Utilizing Physics-Informed Neural Networks for Modeling 3D Fluid Flows Incorporating Parametric Boundary Conditions

Numerical methods to solve partial differential equations (PDEs) have become indispensable in the field of fluid mechanics. Despite the intensive development of numerical methods such as the finite volume method and the finite element method over the past decades, these methods still have certain limitations, especially when dealing with numerical modeling of complex three-dimensional fluid flows. Moreover, a new simulation is needed for each modification of the domain, boundary conditions and material properties, which make the use of these methods inefficient for parameter studies in the design process or optimization. A new approach to solve PDEs has been recently introduced in the field of scientific machine learning. Physics-informed neural networks (PINNs) utilize the residuals of one or more PDEs as the loss function of an artificial neural network (ANN), while the boundary conditions are imposed in a supervised manner. Instead of solving a system of equations, with the PINN approach a nonconvex optimization is performed to approximate the specific solution of the PDEs by an ANN. Although this relatively new method cannot yet compete with classical numerical methods in terms of accuracy especially for complex geometries, this approach shows promising potentials, as it is mesh-free and suitable for parametric solution of PDE problems. As an exemplary application, we examine a three-dimensional pipe flow problem featuring a variable inlet boundary condition and a twisted baffle that mimics a static mixer. The flow fields predicted by the PINN model are compared and validated with CFD simulations.