Computational Fluid Dynamics (CFD) simulations are used for many air flow simulations including road vehicle aerodynamics. Numerical diffusion occurs when local flow direction is not aligned with the mesh lines and when there is a non-zero gradient of the dependent variable in the direction normal to the streamline direction. It has been observed that typical numerical discretization schemes for the Navier-Stokes equations such as first order upwinding produce very accurate solutions without numerical diffusion when the mesh is aligned with the streamline directions. On the other hand, numerical diffusion is maximized when the streamline direction is at an angle of 45° relative to the mesh line. The amount of numerical diffusion can be reduced by mesh refinements such as aligning mesh lines along the local flow direction or by introducing higher order numerical schemes which may introduce potential numerical instability or additional computational cost. Couple test cases of a simple steady-state incompressible and inviscid air flow convection problem were used to investigate whether numerical diffusion occurs when using Physics Informed Neural Networks (PINNs) that rely on automatic differentiation as opposed to numerical techniques used in traditional Computational Fluid Dynamics (CFD) solvers. Numerical diffusion was not observed when PINNs were used to solve the Partial Differential Equation (PDE) for the simple convection problem irrespective of flow angle. The PINN correctly simulated the streamwise upwinding, which has great potential to improve the accuracy of Navier-Stokes solvers.
Pi-fusion: Physics-informed diffusion model for learning fluid dynamics
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Chinese Academy of Sciences（中国科学院大学）；University of Macau（澳门大学）；University of Electronic Science and Technology of China（电子科技大学）
Physics-Informed Video Diffusion For Shallow Water Equations
Ludwig-Maximilians-Universität München (LMU Munich)（慕尼黑路德维希-马克西米利安大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Huawei Heisenberg Research Center（华为海森堡研究中心）；DLR-German Aerospace Center（德国航空航天中心）；University of Tromsø（特罗姆瑟大学）
A Physics-Driven Framework for Parametric Periodic-Flow Modeling and Finite-Amplitude Aeroelastic Response Analysis
Northwestern Polytechnical University（西北工业大学）；Institute of AI for Industries, Chinese Academy of Sciences（中国科学院工业人工智能研究所）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；International Joint Institute of Artificial Intelligence on Fluid Mechanics, Northwestern Polytechnical University（西北工业大学流体力学人工智能联合研究院）
PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction
Zhejiang University（浙江大学）；College of Control Science & Engineering（控制科学与工程学院）；Institute of Cyber-Systems & Control（cyber系统与控制研究所）；School of Mathematical Sciences（数学科学学院）
Design of Turing Systems with Physics-Informed Neural Networks
Nanyang Technological University（南洋理工大学）；Institute of Bioengineering and Bioimaging, A*STAR（新加坡科技研究局生物工程与生物成像研究所）；Bioinformatics Institute, A*STAR（新加坡科技研究局生物信息学研究所）；Institute of High Performance Computing（高性能计算研究所）；Centre for Frontier AI Research（前沿人工智能研究中心）
