2D unsteady cylinder flow

This guide introduces how to build a PINN model with continuous time method for simulating 2d unsteady flow passing over a cylinder in PaddleScience.

Use case introduction

The example of 2d unsteady flow over a cylinder simulate solution (pressure and velocity) of following equations.

The following graphs show the velocity in x direction from training the model on given node from openFoam.

The result simulated from PINNs is shown below, which is similar with that from openfoam.

How to run the model

Model composition

The model contains 4 main parts which are datasets, pinn_solver, train or predict code, and dataload module.

Run model

a. Download PaddleScience code

• Confirm working directory

• Downlaod paddlescience code from github, git clone also works by the following code:

git clone https://github.com/PaddlePaddle/PaddleScience.git

b. Install dependent libraries

• Rename the folder name as PaddleScience if not

• Change working directory to PaddleScience

• Install dependent libraries by pip install -r requirements

c.Set environment variables

-Set environment

Setting environment by %env PYTHONPATH=/user_path*/PaddleScience, and if editing bash files, using export PYTHONPATH=$PYTHONPATH:/user_path*/PaddleScience/ instead

d. Start simulation

-Loading data

The trainning data and supervised data are obtained from openFoam that need to be loaded before simulation.

# Loading data from openfoam 
path = './examples/cylinder/2D_unsteady/datasets/'
dataloader = cfd.DataLoader(path=path, N_f=9000, N_b=1000, time_start=1, time_end=50, time_nsteps=50)
training_time_list = dataloader.select_discretized_time(num_time=30)

-Define fluid properties

The flow domain is set before simulation. The grid was loaded from openFoam.

The fluid propery is represented by fluid viscosity nu. Based on the Reynolds number equation Re=U*D/nu, the default inlet velocity is a constant 2, and the Reynolds number can be modified by given various viscosity. In this task, the default Reynolds number is 100, and the cylinder diameter is 1, so we have viscosity equals to 0.02.

-Define Loss weight

Loss function consist of weighted eq_loss, bc_loss, ic_loss, outlet_loss and supervised_data_loss. The weight of each loss can be modified during training process.

PINN = psolver.PysicsInformedNeuralNetwork(
    layers=6, nu=2e-2, bc_weight=10, eq_weight=1, ic_weight=10, supervised_data_weight=10, 
    outlet_weight=1, training_type='half-supervised', checkpoint_path='./examples/cylinder/2D_unsteady/checkpoint/', 
    net_params=net_params, distributed_env=distributed_env)

-Define training parameters

A fully connected neural network is used by default. The network information is defined as 10* 50：

def initialize_NN(self, num_ins=3, num_outs=3, num_layers=10, hidden_size=50):
    return psci.network.FCNet(
        num_ins=num_ins,
        num_outs=num_outs,
        num_layers=num_layers,
        hidden_size=hidden_size,
        dtype="float32",
        activation='tanh')

Adam optimizer is employed in this task. The default training epoch numbers and learning rate are as following:

adm_opt = paddle.optimizer.Adam(learning_rate=1e-5, parameters=PINN.net.parameters())
PINN.train(num_epoch=10, optimizer=adm_opt)

-Training Model

This use case has provided the pre-trained network and saved it in the checkpoint folder. The pre-trained network can be trained continuously when defining net_params = './examples/cylinder/2D_unsteady/checkpoint/pretrained_net_params' in cylinder2d_unsteady_train.py. If net_params = None，a new training process is about to begin.

net_params = './examples/cylinder/2D_unsteady/checkpoint/pretrained_net_params'
train(net_params=net_params)

-Predictint Model

After the training, the optimal network will be generated and saved in checkpoint. Selecting the network and executepython cylinder2d_unsteady_train.py. vtk files are generated and saved in vtk folder during predicting. These vtu files can be displayed in Paraview.

if __name__ == "__main__":
    net_params = './examples/cylinder/2D_unsteady/checkpoint/pretrained_net_params'
    vtk_filename = './examples/cylinder/2D_unsteady/vtk/uvp_t_'
    predict_once_for_all(net_params=net_params, vtk_filename=vtk_filename)