# Fenton benchmark

## 1 Test description

This tests verify that the wave elevation and wave particle velocity and accelerations produced by Ashes when using Stream function waves are the same as those obtained using the code available at http://johndfenton.com/.

## 2 Model

The only purpose of the model in this test is to have nodes at different depths to be able to read wave kinematics at those depths. In the current test, the model has nodes at 10 and 15 m below the mean sea level, respectively. The seabed is 10 m below the mean sea level. The simulation is run as Loads only (see Analysis).

Several regular waves are tested, with different heights, periods and number of Fourier coefficients. They are listed in the table below:
 Period $$T$$ [s] Height $$H$$ [m] Number of coefficients $$N$$ [-] 5 2 5 5 5 11 10 5 11 10 8 11 10 10 11

The other parameters related to the stream function wave algorithm are left as their default value, i.e. Converence criterion of 0.0004, 10 height steps and a maximum number of iterations of 20.

## 3 Benchmarked solution

We compare the Wave elevation, the Particle velocity and the Particle acceleration produced by Ashes with those produced by Fenton's code. The simulation is run for one wave period and the time step is one twentieth of the wave period.

The figures below illustrates the results obtained with Fenton's code for the case T = 10 s, H = 10 m, N = 11. The particle kinematics are given at 10 m water depth.

Note: because of the way the testing is done in Ashes, we compare the magnitude of the wave particle kinematics, rather than its component values. Therefore, you will only see one graph for the particle velocity and one graph for the particle acceleration.

## 4 Results

The test is considered passed when the results from Ashes are within 0.5% of those produced by Fenton's code.
The reports are available on the following links:

https://www.simis.io/downloads/open/benchmarks/current/Stream function T = 5 H = 2 d = 20 N = 5.pdf
https://www.simis.io/downloads/open/benchmarks/current/Stream function T = 5 H = 5 d = 20 N = 11.pdf
https://www.simis.io/downloads/open/benchmarks/current/Stream function T = 10 H = 10 d = 20 N = 11.pdf
https://www.simis.io/downloads/open/benchmarks/current/Stream function T = 10 H = 8 d = 20 N = 11.pdf