Physical Backgroud

Numerical computation

Classical errors

The module ARTEMIS solves the BERKHOFF equations by a finite elements methods. Therefore, it takes into account wave reflexion, refraction and diffraction of a linear houle in a domain where the bottom height vary slowly. The applications fall into computation of wave propagation near coastal region such as computation of agitation in a port.At every point of the grid, ARTEMIS compute the velocity potential and deduce then the following results :

Wave heightWave directionPhasevelocity of the free flow

In this section, we give a description of the module ARTEMIS and the main possibilities of computation. Moreover, you can find a full example of a computation in the part :

Wave propagation is completly described by the equations of Navier-Stockes. However, in order to solve this equations, some simplifications are made. In our case, wave propagation is represented by the equation of BERKHOFF which take into account reflexion, diffraction and refraction.

Firstly, let us consider some notations :

The equations of Berkhoff is deduced from the equations of Navier-Stockes with the following hypothesis :

no viscosityirrotationnal flow which allows to introduce the velocity potentialH/L <<1 : small curveH/h <<1low deep variationWith this simplifications, we obtain the equations of Berkhoff :

The form of the velocity potential is :

The equations which is solved :

Where C and Cg are respectively phase and group velocities

1. Input / Output

There is at least 4 files to provide in order to carry out a computation with Artemis. Indeed, if you want to continue a previous computation, you have to provide the previous result file. Firstly, we give a short description of this file.1.1 The geometry file

It contains the co-ordinates of the the computational grid, created by MATISSE, or an another mesh generator which is compatible with Telemac modelling system.

1.2 The parameters file

It is a text file which contains all the key-words which are necesary for the computation such as initial condition, numerical parameters or physical parameters.

1.3 The Fortran file

It contains all the subroutine of telemac which have been modified by the user. Moreover, it contains the principal program of Telemac. The main function of this program is to fix the language (french or english), and to fix the memory space by dimension the table A (real) and IA (integer)

1.4 The boudary conditions file

It contains the definition of the boundary (fixed flow, fixed height, wall...). This file is created by the mesh generator. However, in Artemis, the boundary conditions are defined in the fortran file. The boundary condition file is important in order to know the position of the boundary. This point is full explained in the next part. Be carefull because it can be a source of lots of problems

1.5 The listing file

It contains all the information concerning the computation

1.6 The results file

It contains the results of the computation. It is the file which will be compute with RUBENS

2. Maritim computation

In telemac, the boundary condition can be fixed in the parameter file because there are defined by matisse. However, in Artemis, as we use the same Mesh generator (Matisse), some file must be modified in order to redefine the boundary condition.

2.1 Bondary conditions

2.1.1 Definition of the type

There are four kinds of boundary conditions in Artemis :

Solid frontier such as a beach or a portIncident wave conditions which correspond to the "entry" of the domainFree outletImposed wave conditionsThe type of conditions is fixed by the variable LIHBOR (which corresponds to the first columns of the boundary conditions file) according to the following values :

LIHBORType of conditionsKOND=1Incident wave conditionsKLOG=2Solid frontierKSORT=4Free outletKENT=5Imposed wave conditions

The files where the user can defined this conditions can be the boundary conditions file or the Fortran file. Indeed, the values of LIHBOR is fixed in the boundary conditions file :

The boundary conditions file is as the following :

In artemis, only the first and the two last columns are used :

The first gives the value of LIHBORThe two last correspond to the number of grid point :global and boundary pointsLet us consider an example in order to illustrate this point

Note : In artemis, the boundary points are count in the direct sense, except for the island which are count in the inverse sense.

In this example, the boundary condition file must be as the following :

First column...Last column2..12..22..32..42..52..64..72..82..92..101..111..12

How to fix the type with Matisse

You can see in Matisse manual that there are no definition of solid boundary, incident wave ... Indeed, in order to have this condition, you must be very carefull when you define the "entité". For Artemis, only the first columns of the table "entité" is used.The correspondance is the following :The line are count in this order : 0, 1, 2, 4, 5 which correspond to the value of LIHBOR.

2.1.2 Definition of the parameter

The definition of wave condition is achieved in the parameter file in the sub routine BOHR or in the Fortran file. There is two possibility : Linear wave or spectral wave. First, let us consider the 4 types of conditions. Secondly, a table sum up all this points.

Incident wave conditions or Imposed wave conditions.

For this segment, there is two parameters to define in the subroutine BOHR :

HB : wave heightTETAB : wave directionNotes : convention for TETAB :

The wave height is fixed to 1 meter by default

The other parameters such as Period of Spectrum charasteristic are fixed in the Parameter file

Free outlet.

There is nothing to define

Solid Boundary

There is 3 parameters to define in the sub routine BOHR :

Reflexion coefficient RPThe angle of "attaque" TETAPDifference of phase induces by the boundaryNotes :

a. definition of TETAP

b. When ALFAP = 0 and RP = 1, the value of TETAP is not important.

2.2 The parameter file.

It is a list of Key-Words where the user define the name of the different file (input and output). moreover, some general charasteristic are defined.

2.3 The fortran file.

This file is composed of the main program of artemis and several sub-routines such as BOHR which allows to define the boundary conditions.

Description :The main program is called princi.

The sub-routines:

BOHR : definition of the boundary conditions.CONDIH : Definition of the initial conditions.NOMVAR : Name of the graphic output.CORFON : modification of the bottom deepCORRXY : modification of the co-ordinates of the mesh.

2.4 Run the computation.

In the dos control window, type : artemis name_of_the_parameter_file. The computation run automaticly. (There is also a batch mode : use the option artemis -b name_of_the_parameter_file

2.5 Control the solution

At the end of the computation, you must have "FIN NORMALE DU PROGRAMME" in the dos control windows.

3.1 Size of IDIMA and IDIMIA.

The computation stop if the size of these tables is too little. Therefore, be carreful and when you achieved mesh in Matisse, don't forget to note the number of grid point.

3.2 The boundary condition file.

The correspondance between the type in the boundary conditions files and their definition in the fortran file must be exactly the same.