattern. Ifpossible, one is advised to choose the axes such that in the important region the dam involved is parallel to either the x- or the y-axis.

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In the printing of the computed results the x-axis is horizontal, and the y-axis is pointing vertically upward. The width of the print paper is limited, so that only a limited number of points in x-direction can be printed. It is therefore advised to choose the x-axis along the shorter side of the model. The coordinate system can be left-oriented (i.e. counterc1ockwise from the positive x-axis to the positive y-axis) or right-oriented. The choice is determined in the command GRID.

y y

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0--- X

X

---0

LEFT-oriented RIGHT-oriented 4.2. Bottom schemetisation

Sharp transitions in the bottom level may cause problems, especially when located near a boundary, where the water level is prescribed. There are two ways to attack such problems. The first is to use the HBSMTH parameter (see the command

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DUCHESS User Manual

SET). The other is to smoothen the bottom. If necessary the boundary should be shifted outward somewhat,if one does not want to change the bottom configuration in the model, and one still needs to carry out some smoothing near the boundary.

4.3. Time step mesh size ratio

Although the computational scheme is formally unconditionally stable, the Courant number CAt! AX(c being the propagation velocity of the waves) should not be too

large in view of the computational accuracy. A reasonable upper limit is about 10. Often in the initial phase of the computation one should use a smaller time step. After the initial disturbances have more or less relaxed, the time step can be increased. The user does not have to worry about boundary conditions or output requests, since these are not affected by a change in the time step. The sequence of commands can be for instance as follows:

SET STEP=150.

<

model description

>

<

output requests

>

COMPUTE 1800. SET 300. COMPUTE 5400. SET 600. COMPUTE 60000.

4.4 Time reguired to get periodical solution

As a rule the time necessary to get rid of the influence of the initial condition can be taken equal to several times the time the surge wave needs to travel through the model. In the case of a periodic computation (for instance tidal computations) one can check whether the results have become periodic by comparlng the states at times one period apart. Therefore in periodic computations it is important to choose the interval between two output times equal to an integer part of the (tidal) periode

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DUCHESS User Manual 19

4.5. Mesh refinement

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Many users of DUCHESS are primarily interested in the consequences of a rather local feature, such as the building of new harbour entrance, the dredging of a shipping channel etc .. Boundary conditions in the neighbourhood are usually not available, and if they are, it must be supposed that they may be influenced by the project that one wants to simulate. Therefore one usually has to start with a computation over a larger region, with rather large meshes. These meshes cannot be too small, in order to keep the number of nodes in the model within reasonable bounds. The total number of nodes (points permanently dry not taken into account) should not be much larger than 5000, if one wants to keep the computational cost limited. From this coarse model the boundary conditions are obtained for the more refined model. One should determine in advance the positions of the boundary points of the refined model. These points do not have to coincide with points in the coarse model. The values computed in the coarse model are written onto secondary storage (see comrnand OUTPUT .. NEST ..),and are read from secondary storage to be used as boundary values for the computation in the refined model (see command BOUNDARY .. NEST .. ). The refinement should not be done in too large steps. A refinement factor of 2, 3 or 4 is reasonable. In a periodic problem one needs to write only the results of the last tidal period to secondary storage. It must be borne in mind that in case of a mesh refinement often the time step is to be reduced too.

Note that the spatial mesh size cannot be changed during a computation. The time step on the other hand can be changed, as explained in section 4.3.

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DUCHESS User Manual

5. LIST OF COMMANDS

5.1. Format of the input

The input for DUCHESS is organized in the form of commands. Each command is designated by a keyword consisting of letters and (sometimes) digits, but always beginning with a letter. Af ter this keyword usually other data appear, such as real or integer numbers, or character strings. Character strings must always be enclosed in quotes; keywords are not in quotes. Strings and keywords have an entirely different meaning to the program; a string is a variable, a keyword has a fixed meaning instructing the program to perform certain actions.

It is not always necessary to actually write down all the data required by the program. In many cases the program will assume reasonable values for variables that do not appear in the commando The command description will mention whether an initial value or a default value is assigned to a variable, An initial value is assigned by the program at the very start of the job, whereas a default value is assigned at the moment that the command is executed. Often an initial value and a default value are different.

Command descriptions are of the following form:

_QT 'NAME' [X] [Y]

KEYWORD < > ->

NU

[RA] [RB]

The following rules apply for the command description:

- Keywords are not enclosed by square brackets or quotes, the letters that are underlined must be copied literally; other letters or digits may be added, as well as the characters - and _. So in the command outlined above one may write: KEY or KEYW or KEY-WORD or KEYHOLE etc.

The first keyword in the command scheme is also the command name. In keywords

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DUCHESS User Manual 21

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both upper and lower case letters may be used.

- A name between square brackets is to be replaced bya (real or integer) number; a name between quotes is to be replaced by a string, also enclosed in quotes. In the command description one can find what the program does if a variabie is not assigned a value by the user.

The description also should make clear whehter a real or integer number is expected.

Note: a decimal point is not permitted in an integer number. The data must be given in the same order as they appear in the description. If one wants to assign the value 6 to the variabie [RA], one writes 6 or 6., or RA=6.

- If one line of input is not large enough to hold the data for one command, the command can be continued on the next line, if the last one has a continuation mark as its last item. The following continuation marks can be used: & or _ (the underscore, not the minus sign). In the command descriptions the & also signifies a continuation mark.

- A group of data between parentheses ( ) is optional; the command description tells what happens if the group of data does not appear int the user' s commando - A group of data within angle brackets

< >

can be given repeatedly. In the user's input the end of the repetition is indicated by the end of the line, by the appearance of a keyword, or by one of the following characters: / or ]. The group of data must be given at least once, unless it is also surrounded by parentheses.

- Alternative options in the command are written between braces of the following form:

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< >

Each alternative is characterized by a keyword (in the above example: ST and NU). If an arrow appears before one of the alternatives (-

> ),

this alternative is chosen if none of these keywords appears.

- Data are separated by blanks and/or commas. A keyword is closed by a blank or one of the following characters: = or :. An empty data field in a series of data fields is recognized only if it is surrounded by commas. Also the program will assume that a data field is empty is it finds a keyword where a data item is expected.

-If the user wants to write a set of identical data fields, he can use the repetition factor, e.g.6 * 'I.O.U.',3*O.,

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DUCHESS User Manual

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as the fint on a new line of input, nor can it be used to give a number of empty data fields.

- To c1arify the meaning of the input, one can insert comment. Comment must be enclosed in $ signs. If there is only one $ sign on a line it is assumed that the end of the line is the end of the comment; the next line is considered again as ordinary input.

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DUCHESS User Manual 23

5.2. Genera! commands:

PROJECT 'PROJ' 'NR'

'TITLE1' 'TITLE2' 'TITLE3'

This command specifies the run data:

'PROl'

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a project identifier, at most 16 characters long.

the run identification, a string of at most 4 characters long identifying the run at hand. The quotes must be given also if the string consists only of digits; '15A' is also allowed.

Init: ".

A description of the run is given in the 3 lines 'TITLEI', 'TITLE2' and 'TITLE3'. Each of these is max. 72 characters long. The lines will be reproduced in the output

'NR'

by the program. Initially all three lines are empty.

CONDITION [NSTOP]

The DUCHESS program sometimes detects errors in the user's input. Chapter 6 gives further information on the classes of errors that may occur.

The command COND determines under what conditions the computation will be started. This facility has the purpose to prevent waste of computer time on jobs which are probably faulty. The computation is not started on occurrence of:

Errors and worse, if [NSTOP] = 1 Severe Errors and worse, if [NSTOP] =2 Termination Errors, if [NSTOP] =3 Init: [NSTOP] =2

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DUCHESS User Manual

TEST [ITEST] [ITRACE] (POINTS < [IXTS] [IYTS]> )

The computational part of the program will produce test output for the points ([IXTS], [IYTS]), .... The number [lTEST] controls the amount of test output. This does not influence the output for test points.

Init: [ITEST] =0 (no test output); default: [ITEST] =20 .

The printing of test output is terminated if [ITEST] is made 0 again (this can be done by the user by issuing a second TEST command).

If [ITEST] = 120 or greater, the bottom levels in the command BOTTOM, the friction values in FRIC, and the wind stress components or air pressure in the command STORM are printed.

If [ITEST]=-I, the program will not print wamings nor wil it print ZERODIVIDE messages. This feature can be used to prevent waste of paper.

In case a high value has been assigned to [ITEST] in order to check the correctness of input, it is wise to give [lTEST] some lower value, e.g. [lTEST] =0, to suppress large amounts of test output.

SET [STEP] [TIME] [GRAV] [COR] [OTH] [HBSMTH]

With this command one can assign values to certain parameters. Most of these parameters have an initial value; in that case the SET command is necessary only if this initial value must be modified.

[STEP] is the upper limit of the time step; the program will choose a smaller time step, if necessary to accomodate output requests.

[TIME] start time of the computation; init: O.

[GRAV] gravitational acceleration; init: 9.81 [COR] Coriolis parameter; init: O.

With left orientation of the axes (option LEFT in command GRID) ,

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DUCHESS User Manual 25 value of [COR] is -1.454E-4*Sin(latitude). At the latitude the Netherlands it is 0.11461E-3, and with right orientation the axes -0. 11461E-3

[DTH] friction threshold depth; init: 0.1 .

For explanation see command FRICTION.

[HBSMTH] a coefficient that may help to make the veloeity field smoother near a boundary where H is prescribed. lts effect is to distribute the kinetic energy transported into the model more evenly over the boundary. Default: O. (no smoothing effect). Range is between O. and 0.5.

UNITS 'UT' lUL' 'UH' 'UQ'

'uv'

[CLOCK]

This comrnand defines the names of the units for the various variables used in the program. These names are used only for output; they do not affect any numerical results of the program.

'UT' unit of time; init: 'sec'; max. 6 characters long. 'UL' unit of length; init: 'm'.

'UH' unit of water and bottom level; init: 'm'. 'UQ' unit of current; init: 'm2/s'.

'UV' unit of veloeity; init: 'mis'.

[CLOCK] doek speed, i.e. doek angle per unit of time; init: 2. *PI/3600. ; is made 2. *PII3.6, if UT is equal to 'ks'. This value is used only for plotting a doek in the view plots made by OUTPUT .. VIEW .

Example: UNITS 'ks', 'km'

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This command changes the default mode for reading time-data from the user' sinput into the HMS-mode (i.e. time in days, hours, minutes and seconds). Itcan be usefull to increase the readibility of the input to DUCHESS and the output produced by the program.

With the HMS option on, the commands in which some time-input data appear, have a slightly different form than it is described in the following chapters of this manual.

A single real value for an input list item (e.g. [STEP] or [BEGIN]) is replaced by four integer values:

[DA] [HO] [MI] [SE] where:

[DA] - number of days (default: 0) [HO] - number of hours (default: 0) [MI] - number of minutes (default: 0) [SE] - number of seconds (default: 0)

Remark: HMS command does not change the intemal representation of time in the program and also has no influence on the way it reads data from files other than the INPUT-file containing user's commands. Therefore time-values on these files (e.g. boundary data file) should be in seconds.

Example: If the requested time step is to be 1 hour 20 minutes, the appropriate SET command will be:

SET STEP HO=1 MI=20 or: SET STEP "1,20,,

or: SET STEP= HO 1, MI=20

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DUCHESS User Manual 27

Note, that the equivalent command: SET STEP SE 4800

will be also accepted by the program.

NUM [THETA]

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This command controls the amount of numerical damping in the model. The coefficient [THETA] corresponds to THETA in chapter 2.3. The initial value of [THETA] is 0.5,in which case there is no numerical damping. If [THETA] is made larger than 0.5, damping is introduced. The damping affects primarily the computation of the gravitational waves. Limitations: 0.5

<

= [THETA]

<

= 1.

ALARM [HCH] [QCH] [SMA] [NOC]

In order to verify whether the results of the model are well-behaved, the command ALARM is introduced. The program will carry out the following checks during the computation, viz:

IHI

<

[HCH]

IQxl

<

[QCH] , IQyl

<

[QCH] .

Furthermore it will check whether the diagonal elements in the solution matrix are (in absolute sense) larger than [SMA]. This matrix is generated during the implicit computation along a line parallel to the x- or y-axis. If any of the above conditions is violated, the program will issue a message; in order to prevent waste of computer capacity, it will terminate the computation after [NOC] occurrences of such messages.

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COMPUTE [TEND]

This command starts the computation. The computation will continue until the time [TEND] is reached. The value of [TEND] is required.

The computation is based on information contained in previous commands. One can give more than one COMPUTE command in order to apply intermediate changes in e.g. boundary conditions, or in order to modify the output commands.

RECALL [TEND] 'FNAME'

Instead of performing a computation the program will reeall results from a computation carried out in a previous job; these results must have been stored by means of the command OUTPUT .. BACKUP. The first time the command RECALL is used, the filename must be given; the default filename is: RECALL. See the appendix for limitations on the filenames and on job control statements. The program will continue to read data from the file until the time [TEND] has been reached, or until the end of the file is encountered. If [TEND] is not given by the user, a very large number is assurned, so that the program will read the data to the end.

If output requests have been given before the RECALL command, the program will

carry out these output requests. In this way the command RECALL (in combination with output requests) can be used to analyse the results of a previous computation further.

The RECALL command can be given a number of times, just like the COMPUTE commando

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5.3. Commands for model definition

BIGHT GRID [MX] [MY] [SX] [SY] <

-> LEFT

This command defines the grid on which the computation is performed; for the same grid points bottom levels and (optionally) wind forces have to begiven.

Meaning of the variables:

[MX] number of grid points in x-direction [MY] number of grid points in y-direction [SX] mesh size in x-direction

[SY] mesh size in y-direction (default: [SY]=[SX])

RIGHT: coordinate system is right oriented, i.e. clockwise from positive X to positive Y-axis; LEFT has opposite meaning.

This command must be given once. It must preeede the commands PLAN ,BOTTOM, FRICTION, STORM etc.

In print and plot output the y-axis is always vertically upward; the x-axis points to the right (in LEFT orientation of the axes) or to the left (in RIGHT orientation); see also chapter 4.

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DUCHESS User Manual 31

EXCL [IX1] [IX2] [IY1] [IY2]

BOTTOM [ZLIM] READ

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With this command the user indicates which points in the grid are computational points proper, and which points must be kept outside the computation, either because they are permanently dry, or because a boundary condition holds in these points. Initially all points are permanently dry, so at least one PLAN command is necessary to indicate the computational points.

Options:

ALL: all points are computational points, except those for which ix = I, or iy=1.

No values for H will be computed in all points (ix.iy), for

which [IXl] < =ix < = [IX2]and [IYl] < =iy < =[IY2]R.estrictions: 1< = [lXI] < = [IX2] < =[MX],1 < =[IYl]

<

= [IY2]

<

=[MY]. Required: [IXI] and [IYl].

Defaults: [IX2]=[IXl], [IY2]=[IYl].

Note: this command must be preceded by: PLAN ALL or by PLAN READ.

points (ix,iy) are exc1uded in which the bottom level is above [ZLIM].

Note: the command PLAN BOTIOM must be preceded by the command BOTIOM (see later) and by PLAN ALL or PLAN READ. The status of each point must be indicated individually by a 0 or al;

0: exc1uded point, 1: computational point. The numbers must immediately follow the PLAN command, in the following format: EXCLUDE:

BOTIOM:

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e(l,l) e(2,1) e(3,1) e(1,2) e(2,2) e(3,2)

e (MX, 1) e(MX,2) e(l,MY) ••••••••••••••••• e(MX,MY)

The numbers e(i,j) must be 1 if h(i,j) is to be computed in the point, using the equation of continuity and the equation of motion, and 0 if h(i,j) is not to be computed. The number 0 and 1 are to be given adjacent to one another, so not separated by blanks or commas. A blank is interpreted as a O.

The numbers e(i,j) are printed if the command PLAN is preceded by: TEST The command PLAN must be given at least once. It can be used repeatedly, for instance in the following way:

PLAN ALL PLAN BOT 1.25

PLAN EXCLUDE 24, 16, 38

Note: the line between active and permanently dry points is assumed to be an imperrneable wall, unless another boundary condition is specified in these points.

SHOW PLAN [IX1] [IX2]

This command will visualise the computational grid on printed output.

Internal H-points, U- and V-connections are marked, and boundary points are marked with different symbols. This enables the user to verify whether the boundary points are in the right place; this is important especially if dams are present in the model. [IX1] and [IX2] indicate the limits of the region in X-direction. Due to the limited width of the printing paper in X-direction only 60 points are printed, and [IXI] and [IX2] are the integer x-coordinates of the leftmost and the rightmost gridpoints in the figure. One does not have to specify [IX1] and [IX2] if [MX]

<

=60.

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DUCHESS User Manual 33

Default values: [IXl]=l, [IX2] = Min([MX] , [IXl]+59).

The best place to use the command is after the PLAN and the boundary conditions are defined; usually short before the COMPUTE commando Qx- and Qy-connections are calculated onlyafter COMPUTE is called. If one wants to see these connections also, one should give:

COMP

o.

SHOW PLAN

CONSTANT [ZB] (REGION [IX1] [IX2] [IY1] [IY2]) BOTTOM <

OCPACK 'PROG' FILE 'FNAME' [FAC] <

-> [IDLA] [NHED] 'FORM' FORMAT < [IDFM] < -> FREE & UNFORMATTED

With this command the bottom configuration is given to the program. Initially all bottom levels are 0; the command BOTTOM must be used (if necessary a number of times) to specify the bottom used in the computation.

CONSTANT: the bottom levels are all made equal to [ZB]; if a REGION is defined, the bottom is made equal to [ZB] only in that region. Restrictions: 1<=[IXl] < = [IX2]<=[MX],<=[IYl] < = [IY2] <=[MY].

Defaults: [IXl]=l, [IX2]=[MX], [IYl]=l, [IY2] = [MY] (i.e. the whole computational region).

Note: the command BOTTOM CONST can be given a number of times to define constant bottom depths in various parts of the grid. FILE: the bottom level are read from a file on secondary storage.

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'FNAME' etc.: the values are read from dataset with filename 'FNAME'. This dataset can be either a standard Ocean Pack transfer file, or another type of file, for which the characteristics have to be specified. Default filename: 'BOTIOM'. See the appendix for limitations on the filenames to be used.

the depth or velocity values as they appear in the file, are multiplied by the factor [FAC]. For instance if the depths are given in dm, one should make [FAC]=O.I. Default: [FAC] = 1. OCPACK If the keyword OC is present, it is assumed that the file is a standard Ocean Pack transfer file, generated byanother program, named

'PROG'.

the name 'PROG' is checked against the origin as it is found in the file itself.

[FAC]

'PROG'

For non-standard files the lay-out of the data and the format must be given, at least the first time the filename is mentioned in the input.

[IDLA] prescribes the order in which the values are read (default: [IDLA] = 1)

=1: values appear line by line (on the screen: x-axis to the right, y-axis vertically upward)

(l,MYB+ 1), (2, MYB+ 1), ... (MXB+ 1,MYB+ 1) (l,MYB), (2,MYB), ... (MXB+ 1,MYB)

(1,1), (2,1), (MXB+1,1)

value for a new line of the grid should start on a new line of input. =2: order of values as with [IDLA] = 1, but now a new line in the grid must not necessarily start on a new line of input.

= 3: values appear line by line: (1,1), (2,1), (MXB+ 1,1) (1,2), (2,2), ... (MXB+ 1,2)

(l,MYB+ 1), (2, MYB+ 1), ... (MXB+ 1,MYB+ 1)

values for a new line of the grid should start on a new line of input. =4: order of values as with [IDLA] =3, but now a new line in the array must not necessarily start on a new line of input.

=5: values appear column by column: (1,1), (1,2), ... (l,MYB+ 1)

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DUCHESS User Manual

35

(2,1), (2,2), ... (2,MYB+l)

(MXB+l,I), (MXB+l,2), ... (MXB+l,MYB+l)

values for a new column of the grid should start on a new line of input. =6: order ofvalues as with [IDLA] =5, but now a new column in the grid must not necessarily start on a new line of input.

[NHED] is the number of heading lines that appear before the data. If there are more than one grids that are read from the file, it is assumed that the heading lines appear before each grid. Default value: O.

FREE Free format is default. The free format conventions in reading from a file are almost the same as the conventions for the command input; the most important differences are: 1. there are no continuation marks, reading continues until the required number of data has been entered, or until a / is encountered, 2. comment is not allowed. With free format empty fields, repetition factors, and closure of a line by a slash, can be used. UNFORMA TIED is a form ofreading without conversion. Not recommended for

ordinary use.

FORMAT means that fixed format is used. The format can be defined in one of two ways, by giving the format number [IDFM] or the format string 'FORM'.

[IDFM] The format number is interpreted as follows:

=1:Format according to BODKAR convention Format (10X, 12F5.0).i.e. first ten place are skipped; then 12 number in field of 5 places each are read .

=5: Format (16F5.0), i.e. an input line consists of 16 fields of 5 places each. Write one number per field, preferably with the decimal point.

=6: Format (12F6.0), 12 fields of 6 places each. =8: Format (lOF8.0), 10 fields of 8 places each.

'FORM' a user-specified format according to FORTRAN-77 convention, i.e. '«lOX, 12F5.0»'

Defaults: [FAC] = 1., FNAME='BOTTOM', FREE format, and [IDLA]=1. The appendix gives information on limitations of the filenames, and on job control statements to be used. Rules for ordinary Fortran input apply; i.e. continuation marks are not allowed. Simply continue on the next input line if a line is not long enough to hold all the numbers.

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DUCHESS User Manual 36

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values of the bottom are O. With free format empty fields and repetition factors can

be used.

Remark: DUCHESS uses the level of the bottom with respect to a common datum, positive in the upward direction. Therefore a positive bottom level will mean a bottom above the datum. If necessary the sign of the values read from the file can be corrected by assigning a negative value to the number [FAC].

It is important to check the correctness of the bottom data, certainly if they are used for the first time. To do this, one cao obtain a contour plot of the bottom levels by the following command:

OUTPUT INTERV = 1.ElO PLOT &

TITLE= 'BOTTOM CONTOURS,INTERV AL 5 M' & BOUND ISO BOTTOM 5.

If an read error occurs during the reading of the bottom values, the

program will print the values read. The print will also occur, if the BOTTOM

command is preceded by: TEST 120 (or a higher number). The print can be used to check the correctness of the input.

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DUCHESS User Manual 37

CONSTANT [RV] (REGION [IX1] [IX2] [IY1] [IY2]) LOGARITHM [Wl] [W2] [W3]

FRICT <

OCPACK 'PROG' FILE 'FNAME' [FAC] <

-> [IDLA] [NHED] & 'FORM'

FORMAT <

[IDFM] < -> FREE

UNFORMATTED

The friction coefficient used in DUCHESS is related to the Chezy coefficient in the following way: fr=g/C' . The initial value of the friction coefficient is O.

The options CONSTANT and FILE are defined in the same way as in the command BOTTOM. The default filename is here: 'FRIC'.

Option LOG: The Chezy coefficient C is calculated in each H-point by means of the formula: C=[Wl]*log([W2]*([W3]-Zb», where Zb is the bottom level in that point. Remark: 'log' represents the lO-logarithm. The C-values are transformed into fr-values according to: fr=g/C2•

Note that the fr-values depend on the bottom level, not on the actual depth; so the depth computed during the computation does not alter this fr-value.

If one uses the option LOG, the command FRIC must always be preceded by the command BOTTOM.

In the friction term appearing in the equation of motion, the friction coefficient is divided by the depth. So, if a certain area falls dry, the friction term will tend to infinity, which may disturb the stability of the computation. In order to prevent this, the depth used in the friction term is taken equal to [DTH], as soon as the depth drops below the value of [DTH]. [DTH] is the threshold depth. It is assigned a value by e.g.: SET DTH=0.05 . The initial value of [DTH] is 0.1.

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VISC [EV] [EVQ] [EV2] [CSLIP]

This command defines the coefficient for horizontal transfer of momentum (eddy viscosity). The total eddy viscosity consists of a constant part, and a part depending on velocity and depth:

E = [EV]

+

[EVQ]

*

IQI

+

[EV2]

*

IQI2

[CSLIP] controls the boundary condition along boundaries for which the current normal to the boundary is given. [CSLIP] =0. means free slip, [CSLIP] = 1. no slip. Any real number in between is allowed.

Init: [EV] =0. , [EVQ] =0. , [EV2] =0. , [CSLIP] =0.

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DUCHESS User Manual 39

VELOCITY STEADY [WFX] [WFY]

UNIFORM < > <

STRESS UNSTEADY 'FNAME'

STORM <

PRESSURE

[INTERV] < VELOCITY > [SC] & STRESS OCPACK 'PROG' 'FNAME' < 'FORM' FORMAT < [IDFM] -> [IDLA] [NHED] < -> FREE

UNFORMATTED

With this command the external forces due to a storm field can be given. In the case UNIFORM STEADY [WFX] and [WFY] are either the x- and y- components of the wind velocity at 10 m height (option VEL), or the components of the shear force that the wind exerts on the water body, per unit of surface and divided by the density of the water (option STR). If wind veloeities are given the wind shear stresses must be calculated from them. The command STRESS (see below) can be used to give the values of the parameters appearing in the wind stress formula. Init: [WFX] = [WFY] =0.

In the case UNIFORM UNSTEADY the values of the time, and the values of [WFX] and [WFY] are read from the dataset with filename 'FNAME'. For intermediate times the values are interpolated linearly. The contents of the file is

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40

of the following form: Timel, Wfxl, Wfyl Time2, Wfx2, Wfy2

Note: time must be in seconds

In the case FILE the non-uniform values for the whole field are read from a file. In this case the command is analogous to the BOTIOM command (see there). The default filename is: 'STORM'. Now also a pressure field can be given. The pressure values should be divided by the density of the water and by the gravitational acceleration; in other words it should be given in terms of water column, i.e. in m. If the keyword PRESSURE is given, the program will read pressure data from the file. If the keyword VEL is present, it will read wind velocities; in case of the keyword STRESS shear stress values (divided by the density of the water). In both cases the values read from the dataset are multiplied by [SC]; for pressure and wind stress or velocity a different factor can be introduced.

If the wind stresses or veloeities are read from a dataset, first all x-components are read, and then all y-components. The values are read every time after the interval [INTERV]. If [INTERV] is not given by the user, the program assumes that the values have to be left unchanged during the computation; thus they will be read only once. Between two readings the pressures and the shear values are kept constant.

Note: for [IDLA] etc. see command BOTTOM.

STRESS [CWF]

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One may combine variabIe pressure and uniform wind stress field, as in: STORM VARIABLE PRESSURE

STORM UNIFORM UNS ...

If both air pressure and wind stress are given, they should be on two different files.

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DUCHESS User Manual 41

w

=

[CWF]

lwl.a

where Wis the wind shear stress (divided by the density of the water) and wis the wind velocity at 10 m height. The factor [CWF] is dimensionless; its default value is: 0.0012

NOCQ

In the equation of motion the convective acceleration terms uc3u/

ax

etc. are neglected, if this command is issued.

:CONST [ZB](REG [IX1] [IX2] [IY1] [IY2]) INIT< QX > <

OCPACK 'PROG' FILE 'FNAME'[FAC] <

-> [IDLA] [NHED] & 'FORM'

FORMAT <

[IDFM] < -> FREE

UNFORMATTED

Reads the initial values of the water level or the current components according to the same rules described with the command BOTT. This time the default filename is: 'INIT'.

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DUCHESS User Manual

level. Therefore it is advised to define the bottom levels before giving the initial values of H.

-> I

SHOW ARRAY [JA] < BEAL > ~IN

Most of the data used internally in DUCHESS is stored in so-called dynamic arrays. With this command the contents of the dynamic array with seq. no. [JA] is printed, either in the form of integer numbers (keyword I, default), or in the form of real numbers (R), 'or in hexadecimal form in order to display binary information (B). This command is mainly for debugging purposes; it is usually only useful if one has access to the program documentation.

[JA] contents of array 1 status of grid points

2 water levels

3 x-component of current 4 y-component of current

5 bottom levels

17 boundary conditions

19 directory of output requests

20 output requests

SHOW LOCATIONS [LSC] 'TITLE'

This command serves to visualize part of the user's input. A figure will be plotted,

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DUCHESS User Manual 43

which shows the locations of the output points, defined in OUTPUT TABLE, the circumference ofthe plot regions defined in OUTPUT PLOT and OUTPUT VIEW,

the model boundary as defined by the PLAN and BOUNDARY commands.

[LSC] is the length scale of the figure; its default value is such that the figure will fit on A4-size paper.

The 'TITLE' will be plotted under the figure. Default: blank.

Notice: SHOW LOC should be given before the output commands. It remains in

effect until one of the commands COMPUTE, RECALL or STOP is encountered.

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DUCHESS User Manual 5.4. Boundar.y conditions

BOUNDARY < > &

-> CONSTANT [F] < [IX] [IY] > <

HARMONIC

< [IX] [IY] < > >

->

[MEAN] < [PER] [AMPL] [PRASE]

>l

This command defines two types of boundary conditions, either for the water level (H), for the x-component of the current (QX), or for the y-component of the current (QY).

The boundary conditions involving the reading from a file are described further down. Two types of boundary conditions are described here:

CONSTANT: [F] is the value in the points ([IX], [IY]).

HARMONIC: the behaviour is given in the form of a sum of a mean value and a set of sine functions, each eharaeterized by [PER], the period, [AMPL], the amplitude of the sine function, and [PHASE] is the phase of the harmonie component in radians:

f(t)

=

[MEAN]

+

Sum ( [AMPL]j * Cos(2*pi*Time/[pER]j - [PHASE]j)

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DUCHESS User Manual 45 The number [IX] etc. must appear on a new line (only in the case HAR). Ifthe keyword ID appears after a point, the value for this point will be copied from the previous boundary point; so ID may not be used for the first point in a BOUNDARY commando

If two consecutive points are on the same line parallel to the x- or y-axis, or on the same diagonal (line with slope equal to l:J.y/ I:J.Xor -l:J.y/ I:J.x),all points between the two are assumed also to be boundary points; the value in those points is found by means of a linear interpolation between the corner points.

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BOUNDARY NEST 'FNAME' ([ PER] )

There are two options in the BOUNDARY command for boundary values which are read from a file. The option NEST is intended for a nested model.

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The values of H, Qx and Qy all around the grid are read from the file with filename 'FNAME'. The data on that file must have been written in a previous computation using the command OUTPUT .. NEST.

If this dataset is exhausted, an error message occurs, unless a positive period [PER] is given; in this case the boundary condition is assumed to be periodic, and the reading starts again at beginning of the file.

A second effect of this option is that on the whole boundary a weakly reflecting condition (as described in the command NREFL, see further down) is assumed.

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DUCHESS User Manual

BOUNDARY FILE 'FNAME' [PER] &

< < > < [IX] [IY] (ID) > >

The option FILE in the BOUNDARY command is intended to read boundary values from a file on secondary storage.

The values for the points ([IX], [IY]) are read from the file with filename 'FNAME' . If this file is exhausted, an error message occurs, unless a positive period [PER] is given; in this case the boundary condition is assumed to be periodic. If the keyword ID is typed after the coordinates of a point, its values will not be read from the file; the program will assume its value to be identical with the value in the preceding point.

Otherwise boundary values for water level or current will be read from the file 'FNAME' in the same order as specified in this commando The contents of the file must be of the following form:

Time, VI, V2, V3 etc. Time, VI, V2, V3 etc. etc.

A file of this form is generated by the command OUTPUT TABLE. For Job Control on the file with name 'FNAME' see the appendix.

The time for which the values on the file hold, are read from the file together with the values themselves. Values for intermediate times are calculated by linear interpolation.

Note: Each BOUNDARY FILE .. command must refer to a separate file. Example:

BOUNDARY FILE 'BOUND' H 1,1,1,7 & QY 1,9,1,11,1,13 ID

In this case the values of time, H(l,l), H(1,7), Qy(1,9) and Qy(l,11)

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DUCHESS User Manual 47 must be present on file 'BOUND'.

QX [IX] [IYl] [IY2] NREFL <

QX [IY] [IXl] [IX2]

This command defines a weakly reflecting boundary condition in either Qx or Qy. Waves approaching such a boundary from the interior of the computational region will be (partially) absorbed.

The boundary condition used here is a linearized version of the exact characteristic relationship, which reads:

u

+ 2 Jg (H-Z)

=

Uo + 2Jg (Ho - Z)

Here Uo and Ho are the values outside the model, representing the waves coming from outside. The linearization is allowed if

I

H-Ho

I

< <

H-Z.

In the model Qx is calculated by the following formula:

in all Qx-points (ix,iy) for which ix=[IX] and [IYl]

<

= iy

<

= [IY2]

In the above formula Hl and H2 are the water levels at both sides of the Qx-point;

Hl =H(ix,iy) ' H2=H(ix+l,iy). Qx' represents the term with Uo in the characteristic relationship. lts value is introduced in the model by assigning a value for Qx to the same point bya BOUNDARY QX.. commando If this command is absent, Qx' is assumed to be zero.

One of these H-points must be an intemal point, the other a boundary point (a point with given water level). The program will issue a

waming if this condition is not fulfilled.

Hl and H2 are taken on the new time level; H-Z, the local depth, is taken on the

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DUCHESS User Manual 48 The boundary values (values of Ho and Uo or Qx') serve to represent the waves coming from outside into the model; often it is assumed that there is no such wave, so then levels in the boundary points are constant.

Usually [IX] will be I or [MX]-l, with water level given for respectively I or [MX]. Hence the following restrictions:

[IX]

>

=I , and [IX]

<

[MX] . furthermore: [IY1]

>

1 , and [IY2]

>

[IY1] , and [IY2]

<

=[MY] . For Qy the situation is analogous.

Example: BOUNDARY H CONST 0.5,5,31,17,31 BOUNDARY QY CONST -2.,5,30,17,30 NREFL QY 30,5,17

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DUCHESS User Manual

49

5.5. Output requests.

The DUCHESS system has several output facilities:

1. in numerical form to the printer for the information of the user .

2. in numerical form to secondary storage to use as input to other computer programs.

3. in graphical form to the plotter.

Every output request has the following format:

OUTPUT {NRQ] [BEGIN] [INTERV] 'FNAME' &

output-specification [NRQ]

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is the output request number, used as identification of the request. DUCHESS assigns numbers 1, 2, 3 etc. to each subsequent output request. By reference to this number the user can modify or cancel the output request. Default value of [NRQ]: one higher than the previous output request .

One is advised to either specify the numbers for all requests, or for none.

[BEGIN] begin time of the output. Default value: equal to the value of the time at the moment that the output request is read. So by default the requested output starts immediately in the next computation; the user can delay the start of the output by assigning a proper value to

[BEGIN].

[INTERV] time interval between outputs, in seconds (real number). Default: [INTERV] =-1.; then output will take place at every time step. The value

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DUCHESS User Manual

of [INTERV] is required in the case of plots.

'FNAME' the filename of the file to which the output is directed.

Whether the filename must be present, is found in the description of the output specifications below.

output-specification specifies the output requested by the user. The possibilities are described below. If [NRQ] is the number of an existin output request, and if there is no need of modifying the specification, the output specification may be left out. The following output specifications are available:

BLOCK block table of variabie in certain region

BACKUP copies entire state of the model to sec. storage

TABLE table of certain variabie in certain point or set of points PLOT

NEST ESTRA

plots velocity or current vectors, contour lines, shorelines etc. to prepare boundary values for a nested computation.

to prepare flow data to be used for a transport computation by the program ESTRA; see the user documentation of that program.

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DUCHESS User Manual 51

OUTPUT &

DISK

BLoeK < > [IX1] [IX2] [IY1] [IY2] [DIST] &

PAPER DEP .H QX & < < QX > [UNIT] > VX VY

This command produces a block table. The output can either be made on paper, file or standard transfer file for further processing.

The block for which the values are given is defined by the grid points [IXI], [IX2] etc. The rules are the same as in the command BOITOM. Default values, assumed by the program, are: [IXl] = 1, [IX2]=MX, [IYl]=1 and [IY2]=MY.

In both the x- and y-direction the points for which values are given, are [DIST] meshes apart. [DIST] is an integer, default 1.

The block print can be made for several different variables: DEP the depth

H the waterlevel

QX the local discharge in x-direction QY the local discharge in y-direction

VX the x-component of the current velocity VY the y-component of the current velocity

The quantities are multiplied by [UNIT], the unit used for the print. If H is in meters, and one wants a print giving H in cm., [UNIT] has to be 0.01. The default

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