Solving navier stokes equations with physics informed neural network for calculation of aerodynamic forces

Official URL: https://risc01.sabanciuniv.edu/record=b2771019_(Table of contents)

Understanding of flow dynamics is crucial in a comprehensive set of scientific disciplines, such as astrophysics, chemistry, biology, meteorology, biomedical engineering, and mechanical engineering. Nevertheless, fluid dynamics properties cannot be well-understood in a case of complex geometry, high Mach number flow, turbulence, stall, and complex reactions. Experiments can provide some insights to study these complicated phenomena. Yet, certain information may not be obtained accurately because of low fidelity and experimental limitations. On the other hand, Navier-Stokes as a governing equation of viscous flow of an incompressible fluid can be solved numerically to obtain flow properties. However, such numerical analysis relies heavily on computational power which requires long duration to conclude and modelling ability. As an alternative approach, we deal with this problem by implementing a physicsinformed neural network (PINN). As a scientific machine learning algorithm, PINNs are developed to solve partial differential equations approximately. In this thesis, we first implement PINNs for solving Navier-Stokes equations for laminar flow over a cylinder. Then, we apply PINN for turbulent flow over a stationary NACA0018 airfoil with a high angle of attack. We implement the PINN approach with sparse data from the numerical CFD study. Our results reveal that the PINN is able to recover missing data with excellent accuracy for both laminar and turbulent flow problems. The PINN model is also used to calculate aerodynamic forces acting on the cylinder and on the airfoil. For force calculations, two different methods are applied to find the optimum application with less error from the PINN approach. Results show that gradient-based stress integration method ends up with more accurate results than integral-based control volume approach