Physics-Informed Neural Networks applied to pressure field estimate

• Grant number: 22/11221-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2022
• End date: September 30, 2023
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Leandro Franco de Souza
• Grantee: Brian Nicholas Alves Rondon Lahr
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The process of changes that affect the laminar flow, leading it to the turbulent regime, is known as the laminar-turbulent transition. The analysis of this change is known as hydrodynamic stability analysis. The group with which this project will be developed works with numerical simulation of this transition process, analysing the amplification or decay of a given perturbation. The formulation adopted by the group is based on vorticity-velocity. The governing equations are rewritten with this formulation, eliminating the pressure term. In this way, all equations are solved without knowing the distribution of the pressure field in the domain. This pressure field can be obtained by solving a Poisson equation, but in the present project, we intend to get this field through the solution using neural networks informed by physical laws. In this way, the current project focuses on developing and improving a physical informed neural network (PINN) by physical laws, which in this case will be the momentum and continuity equations, to obtain the pressure field. The results will be compared with analytical results (if any) and with results obtained by solving the Poisson equation.