Abstract

Simulations play a key role in product development and their usage has exponentially increased in the past decade. This has created the ever-increasing need for reducing the simulation execution time so that better product designs can be achieved. Traditionally, higher CPU cores have been used to achieve this purpose. But, the limitations in current approaches do not lead to linear scalability and often the high-fidelity simulations are run over several days or weeks. On the other hand, deep neural networks have proven to be good approximators for predicting solutions for given inputs in a number of domains. Deep convolutional networks, one of the kinds of deep neural networks, have proven to be a viable approach for learning image representations. Recently, Deep convolutional networks have been applied for predicting fluid flows with good success [Guo et al 2016, Hennigh 2017, Ribeiro et al 2020]. The present work is to extend the deep convolutional networks to 2D lid driven cavity flows with an additional object inside the cavity. A square cavity of side 0.2 m is considered. Random shapes of triangular and rectangular objects are placed at the centre of cavity leading to 600 different configurations. The top boundary moves at a uniform speed of 50 m/s corresponding to a Reynolds number of 1000. Gmsh, an open-source meshing software, is used to create triangular meshes and the OpenFOAM solver icoFoam is used to evaluate the incompressible laminar fluid flow in the cavity. The data from these 600 simulations are extracted in the form of shape distance function to represent the input domain. The resulting velocity components in x and y directions are used as the target values. A U-net architecture with skip connections is used to approximate the fluid flow. The U-net architecture contains an encoder and decoder part with skip connections from encoder to decoder. This architecture was first proposed for medical image segmentation and has since been applied to various other fields. In the current approach, the encoder contains 3*2 convolution layers followed by max pooling layers. The decoder part contains transpose convolution layers with appropriate zero padding to match the input dimensions. The network was trained with a learning rate of 1e-4. The input data from the 600 simulations was split into three parts for training, testing and validation purposes. The results comparing the streamlines for different shapes from both OpenFOAM and U-net architecture are highlighted. The opportunities for additional improvements are discussed.