2nd Workshop of ISOPE Numerical Wave Tank Group

Brest. May 1999

Benchmark test cases for radiation force



The Numerical Wave Tank (NWT) group of the International Society of Offshore and Polar Engineers was established at the 5th ISOPE conference in The Hague (1995). This grope is open freely to everybody interested in this topic.

At the 7th conference in Honolulu (1997), it was decided by the member of the group to begin series of informal workshop meeting where computational benchmark cases will be defined and their results discussed and commented in a special session during the forthcoming ISOPE conference. A free access data bank will be created and enriched with the numerical results of the participants; this data bank will be accessible freely and permanently in an ftp site via Internet (see below). Then everybody will be able to get data files and to perform his own analysis and comparison with any other participant. The files will contain not only numerical results, but also a short text section where the numerical technique will be summarized and related bibliographic references will be given.

The first special NWT Workshop session was held in ISOPE-98 Montreal Conference and the second NWT Workshop session will be held in ISOPE-99 Brest Conference.  The results, gathered and analyzed, will be presented by the NWT grope leader (currently Katsuji Tanizawa), then openly discussed by all the present participants (contributing or not).

1999 Benchmark series : the topic of this second workshop is the radiation force computation by numerical wave tanks. In this test case, hydrodynamic force acts on a heaving wedge is considered. Pressure computation on the heaving wedge is the key point.

Sending your result files : result files must be sent to Katsuji Tanizawa (Ship Research Institute of Japan) via email or FTP. Data file structure and format are given in the sections below. From the filename by appending the test case number to your name (or to a pseudo for anonymous contributors).  One data file per test case via FTP, or attached to an email at:

If you use FTP, please send me also an email to inform me. If you want to contribute anonymously, inform me in the mail, replace you name in the file by a four digit number of your choice, and give any chain of characters instead of your email in the data files.

Please, limit the size of each data file to 3 Mbyte by skipping time step or boundary vertices, and/or by gziping the file.

Deadline : 15th March 1999

Loading files from NWT FTP site : After checking and analysis, your files will be put in a permanent data bank freely accessible to everybody on the SRI FTP server at:

Everybody will thus be able to read results files of any other participant, and perform his own analysis and comparisons. You can also use these files as guidelines to write your result files in a correct format.


Benchmark test of radiation problem

Wave radiation by sinusoidal heave motion of a wedge



Description of benchmark test


w2 a / g


T / (a/g)0.5


l / a



The numerical simulation is started from the calm condition at time t=0, and should be continued until the wave field is converged to the periodically steady state. Any type of gradual start sequence of wedge motion and any type of numerical wave absorption method can be used at open end. The absorption of wave will begin at x=L and may extended beyond this limit. If a numerical beach is used, it must begin at x=L and extend further. R is the right boundary of the computational domain; it must located such that : XR L

All the variables are nondimensionalized by half breadth of wedge : a, gravitational acceleration : gand density of fluid : r. Units of variables are given in the following table.





fluid density



(a / g)0.5


(g / a)0.5


(a g)0.5


rg a

force/unit width

rg a2


a (a g)0.5


Benchmark test number

w2 a / g


A / a = 0.2


A / a = 0.4


A / a = 0.6



Result file structure                     (ASCII character set, possibly compressed by gzip)

c Your name, e-mail address and benchmark number

write(*,*) your.name

write(*,*) your@email

write(*,*) benchmark.test.number

c(1st block) Simulated heaving radiation force on the wedge

write(*,*) Ntime

begin time loop from 1 to Ntime

write(*,*) time,Y,F

end time loop

c(2nd block)  Boundary values for one heave period of the periodically steady state

write(*,*) Mtime,Nfreesurf,Nwedgesurf

begin time loop from 1 to Mtime

write(*,*) time

begin free-surface nodes loop from 1 to Nfreesurf

write(*,*) X(i),Y(i),U(i),V(i),[f(i),ft(i)]

end free-surface nodes loop

begin wedge surface nodes loop from 1 to Nwedgesurf

write(*,*) X(i),Y(i),U(i),V(i),P(i),[f(i),ft(i)]

end wedge surface nodes loop

end time loop

c(3rd block) Information of your simulation method

write(*,*) the first line - 80 characters max.
...... (as many comment lines as necessary)

write(*,*) the last line - 80 characters max.


1st block : Time history of wedge motion and heaving force will be given from the beginning to the end of the simulation. At the end of simulation, the wave field must be converged to periodically steady state.

2nd block : Boundary values are given in the 2nd block. Please select one heave period to fill 2nd block after simulated wave field converged to the periodically steady state. Boundary values for x > 4 l are not necessary.

3rd block : After the numerical data, participants are requested to append to the file any relevant matters such as : type of simulation method, the wave absorption technique at open end, velocity calculation method at the intersection point of wedge and free-surface and references about simulation codes. In particular, potential flow participants are requested to mention the method to compute ft(i).

(1) Finite difference method

(2) From the solution of the B.V.P. on ft

(please describe the boundary condition on wedge surface)

(3) Others (Please describe in detail)

Technical computational details as: type of computer, operation system, programming language, program size, cpu time are also welcome. For this final part of the file, use as many lines of 80 character (max.) as necessary, within the limit of 3 Mbyte/whole file. Please use a Keyword writing style to save space.

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