Physics informed neural networks for computational fluid dynamics

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2023-1-17

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Aygün, Atakan

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In this work, we use physics-informed neural networks (PINN) to model the problems generally used in computational fluid dynamics (CFD). Since PINN does not need any discretization scheme or mesh generation, this approach is easier to implement compared to conventional numerical methods. In the context of CFD problems, the effect of network parameters is shown in the convergence and the accuracy of the solution. The solutions to forward problems are chosen with simple geometries since as the nonlinearity increases in the PDE, the PINN has difficulties providing physically meaningful solutions. Therefore, the provided solutions to flow problems are in low Reynolds number regions. Applications in this thesis include the solution of flow problems represented with Navier-Stokes and Euler equations. The problems in Euler equations are in a one-dimensional domain. The solution of thermal convection equations that couples the flow equations with the energy equation is presented. The effect of weighting in each loss term is presented along with different neural network types. Mesh deformation for moving boundary problems in CFD is presented. The deformation is modeled with elliptic equations. The exact boundary values are enforced on the network output to ensure the boundary is in its exact position. The quality of the mesh is presented with the element shape and area changes. PINN can be used in sub-tasks that do not affect the accuracy of high-fidelity solvers.

Subject Keywords

Physics-informed neural networks, Computational fluid dynamics, Thermal convection, Mesh deformation

URI

https://hdl.handle.net/11511/102050

Collections

Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

A. Aygün, “Physics informed neural networks for computational fluid dynamics,” M.S. - Master of Science, Middle East Technical University, 2023.