MIKE 21 FLOW MODEL FM

Transport Module

User Guide

MIKE by DHI 2014

2
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Printing History
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3
4 MIKE 21 Flow Model FM
CONTENTS

5
1 ABOUT THIS GUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Assumed User Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 General Editor Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Navigation tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Editor window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Validation window . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Online Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Application Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Funningsfjord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.1 Purpose of the example . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.2 Defining the problem . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2.3 Presenting and evaluating the results . . . . . . . . . . . . . . . 20
4.2.4 List of data and specification files . . . . . . . . . . . . . . . . . . 22
5 TRANSPORT MODULE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.1 Component Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Solution Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.3 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3.1 Horizontal dispersion . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3.2 Recommended values . . . . . . . . . . . . . . . . . . . . . . . . 25
5.4 Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.4.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.5 Precipitation-Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.5.1 Recommended values . . . . . . . . . . . . . . . . . . . . . . . . 28
5.6 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.6.1 Source specification . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.6.2 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.7 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.8 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.8.1 Boundary specification . . . . . . . . . . . . . . . . . . . . . . . . 31
5.9 Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.9.1 Output specification . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.9.2 Output items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6 MIKE 21 Flow Model FM

6 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7
8 MIKE 21 Flow Model FM
Purpose

1 ABOUT THIS GUIDE

1.1 Purpose
The main purpose of this User Guide is to enable you to use, MIKE 21
Flow Model FM, Transport Module, for applications of transport phenom-
ena in lakes, estuaries, bays, coastal areas and seas.

The User Guide is complemented by the Online Help.

1.2 Assumed User Background

Although the Transport Module has been designed carefully with empha-
sis on a logical and user-friendly interface, and although the User Guide
and Online Help contains modelling procedures and a large amount of ref-
erence material, common sense is always needed in any practical applica-
tion.

In this case, “common sense” means a background in coastal hydraulics

and oceanography, which is sufficient for you to be able to check whether
the results are reasonable or not. This User Guide is not intended as a sub-
stitute for a basic knowledge of the area in which you are working: Math-
ematical modelling of transport phenomena.

It is assumed that you are familiar with the basic elements of MIKE Zero:
File types and file editors, the Plot Composer, the MIKE Zero Toolbox,
the Data Viewer and the Mesh Generator. The documentation for these can
be found by the MIKE Zero Documentation Index.

1.3 General Editor Layout

The MIKE Zero setup editor consists of three separate panes.

1.3.1 Navigation tree

To the left there is a navigation tree showing the structure of the model
setup file, and it is used to navigate through the separate sections of the
file. By selecting an item in this tree, the corresponding editor is shown in
the central pane of the setup editor.

9
 About This Guide

1.3.2 Editor window

The editor for the selected section is shown in the central pane. The con-
tent of this editor is specific for the selected section, and might contain
several property pages.

For sections containing spatial data - e.g. sources, boundaries and output -
a geographic view showing the location of the relevant items will be avail-
able. The current navigation mode is selected in the bottom of this view, it
can be “zoom in”, “zoom out” or “recenter”. A context menu is available
from which the user can select to show the bathymetry or the mesh, to
show the optional GIS background layer and to show the legend. From
this context menu it is also possible to navigate to the previous and next
zoom extent and to zoom to full extent. If the context menu is opened on
an item - e.g. a source - it is also possible to jump to the item’s editor.

Further options may be available in the context menu depending on the

section being edited.

1.3.3 Validation window

The bottom pane of the editor shows possible validation errors, and it is
dynamically updated to reflect the current status of the setup specifica-
tions.

By double-clicking on an error in this window, the editor in which this

error occurs will be selected.

1.4 Online Help

The Online Help can be activated in several ways, depending on the user's
requirement:

z F1-key seeking help on a specific activated dialog:

To access the help associated with a specific dialog page, press the F1-
key on the keyboard after opening the editor and activating the specific
property page. See Figure 1.1.

z Open the Online Help system for browsing manually after a spe-
cific help page:
Open the Online Help system by selecting “Help Topics” in the main
menu bar.

10 MIKE 21 Flow Model FM

Online Help

Figure 1.1 Online Help system for MIKE 21 Flow Model FM

11
 About This Guide

12 MIKE 21 Flow Model FM

2 INTRODUCTION
MIKE 21 Flow Model FM is a new modelling system based on a flexible
mesh approach. The modelling system has been developed for applica-
tions within oceanographic, coastal and estuarine environments.

Figure 2.1 Mariager Estuary, Denmark. Computation mesh used in MIKE 21

Flow Model FM for studying flow circulation due to combined tide,
wind and run-off.

MIKE 21 Flow Model FM is composed of following modules:

z Hydrodynamic Module
z Transport Module
z ECO Lab / Oil Spill Module
z Mud Transport Module
z Particle Tracking Module
z Sand Transport Module

The Hydrodynamic Module is the basic computational component of the

entire MIKE 21 Flow Model FM modelling system providing the hydro-
dynamic basis for the other modules.

13
 Introduction

2.1 Application Areas

The application areas are generally problems where flow and transport
phenomena are important with emphasis on coastal and marine applica-
tions, where the flexibility inherited in the unstructured meshes can be uti-
lized.

14 MIKE 21 Flow Model FM

3 GETTING STARTED
The hydrodynamic basis for the Transport Module must be calculated
using the Hydrodynamic Module of the MIKE 21 Flow Model FM model-
ling system.

If you are not familiar with setting up a hydrodynamic model you should
refer to the comprehensive step-by-step training guide covering MIKE 21
Flow Model FM. This training guide (in PDF-format) is provided with the
DHI Software installation and can be found in the installation folder at

.\MIKE Zero\Manuals\MIKE_21\FlowModel_FM\HD\
MIKE_FM_HD_Step_By_Step.pdf.

15
 Getting Started

16 MIKE 21 Flow Model FM

General

4 EXAMPLES

4.1 General
One of the best ways of learning how to use a modelling system such as
MIKE 21 Flow Model FM is through practice. Therefore an example is
included which you can go through yourself and which you can modify, if
you like, in order to see what happens if one or other parameter is
changed.

The specification files for the example is included with the installation of
MIKEZero. A directory is provided for the example. The directory name
are as follows (default installation):

z Funningsfjord example:
.\Examples\MIKE_21\FlowModel_FM\TR\Funningsfjord

4.2 Funningsfjord
4.2.1 Purpose of the example
Funningsfjord is a small fjord situated at the NE corner of the Faroe
Islands. The computational domain and bathymetry is shown in
Figure 4.1. Here is shown a typical example of calculation of the fjord cir-
culation. The exhange of water between the fjord and the ocean generates
a continuous dilution of the river water that enters the southernmost part
of the fjord. One measure of the water exchange is the residence time,
which for a well mixed water body can be given as T=V/Q. In the real
world the picture is more complicated as the exchange depends on tides,
wind circulations etc. The residence time is here estimated as the age (see
Delhez et. at. (2003)). It should be noted that artificial forcings has been
used to highlight the aspects of the test.

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 Examples

Figure 4.1 Computational domain and bathymetry.

4.2.2 Defining the problem

The main condition defining the hydrodynamic problem is:

z An unstructured mesh with 1802 elements and 1033 nodes is used. The
mesh is shown in Figure 4.2.
z The starting time of the simulation is 2/8/1985 03:00:00. The time step
of 1 seconds is selected and the duration time of the simulation is 10
days (864000 time steps).
z The horizontal eddy viscosity type has been chosen to Smagorinsky
type and a constant value of 0.28 m1/3/s is applied for the Smagorinsky
coefficient.
z The bed resistance type has been chosen to Manning number and a
constant value of 32 m1/3/s is applied.
z The wind is specified as varying in time and constant in domain. A
data file containing timeseries of measured wind speeds and directions
are given. The length of soft start interval (warm-up period) for the
wind has been chosen to 2 hours (7200 seconds) to avoid chock effects.

18 MIKE 21 Flow Model FM

Funningsfjord

z A point source discharging 250 m3/s is applied at the southernmost

point in the computational domain.
z Tidal elevations, consisting of a M2 component with amplitude 1.0 m,
are applied at the open boundary along the NE section.

The main condition defining the hydrodynamic problem is:

z Transport calculations are performed for two components: One con-

servative and one decaying.
z The decaying component is decaying with a constant decay constant
k =10-5.
z The source concentration of the two components are both set to 1.
z The initial conditions and boundary conditions for both components at
constant values of 0.

Figure 4.2 Computational mesh.

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 Examples

4.2.3 Presenting and evaluating the results

A contour plot of the concentration for the two components is show in
Figure 4.3. The age is calculated using two tracers in the river: one con-
servative and one decaying with decay constant k. The age can then be
estimated as T = -k-1 ln(CDECAY /CCONSERVATIVE).

In Figure 4.4 is shown the development of the age in the four stations indi-
cated on Figure 4.1.

20 MIKE 21 Flow Model FM

Funningsfjord

Figure 4.3 Contour plot of the concentration for the conservative component
(top) and the decaying component (bottom).

21
 Examples

Figure 4.4 Age at four stations. Red line: point 1, black line: point 2, blue line:
point 3 and green line: point 4. The locations for the points are
shown on Figure 4.1.

4.2.4 List of data and specification files

The following data files (included in the \TR\Funningsfjord folder) are
supplied with MIKE 21 Flow Model HD FM:

File name: Funningsfjord.mesh

Description: Mesh file including the mesh and bathymetry

File name: Funningsfjord.m21fm

Description: MIKE 21 Flow Model FM specification file

File name: Wind.dfs0

Description: Wind speed and direction

File name: Tide.dfs0

Description: Tidal elevations at open sea boundary

22 MIKE 21 Flow Model FM

Component Specification

5 TRANSPORT MODULE
The transport module calculates the resulting transport of materials based
on the flow conditions found in the hydrodynamic calculations.

5.1 Component Specification

On this dialog you specify the number of components (or species) and the
name of the components that should be solved for. Each component
defines a separate transport equation.

5.2 Solution Technique

The simulation time and accuracy can be controlled by specifying the
order of the numerical schemes which are used in the numerical calcula-
tions. Both the scheme for time integration and for space discretization
can be specified. You can select either a lower order scheme (first order)
or a higher order scheme. The lower order scheme is faster, but less accu-
rate. For more details on the numerical solution techniques, see the Scien-
tific documentation.

The time integration of the transport (advection-dispersion) equations is

performed using an explicit scheme. Due to the stability restriction using
an explicit scheme the time step interval must be selected so that the CFL
number is less than 1. A variable time step interval is used in the calcula-
tion and it is determined so that the CFL number is less than a critical CFL
number in all computational nodes. To control the time step it is also pos-
sible for the user to specify a minimum time step and a maximum time
step. The time step interval for the transport equations is synchronized to
match the overall time step specified on the Time dialog.

The minimum and maximum time step interval and the critical CFL
number is specified in the Solution Technique dialog in the HYDRODY-
NAMIC MODULE.

5.2.1 Remarks and hints

If the important processes are dominated by convection (flow), then
higher order space discretization should be chosen. If they are dominated
by diffusion, the lower order space discretization can be sufficiently accu-
rate. In general, the time integration method and space discretization
method should be chosen alike.

23
 TRANSPORT MODULE

Choosing the higher order scheme for time integration will increase the
computing time by a factor of 2 compared to the lower order scheme.
Choosing the higher order scheme for space discretization will increase
the computing time by a factor of 1½ to 2. Choosing both as higher order
will increase the computing time by a factor of 3-4. However, the higher
order scheme will in general produce results that are significantly more
accurate than the lower order scheme.

The default value for the critical CFL number is 1, which should secure
stability. However, the calculation of the CFL number is only an estimate.
Hence, stability problems can occur using this value. In these cases you
can reduce the critical CFL number. It must be in the range from 0 to 1.
Alternatively, you can reduce the maximum time step interval. Note, that
setting the minimum and maximum time step interval equal to the overall
time step interval specified on the Time dialog, the time integration will be
performed with constant time step. In this case the time step interval
should be selected so the the CFL number is smaller than 1.

The total number of time steps in the calculation and the maximum and
minimum time interval during the calculation are printed in the log-file for
the simulation. The CFL number can be saved in an output file.

The higher order scheme can exhibit under and over shoots in regions with
steep gradients. Hence, when the higher order scheme is used in combina-
tion with a limitation on the minimum and maximum value of the concen-
tration mass conservation cannot be guarenteed.

5.3 Dispersion
In 2D models the dispersion usually describes transport due to non-
resolved processes. In coastal areas it can be transport due to non-resolved
turbulence or eddies. Especially in the horizontal directions the effects of
non-resolved processes can be significant, in which case the dispersion
coefficient formally should depend on the resolution.

The dispersion is specified individually for each component.

5.3.1 Horizontal dispersion

The horizontal dispersion can be formulated in three different ways

z No dispersion
z Dispersion coefficient formulation
z Scaled eddy viscosity formulation

24 MIKE 21 Flow Model FM

Dispersion

Selecting the dispersion coefficient formulation you must specify the dis-
persion coefficient.

Using the scaled eddy viscosity formulation the dispersion coefficient is

calculated as the eddy viscosity used in solution of the flow equations
multiplied by at scaling factor. For specification of the eddy viscosity see
section 6.5 Eddy Viscosity in the manual for the Hydrodynamic module.

Note: There is no dispersion across open boundaries as the gradient of the

concentration here is assumed to be zero.

Data
Selecting Dispersion coefficient option the format of the dispersion coeff-
icent can be specified as

z Constant (in both time and domain)

z Varying in domain

For the case with dispersion coefficent varying in domain you have to pre-
pare a data file containing the dispersion coefficient before you set up the
hydrodynamic simulation. The file must be a 2D unstructured data file
(dfsu) or a 2D grid file (dfs2). The area in the data file must cover the
model area. If a dfsu-file is used piecewice constant interpolation is used
to map the data. If a dfs2-file is used bilinear interpolation is used to map
the data.

Selecting Scaled eddy viscosity option the format of the scaling factor can
be specified as

z Constant
z Varying in domain

For the case with values varying in domain you have to prepare a data file
containing the scaling factor before you set up the hydrodynamic simula-
tion. The file must be a 2D unstructured data file (dfsu) or a 2D data grid
file (dfs2). The area in the data file must cover the model area. If a dfsu-
file is used piecewice constant interpolation is used to map the data. If a
dfs2-file is used bilinear interpolation is used to map the data.

5.3.2 Recommended values

When more sophisticated eddy viscosity models are used, as the Sma-
gorinsky or k-ε models, the scaled eddy formulation should be used.

25
 TRANSPORT MODULE

The scaling factor can be estimated by 1/σT, where σT is the Prandtl

number. The default value here for the Prandtl number is 0.9, correspond-
ing to a scaling factor of 1.1.

The dispersion coefficient is usually one of the key calibration parameters

for the Transport Module. It is therefore difficult to device generally appli-
cable values for the dispersion coefficient. However, using Reynolds anal-
ogy, the dispersion coefficient can be written as the product of a length
scale and a velocity scale. In shallow waters the length scale can often be
taken as the water depth, while the velocity scale can be given as a typical
current speed.

Values in the order of 1 are usually recommended for the scaling factor.
For more information, see (Rodi, 1980).

5.4 Decay
Here the components which decay linearly in time can be defined. Many
processes can be approximated by a linear decay, such as die-off of E. Coli
due to exposure to light, decay of the activity of radioactive substances or
estimating the age of water bodies.

Linear decay of a component is generally described by

∂c
----- = – kc (5.1)
∂t

where c is the specific concentration and k is the decay constant. In the

model the decay term is added to the general transport equation.

The decay is specified individually for each component.

Data
The format of the decay factor can be specified as

z Constant (in time)

z Varying in time

For the case with time varying decay factors you have to prepare a data
file containing the decay factors. The data file must be a time series file
(dfs0). The data must cover the complete simulation period. The time step
of the input data file does not, however, have to be the same as the time

26 MIKE 21 Flow Model FM

Precipitation-Evaporation

step of the hydrodynamic simulation. A linear interpolation will be

applied if the time steps differ.

5.4.1 Remarks and hints

The decay may affect the stability of the numerical solution, in a way sim-
ilar to the advection or diffusion terms. If the decay represent a very rapid
process such that the product k∆t>1 the decay term may be the source of
instability or at least occurrence of negative concentrations. A solution is
then to reduce the time step.

5.5 Precipitation-Evaporation
If your simulation include precipitation and/or evaporation, you need to
specify the concentration of each component in the precipitated and evap-
orated water mass. The precipitation and evaporation can be included in
two ways

z Ambient concentration
The concentration of the precipitated/evaporated water mass is set
equal to the concentration of the ambient sea water.
z Specified concentration
The concentration of the precipitated/evaporated water mass is speci-
fied explictly.

If you have chosen the net precipitation option in the Precipitation-Evapo-

ration dialog in the HYDRODYNAMIC MODULE, the precipitation con-
centration will be used when the specified net-precipation is positive.
When the net-precipitation is negative, the evaporation concentration is
used.

The precipitation-evaporation is specified individually for each compo-

nent.

Data
Selecting the specified concentration option the format of the concentra-
tion (in component unit) can be specified as

z Constant (in both time and domain)

z Varrying in time and constant in domain
z Varying in both time and domain

27
 TRANSPORT MODULE

For the case with concentration varying in time but constant in domain
you have to prepare a data file containing the concentration (in component
unit) before you set up the hydrodynamic simulation. The data file must be
a time series file (dfs0). The data must cover the complete simulation
period. The time step of the input data file does not, however, have to be
the same as the time step of the hydrodynamic simulation. A linear inter-
polation will be applied if the time steps differ.

For the case with concentration varying both in time and domain you have
to prepare a data file containing the concentration (in component units)
before you set up the hydrodynamic simulation. The file must be a 2D
unstructured data file (dfsu) or a 2D grid data file (dfs2). The area in the
data file must cover the model area. If a dfsu-file is used piecewice con-
stant interpolation is used to map the data. If a dfs2-file is used bilinear
interpolation is used to map the data. The data must cover the complete
simulation period. The time step of the input data file does not, however,
have to be the same as the time step of the hydrodynamic simulation. A
linear interpolation will be applied if the time steps differ.

Soft start interval

You can specify a soft start interval during which the precipitation/evapo-
ration concentration is increased linearly from 0 to the specified values of
the precipitation/evaporation concentration. By default the soft start inter-
val is zero (no soft start).

5.5.1 Recommended values

Usually it is most sensible to set the concentration of the evaporated water
mass to zero, in which case the component is conserved in the water.

5.6 Sources
Point sources of dissolved components are important in many applications
as e.g. release of nutrients from rivers, intakes and outlets from cooling
water or desalination plants.

In the Transport Module the source concentrations of each component in

every sources point can be specified. The number of sources, their generic
names, location and discharges magnitude are specified in the Sources
dialog in the HYDRODYNAMIC MODULE.

Depending on the choice of property page you can see a geographic view
or a list view of the sources.

28 MIKE 21 Flow Model FM

Sources

The source concentrations are specified individually for each source and
each component. From the list view you can go to the dialog for specifica-
tion by clicking on the “Go to..” button.

5.6.1 Source specification

The type of sources can be specified in two ways

z Specified concentration
z Excess concentration

The source flux is calculated as the product of Qsource * Csource , where

Qsource is the magnitude of the source and Csource is the component concen-
tration of the source. The magnitude of the source is specified in the
Sources dialog in the HYDRODYNAMIC MODULE.

Selecting the specified concentration option the source concentration is

the specified concentration if the magnitude of the source is positive
(water is discharge into the ambient water). The source concentration is
the concentration at the source point if the magnitude of the source is neg-
ative (water is discharge out the ambient water). This option is pertinent to
e.g. river outlets or other sources where the concentration is independent
of the surrounding water.

When selecting the excess concentration option, the source concentration

is the sum of the excess concentration and concentration at a point in the
model if the magnitude of the source is positive (water is discharge into
the ambient water). If it is an isolated source, the point is the location of
the source. If it is a connected source, the point is the location where water
is discharged out of the water. The source concentration is the concentra-
tion at the source point if the magnitude of the source is negative (water is
discharge out the ambient water). This type can be used to describe e.g. a
heat exchange or other processes where the temperature (heat) or salinity
is added to the water by a diffusion process.

Data
The format of the source information can be specified as

z Constant (in time)

z Varying in time

For the case with source concentration varying in time you have to prepare
a data file containing the concentration (in concentration units) of the
source before you set up the hydrodynamic simulation. The data file must
be a time series file (dfs0). The data must cover the complete simulation

29
 TRANSPORT MODULE

period. The time step of the input data file does not, however, have to be
the same as the time step of the hydrodynamic simulation. A linear inter-
polation will be applied if the time steps differ.

5.6.2 Remarks and hints

Point sources are entered into elements, such that the inflowing mass of
the component is initially distributed over the element where the source
resides. Therefore the concentration seen in the results from the simulation
usually is lower than the source concentration.

5.7 Initial Conditions

The initial conditions are the spatial distribution of the component concen-
tration throughout the computational domain at the beginning of the simu-
lation. Initial conditions must always be provided. The initial conditions
can be the result from a previous simulation in which case the initial con-
ditions effectively act as a hot start of the concentration field for each
component.

The initial conditions are specified individually for each component.

Data
The format of the initial concentration (in component unit) for each com-
ponent can be specified as

z Constant (in domain)

z Varying in domain

For the case with varying in domain you have to prepare a data file con-
taining the concentration (in component unit) before you set up the hydro-
dynamic simulation. The file must be a 2D unstructured data file (dfsu) or
a 2D grid data file (dfs2). The area in the data file must cover the model
area. If a dfsu-file is used piecewice constant interpolation is used to map
the data. If a dfs2-file is used bilinear interpolation is used to map the data.
In case the input data file contains a single time step, this field is used. In
case the file contains several time steps, e.g. from the results of a previous
simulation, the actual starting time of the simulation is used to interpolate
the field in time. Therefore the starting time must be between the start and
end time of the file.

30 MIKE 21 Flow Model FM

Boundary Conditions

5.8 Boundary Conditions

Initially, the set-up editor scans the mesh file for boundary codes (sec-
tions), displays the recognized codes and suggest a default name for each
of them.You can re-name these names to more meningful names in the
Domain dialog (see Boundary names).

Depending on the choice of property page you can get a geographic view
or a list view of the boundaries.

The specification of the individual boundary information for each code

(section) and each component is made subsequently. From the list view
you can go to the dialog for specification by clicking the “Go to..” button.

5.8.1 Boundary specification

You can choose between the following three boundary types

z Land
z Specified values (Dirichlet boundary condition)
z Zero gradient (Neumann boundary condition)

Data
If specified values (Dirichlet boundary condition) is selected the compo-
nent concentration at the boundary (in component unit) can be specified in
one of three ways

z Constant (in time and along boundary)

z Varying in time and constant along boundary
z Varying in time and along boundary

For the case with boundary data varying in time but constant along the
boundary you have to prepare a data file containing the component con-
centration (in component unit) before you set up the hydrodynamic simu-
lation. The data file must be a time series file (dfs0). The data must cover
the complete simulation period. The time step of the input data file does
not, however, have to be the same as the time step of the hydrodynamic
simulation. You can choose between different types of time interpolation.

For the case with boundary data varying both in time and along the bound-
ary you have to prepare a data file containing the component concentra-
tion (in component unit) before you set up the hydrodynamic simulation.
The data file must be a profile file (dfs1). The data must cover the com-
plete simulation period. The time step of the input data file does not, how-

31
 TRANSPORT MODULE

ever, have to be the same as the time step of the hydrodynamic simulation.
You can choose between different types of time interpolation.

Interpolation type
For the two cases with values varying in time two types of time interpola-
tion can be selected:

z Linear
z Piecewise cubic

In the case with values varying along the boundary two methods of map-
ping from the input data file to the boundary section are available:

z Normal
z Reverse order.

Using normal interpolation the first and last point of the line are mapped
to the first and the last node along the boundary section and the intermedi-
ate boundary values are found by linear interpolation. By using reverse
order interpolation the last and first point of the line are mapped to the first
and the last node along the boundary section and the intermediate bound-
ary values are found by linear interpolation.

Soft start interval

You can specify a soft start interval (in sec) during which boundary values
are increased from a specified reference value to the specified boundary
value in order to avoid shock waves being generated in the model. The
increase can either be linear or follow a sinusoidal curve.

5.9 Outputs
Standard data files with computed results from the simulation can be spec-
ified here. Because result files tend to become large, it is normally not
possible to save the computed discrete data in the whole area and at all
time steps. In practice, sub areas and subsets must be selected.

In the main Outputs dialog you can add a new output file by clicking on
the "New output" button. By selecting a file in the Output list and clicking
on the "Delete output" you can remove this file. For each output file you
can specify the name (title) of the file and whether the output file should
be included or not. The specification of the individual output files is made
subsequently. You can go to the dialog for specification by clicking on the
"Go to .." button. Finally, you can view the results using the relevant

32 MIKE 21 Flow Model FM

Outputs

MIKE Zero viewing/editing tool by clicking on the "View" button during

and after the simulation.

5.9.1 Output specification

For each selected output file the field type, the output format, the treat-
ment of flood and dry, the output file (name and location) and time step
must be specified. Depending on the output format the geographical
extend of the output data must also be specified.

Field type
For a 2D simulation, 2D field parameters can be selected. The mass
budget for a domain and the discharge through a cross section can also be
selected.

Output format
The possible choice of output format depends on the specified field type.

For 2D field variables the following formats can be selected:

z Point series. Selected field data in geographical defined points.

z Lines series. Selected field data along geographical defined lines.
z Area series. Selected field data in geographical defined areas.

If mass budget is selected for the field type you have to specify the domain
for which the mass budget should be calculated. The file type will be a
dfs0 file.

If discharge is selected for the field type you have to specify the cross sec-
tion through which the discharge should be calculated. The file type will
be a dfs0 file.

Table 5.1 List of tools for viewing, editing and plotting results

Output format File type Viewing/editing tools Plotting tools

Point series dfs0 Time Series Editor Plot Composer
Line series dfs1 Profile Series Editor Plot Composer
Area series dfsu Data Viewer Data Viewer

33
 TRANSPORT MODULE

Output file
A name and location of the output file must be specified along with the
type of data (file type).

Treatment of flood and dry

For 2D field parameters the flood and dry can be treated in three different
ways

z Whole area
z Only wet area
z Only real wet area

Selecting the Only wet area option the output file will contain delete val-
ues for land points. The land points are defined as the points where the
water depth is less than a drying depth. Selecting the Only real wet area
option the output file will contain delete values for points where the water
depth is less than the wetting depth. The drying depth and the wetting
depth are specified on the Flood and Dry dialog. If flooding and drying is
not included both the flooding depth and the wetting depth are set to zero.

Time step
The temporal range refers to the time steps specified under Simulation
Period in the Time dialog.

Point series
You must specify the type of interpolation. You can select discrete values
or interpolated values.

The geographical coordinates of the points are either taken from the dialog
or from a file. The file format is an ascii file with four space separated
items for each point on separate lines. The first two items must be floats
(real numbers) for the x- and y-coordinate. For 2D field data the third item
is unused (but must be specified). The last item (the remaining of the line)
is the name specification for each point.

You must also select the map projection (Long/Lat, UTM-32, etc.) in
which you want to specify the horizontal location of the points.

If "discrete values" is selected for the type of interpolation, the point val-
ues are the discrete values for the elements in which the points are located.
The element number and the coordinates of the center of the element are
listed in the log-file.

34 MIKE 21 Flow Model FM

Outputs

If "interpolated values" is selected for the type of interpolation, the point

values are determined by 2nd order interpolation. The element in which
the point is located is determined and the point value is obtained by linear
interpolation using the vertex (node) values for the actual element. The
vertex values are calculated using the pseudo-Laplacian procedure pro-
posed by Holmes and Connell (1989). The element number and the coor-
dinates are listed in the log-file.

Line series
You must specify the first and the last point on the line and the number of
discrete points on the line. The geographical coordinates are taken from
the dialog or from a file. The file format is an ascii file with three space
separated items for each of the two points on separate lines. The first two
items must be floats (real numbers) for the x- and y-coordinate. For 2D
field data the third item is unused (but must be specified). If the file con-
tains information for more than two points (more than two lines) the infor-
mation for the first two points will be used.

You must also select the map projection (Long/Lat, UTM-32, etc.) in
which you want to specify the horizontal location of the points.

The values for the points on the line are determined by 2nd order interpo-
lation. The element in which the point is located is determined and the
point value is obtained by linear interpolation using the vertex (node) val-
ues for the actual element. The vertex values are calculated using the
pseudo-Laplacian procedure proposed by Holmes and Connell (1989).
The element number and the coordinates are listed in the log-file.

Area series
The discrete field data within a polygon can be selected. The closed region
is bounded by a number of line segments. You must specify the coordi-
nates of the vertex points of the polygon. Two successive points are the
endpoints of a line that is a side of the polygon. The first and final point is
joined by a line segment that closes the polygon. The geographical coordi-
nates of the polygon points are taken from the dialog or from a file. The
file format is an ascii file with three space separated items for each of the
two points on separate lines. The first two items must be floats (real num-
bers) for the x- and y-coordinate. For 2D field data the third item is unused
(but must be specified).

You must also select the map projection (Long/Lat, UTM-32 etc.) in
which you want to specify the horizontal location of the points.

35
 TRANSPORT MODULE

Cross section series

You must specify the first and the last point between which the cross sec-
tion is defined. The cross section is defined as a section of element faces.
The face is included in the section when the line between the two element
centers of the faces crosses the line between the specified first and last
point. The geographical coordinates are taken from the dialog or from a
file. The file format is an ascii file with three space-separated items for
each of the two points on separate lines. The first two items must be floats
(real numbers) for the x- and y-coordinate. The third item is unused (but
must be specified). If the file contains information for more than two
points (more than two lines), the information for the first two points will
be used. The faces defining the cross section are listed in the log-file.

You must also select the map projection (Long/Lat, UTM-32, etc.) in
which you want to specify the horizontal location of the points.

Domain series
The domain for which mass budget should be calculated is specified as a
polygon in the horizontal domain. The closed region is bounded by a
number of line segments. You must specify the coordinates of the vertex
points of the polygon. Two successive points are the endpoints of a line
that is a side of the polygon. The first and final point is joined by a line
segment that closes the polygon. The geographical coordinates of the pol-
ygon points are taken from the dialog or from a file. The file format is an
ascii file with three space separated items for each of the two points on
separate lines. The first two items must be floats (real numbers) for the x-
and y-coordinate. The third item is unused (but must be specified).

You must also select the map projection (Long/Lat, UTM-32, etc.) in
which you want to specify the horizontal location of the points.

5.9.2 Output items

Field variables
You can select basic output variables and additional output variables.

The basic variables are

z Component concentration [component unit] for each transported com-

ponent

The additional variables are

z Velocity components

36 MIKE 21 Flow Model FM

Outputs

z CFL number

Mass Budget
You can select the mass budget calculation to be included for the flow and
for the transported components. For each selected component the follow-
ing items are included in the output file

z Total area - total volume/mass within polygon

z Wet area - volume/mass in the area within polygon for which the water
depth is larger than the drying depth
z Real wet area - volume/mass in the area within polygon for which the
water depth is larger than the wetting depth
z Dry area - volume/mass in the area within polygon for which the water
depth is less than the drying depth
z Transport - accumulated volume/mass transported over lateral limits of
polygon
z Source - accumulated volume/mass added/removed by sources within
polygon
z Process - accumulated volume/mass added/removed by processes
within polygon
z Error - accumulated volume/mass error within polygon determined as
the difference between the total mass change and the accumulated
mass due to transport, sources and processes

The accumulated volume/mass error contains the contribution due to cor-

rection of the transported component when the values become larger than
the specified maximum value or lower than the specified minimum value.
For the water volume the minimum value is 0, while there is no upper
limit. For the component concentrations the minimum values are -1010,
while the maximum values are 1010.

Discharge
You can select the discharge calculation to be included for the flow and for
the transported components. Each selected component will result in a
number of output items.

You can select between two types of output items:

z Basic
z Extended

37
 TRANSPORT MODULE

The basic output items are as follows:

z Discharge - volume/mass flux through the cross section

z Accum. discharge - accumulated volume/mass flux through the cross
section

The extended output items that are included in the output file in addition
to the basic output items are as follows:

z Positive discharge
z Accumulated positive discharge
z Negative discharge
z Accumulated negative discharge

By definition, discharge is positive for flow towards left when positioned

at the first point and looking forward along the cross-section line. The
transports are always integrated over the entire water depth.

38 MIKE 21 Flow Model FM

6 LIST OF REFERENCES
/1/ Delhez, E. J. M., Deelersijder, E., Maouchet, A., Beckers, J.
M.(2003), On the age of radioactive tracers, J. Marine Systems, 38,
pp. 277-286.

/2/ Holmes, D. G. and Connell, S. D. (1989), Solution of the 2D

Navier-Stokes on unstructured adaptive grids, AIAA Pap. 89-1932
in Proc. AIAA 9th CFD Conference.

/3/ Rodi, W. (1980), Turbulence Models and Their Application in

Hydraulics - A State of the Art Review, Special IAHR Publication.

39
 LIST OF REFERENCES

40 MIKE 21 Flow Model FM

INDEX

41
 Index

A
About this guide . . . . . . . . . . . . .9
Area series . . . . . . . . . . . . . . . 35

B
Boundary conditions . . . . . . . . . . 31

D
Decay . . . . . . . . . . . . . . . . . . 26
Dirichlet boundary condition . . . . . 31
Dispersion . . . . . . . . . . . . . . . . 24
Dispersion coefficient . . . . . . . . . 24

E
Evaporation . . . . . . . . . . . . . . . 27
Excess concentration . . . . . . . . . 29

H
Horizontal dispersion . . . . . . . . . 24

I
Initial conditions . . . . . . . . . . . . 30

L
Line series . . . . . . . . . . . . . . . 35

N
Neumann boundary condition . . . . 31

O
Online help . . . . . . . . . . . . . . . 11
Outputs . . . . . . . . . . . . . . . . . 32

P
Point series . . . . . . . . . . . . . . . 34
Prandtl number . . . . . . . . . . . . . 26
Precipitation . . . . . . . . . . . . . . . 27

S
Scaled eddy viscosity . . . . . . . . . 24
Sources . . . . . . . . . . . . . . . . . 28

U
User background . . . . . . . . . . . . . 9

42 MIKE 21 Flow Model FM