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:

\[u_t + u u_x = \nu u_{xx},\]

An analytical expression can be obtained for the solution, using the Cole-Hopf transform:

\[u(t, x) = - 2 \nu \frac{\phi'}{\phi},\]

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:

IODataset

Examples using create_burgers_dataset¶

KL-SVD on Burgers equation

PCA on Burgers equation