guglielmopadula / lidcavity

Lid Cavity Dataset

Dataset

The dataset is the solution of

$$\frac{\partial u}{\partial t}(t,x,y)+(u(t,x,y)\cdot \nabla) u(t,x,y)-\nu \Delta u(t.x,y)=-\nabla p(t,x,y) \quad x\in (-0.05,0.05), y\in (-0.05,0.05), t\in (0,10)$$

$$\nabla \cdot u=0$$

$$u(0,x,y)=(0,0) \quad x\in (0,1), y\in (0,1)$$

$$u(0,x,0)=(0,0) \quad x\in [0,1]$$

$$u(0,x,1)=(1,0) \quad x\in [0,1]$$

$$u(0,0,y)=(0,0) \quad y\in [0,1)$$

$$u(0,1,y)=(0,0) \quad y\in [0,1)$$

$$p(0,x,y)=0$$

$$u(t,x,y)=(0,0) \quad x\in (0,1), y\in (0,1), t\in (0,10)$$

$$u(t,x,0)=(0,0) \quad x\in [0,1],t\in (0,10)$$

$$u(t,x,1)=(1,0) \quad x\in [0,1],t\in (0,10)$$

$$u(t,0,y)=(0,0) \quad y\in [0,1),t\in (0,10)$$

$$u(t,1,y)=(0,0) \quad y\in [0,1), t\in (0,10)$$

As we are in 2D this system has an unique weak solution (see Ladyzhenskaya (1958, 1959), Lions and Prodi (1959)). For more details on the dateset , see this link.

Note that $u$ is discontinous on $(0,1)$, $(1,1)$. This is not a problem as the dataset is created using the finite volume method, using icoFoam.

$\nu$ varies from $0.01$ to $0.001$, as such the Reynolds number varies from $100$ to $1000.$

The full order simulation as been validated with this paper.

In the dataset class file, some weights useful to compute quadrature formulas are computed.

Package installation guide

First install OpenFoam 2312. Them from this directory do the following:

pip install PyFoam numpy Ofpp tqdm
cd data
openfoam2312
python generate_data.py
cd ..
pip install .

Usage example

from lidcavity import LidCavity
data=LidCavity(batch_size=10)
train_loader=data.train_loader ##Gives a pytorch dataloader