Advancements in Cfd Simulation Techniques

"Can Physics-Informed Neural Networks (PINNs) simulate 3D turbulence?" A question we've been asked repeatedly since developing the framework in 2017. After nearly a decade of progress, we now have a conclusive answer. For the first time, we demonstrate that PINNs can simulate fully developed turbulent flows in 2D and 3D by learning solutions directly from the Navier-Stokes equations without training data or computational grids. Key technical ingredients: -- PirateNet architecture for deep networks -- Causal training strategies -- Self-adaptive loss weighting -- SOAP optimizer for resolving gradient conflicts -- Time-marching with transfer learning Validation on challenging benchmarks: -- 2D Kolmogorov flow (Re = 10⁶) -- 3D Taylor-Green vortex (Re = 1,600) -- 3D turbulent channel flow (Re_τ = 550) Results accurately reproduce key turbulence statistics including energy spectra, enstrophy, and Reynolds stresses. This work demonstrates that PINNs can handle complex chaotic systems, though computational efficiency remains an important area for future improvements. It opens new possibilities for mesh-free modeling and hybrid simulation approaches in computational fluid dynamics. This research was led by the outstanding work of Sifan Wang at Yale University, with key contributions from Panos Stinis at Pacific Northwest National Laboratory and Shyam Sankaran at Penn Engineering. The work was supported by the DOE Advanced Scientific Computing Research program. 📄 Read the preprint here: https://lnkd.in/enGrJJKm #PINNs #CFD #Turbulence #ScientificComputing #MachineLearning #DOE #ASCR #AppliedMathematics

(we quietly open-sourced this last year and never came around to share it) 𝐅𝐋𝐎𝐖𝐕𝐏𝐌: 𝘔𝘦𝘴𝘩𝘭𝘦𝘴𝘴 𝘓𝘌𝘚 𝘵𝘩𝘳𝘰𝘶𝘨𝘩 𝘵𝘩𝘦 𝘳𝘦𝘧𝘰𝘳𝘮𝘶𝘭𝘢𝘵𝘦𝘥 𝘷𝘰𝘳𝘵𝘦𝘹 𝘱𝘢𝘳𝘵𝘪𝘤𝘭𝘦 𝘮𝘦𝘵𝘩𝘰𝘥 FLOWVPM is best known for its coupling with mid-fidelity #aerodynamics models in the FLOWUnsteady framework for simulating #aircraft and #windenergy (https://lnkd.in/gkPxJ_a). However, the code is also a stand-alone tool of unbounded turbulent flows (like open jets, vortex rings, wakes, etc) and it can be easily integrated into other frameworks. • 𝐂𝐨𝐝𝐞: https://lnkd.in/ewwsd_iG • 𝐏𝐚𝐩𝐞𝐫: https://lnkd.in/e4SbitUq ---------------------------------------------------------------------- 𝐒𝐮𝐦𝐦𝐚𝐫𝐲 This code implements the reformulated vortex particle method (rVPM), a new VPM method that is numerically stable developed during my PhD. The rVPM is a meshless #CFD method solving the #LES-filtered incompressible Navier-Stokes equations in their vorticity form. It uses a Lagrangian (meshless) scheme, which not only avoids the hurdles of mesh generation, but it also conserves vortical structures over long distances with minimal numerical dissipation. Furthermore, rVPM is highly efficient since it uses computational elements only where there is vorticity (rather than meshing the entire space), usually being ~100x faster than conventional mesh-based LES with comparable accuracy. The rVPM uses particles to discretize the Navier-Stokes equations, with the particles representing radial basis functions that construct a continuous vorticity/velocity field. The basis functions become the LES filter, providing a variable filter width and spatial adaption as the particles are convected and stretched by the velocity field. The local evolution of the filter width provides an extra degree of freedom to reinforce conservations laws, which makes the rVPM numerically stable (overcoming the numerical issues that plague the classic VPM). This open-source project is funded by #NASA and #NSF. It is led by Prof. Andrew Ning from the FLOW Lab at Brigham Young University, with support of a few companies in electric aviation, like Whisper Aero. #aerospace #aviation #engineering #science #research #ParaView National Science Foundation (NSF) | NASA - National Aeronautics and Space Administration

Heterogeneities, tyranny of scales, and curse of dimensionality In most complex physical systems (and to some extent others like financial markets), competing non-linear forces lead to instabilities and emergent large scale structures. The overall dynamics are controlled by the large scale structures to a great extent but those large structures cannot be accessed directly as they are the result of the small scale interactions. In CFD (Computational Fluid Dynamics), we are stuck in the pursuit of conducting even higher resolving simulations to get to the ground truth by modeling all those small scale interactions that lead to the emergent large scale structures. We are creative in coming up with subgrid models to reduce the computational load to resolve absolutely what we have to and have correlations for the unresolved scales. There are other heuristics that we apply to things like turbulence and drag closures, etc. to make the problems computationally tractable. Having a taste of methods to unravel low dimensional manifolds (my work with Badri Velamur Asokan back in 2007) and also realizing that most systems we are trying to model lie in much lower dimensions (agent based modeling work) than than the millions or now billions of degrees we bring in through CFD, I presented concepts at various venues on how we can use AI/ML to break these vicious dependencies between heterogeneities, tyranny of scales, and curse of ever increasing mesh sizes. Now it is more imperative to revisit as the LLM boom brought us into our laps the neural networks based learning algorithms that give access to low dimensional latent spaces and possibly transfer learning from similar phenomena, hardware co-designed with software for deep learning on large datasets, and plethora of software and data analysis tools available to explore all aspects of heterogeneous structures in complex systems. Below is a short blog post describing my attempt to develop a Dynamic Heterogeneity-Resolving Drag Model (DHRDM) for coarse-grid simulations of FCC risers: https://lnkd.in/gunwY5jQ Interactive website for you to explore this approach is at: https://lnkd.in/grE97R9M Sankaran Sundaresan Madhava (Syam) Syamlal Hans Kuipers Olivier Simonin Raffaella Ocone Shankar Subramaniam Tingwen Li Wei Wang Wei Ge Sanjib Das Sharma, Ph.D Marc-Olivier Coppens David West