burgers module¶
Burgers dataset.
This Dataset
contains solutions to the Burgers’ equation with
periodic boundary conditions on the interval \([0, 2\pi]\) for different
time steps:
An analytical expression can be obtained for the solution, using the Cole-Hopf transform:
where \(\phi\) is solution to the heat equation \(\phi_t = \nu \phi_{xx}\).
This Dataset
is based on a full-factorial
design of experiments. Each sample corresponds to a given time step \(t\),
while each feature corresponds to a given spatial point \(x\).
More information about Burgers’ equation
- gemseo.problems.dataset.burgers.create_burgers_dataset(n_samples=30, n_x=501, fluid_viscosity=0.1, categorize=True)[source]
Burgers dataset parametrization.
- Parameters:
n_samples (int) –
The number of samples.
By default it is set to 30.
n_x (int) –
The number of spatial points.
By default it is set to 501.
fluid_viscosity (float) –
The fluid viscosity.
By default it is set to 0.1.
categorize (bool) –
Whether to distinguish between the different groups of variables.
By default it is set to True.
- Returns:
The Burgers dataset.
- Return type: