Flow Matching Meets PDEs: A Unified Framework for Physics-Constrained Generation

The datasets contain the data for the dynamic stall and Kolmogorov flow cases. You can find the reference paper here.

Dynamic Stall dataset

The design space is defined as a four-dimensional hypercube. The design variables are:

Design variable	Symbol	Description	Range
Free-stream Mach number	$ M_{\infty} $	Ratio of free-stream velocity to speed of sound	0.3 – 0.5
Mean angle of attack	$ \alpha_0 $	Average angle between chord line and flow direction	5° – 10°
Pitching amplitude	$ \alpha_s $	Maximum angular deviation during pitching motion	5° – 10°
Reduced frequency	$ k = \dfrac{\omega c}{2V_{\infty}} $	Non-dimensional frequency of oscillation	0.05 – 0.1

The hypercube is sampled with 128 points for training and 16 points for testing. Each sampled point represents a nominal operating condition.

Each nominal condition is perturbed as follows:

$x_{\text{perturbed}} = (1 + \mathcal{N}(0, 0.02)) \cdot x_{\text{nominal}}$

where $\mathcal{N}(0, 0.02)$ denotes a Gaussian noise term with zero mean and standard deviation 0.02.

This results in 32 perturbed variations per nominal condition, yielding a total of:

$128 \times 32 = 4096$ simulations for training
$16 \times 32 = 512$ simulations for testing

Each simulation that corresponds to a dataset sample has 6 fields of size $128 \times 128$. The fields correspond to:

Absolute pressure
x-wall tangential velocity gradient
y-wall tangential velocity gradient
Temperature
Density
Wall shear stress

Each hdf5 file contains three arrays:

fields with shape (conditions, samples per condition, fields, x, y)
nominal_condition with shape (nominal conditions, samples per condition, design variables)
real_condition with shape (real ominal conditions, samples per condition, design variables)

Kolmogorov flow dataset

The Kolmogorov flow problem spans Reynolds numbers in the range $[100, 500]$, using a spatial resolution of $128 \times 128$. The simulations are performed using TorchFSM. The training dataset includes 32 different flow conditions, while the validation dataset contains 16 conditions. Each condition has $1, 024$ snapshots.

Each simulation that corresponds to a dataset sample has 2 fields of size $128 \times 128$. The fields correspond to:

x-velocity
y-velocity

Each hdf5 file contains two arrays:

fields with shape (conditions, samples per condition, fields, x, y)
reynolds with shape (reynolds numbers, )