[Paper Review] Accurate near wall steady flow field prediction using Physics Informed Neural Network (PINN)

Vinothkumar Sekar, Qinghua Jiang+2 more|arXiv (Cornell University)|Apr 7, 2022

Heat Transfer Mechanisms12 citations

TL;DR

This paper proposes a Physics-Informed Neural Network (PINN) framework to accurately predict near-wall steady flow fields in laminar boundary layers using sparse measurement data located away from the wall. By enforcing the Navier-Stokes equations and boundary conditions within the loss function, PINN achieves high accuracy in reconstructing velocity profiles and skin friction coefficients even with limited sampling points, demonstrating strong potential for experimental flow reconstruction in wall-bounded flows.

ABSTRACT

In this paper, Physics Informed Neural Network (PINN) is explored in order to obtain flow predictions near the wall region accurately with measurements (or sampling points) away from the wall. Often, in fluid mechanics experiments, it is difficult to perform velocity measurements near the wall accurately. Therefore, the present study reveals a new and elegant approach to recover the flow solutions near the wall. Laminar boundary layer flow over a flat plate case is considered for this study in order to explore the ability of PINN to accurately predict the flow field. All the required sampling data for this study is obtained from CFD simulations. A wide range of Reynolds number cases from Re=500 to 100000 has been investigated. First, using PINN, the boundary layer solution is obtained with three different types of boundary conditions. Further, the influence of the location of the sampling points on the accuracy is analysed. From the velocity profiles and the skin friction coefficient distribution, it is clear that PINN results are reasonably accurate near the wall with only a few sampling points away from the wall. This approach has potential application in experiments to obtain the near wall solutions accurately with measurements away from the wall.

Motivation & Objective

• To address the challenge of obtaining accurate near-wall velocity measurements in experimental fluid dynamics.
• To explore the feasibility of using PINNs to reconstruct near-wall flow fields from sparse sampling points located away from the wall.
• To evaluate the impact of sampling point location and boundary condition types on PINN prediction accuracy.
• To validate the method across a wide range of Reynolds numbers (Re = 500 to 100,000) in laminar boundary layer flows.
• To demonstrate the potential of PINNs as a data-driven tool for experimental flow field recovery in wall-bounded flows.

Proposed method

• PINNs are trained using a loss function that enforces the steady-state Navier-Stokes equations in weak form.
• Boundary conditions are incorporated into the loss function, including no-slip at the wall and free-stream conditions.
• Sampling data for training are extracted from high-fidelity CFD simulations of a flat plate boundary layer.
• Three different types of boundary conditions are tested to assess their influence on prediction accuracy.
• The network architecture is optimized to minimize the residual of the governing PDEs and the discrepancy between predicted and sampled data.
• The method leverages physics constraints to generalize beyond the sampled points, especially in the near-wall region.

Experimental results

Research questions

• RQ1 Can PINNs accurately reconstruct near-wall flow fields using only a few sampling points located away from the wall?
• RQ2 How does the location of sampling points influence the accuracy of PINN-predicted velocity profiles near the wall?
• RQ3 What is the impact of different boundary condition formulations on the predictive performance of PINNs in boundary layer flows?
• RQ4 How well do PINN predictions match reference CFD solutions across a broad range of Reynolds numbers?
• RQ5 Can PINNs serve as a reliable tool for experimental flow field reconstruction when direct near-wall measurements are unavailable?

Key findings

• PINN predictions of the velocity profile show excellent agreement with CFD reference solutions, even with only a few sampling points located away from the wall.
• The skin friction coefficient distribution predicted by PINN closely matches the analytical Blasius solution, indicating accurate wall shear stress recovery.
• The accuracy of PINN predictions is robust across Reynolds numbers ranging from 500 to 100,000, demonstrating scalability.
• The location of sampling points significantly affects prediction accuracy, with closer proximity to the wall yielding better results.
• PINNs with proper boundary condition enforcement outperform standard neural networks, highlighting the importance of physics constraints.
• The method enables accurate reconstruction of the full flow field, including the critical near-wall region, from sparse and distant measurements.