Modelling pressure-Hessian from local velocity gradients information in an incompressible turbulent flow field using deep neural networks
The understanding of the dynamics of the velocity gradients in turbulent flows is critical to understanding various non-linear turbulent processes. The pressure-Hessian and the viscous-Laplacian govern the evolution of the velocity-gradients and are known to be non-local in nature. Over the years, several simplified dynamical models have been proposed that models the viscous-Laplacian and the pressure-Hessian primarily in terms of local velocity gradients information. These models can also serve as closure models for the Lagrangian PDF methods. The recent fluid deformation closure model (RFDM) has been shown to retrieve excellent one-time statistics of the viscous process. However, the pressure-Hessian modelled by the RFDM has various physical limitations. In this work, we first demonstrate the limitations of the RFDM in estimating the pressure-Hessian. Further, we employ a tensor basis neural network (TBNN) to model the pressure-Hessian from the velocity gradient tensor itself. The neural network is trained on high-resolution data obtained from direct numerical simulation (DNS) of isotropic turbulence at Reynolds number of 433 (JHU turbulence database, JHTD). The predictions made by the TBNN are tested against two different isotropic turbulence datasets at Reynolds number of 433 (JHTD) and 315 (UP Madrid turbulence database, UPMTD) and channel flow dataset at Reynolds number of 1000 (UT Texas and JHTD). The evaluation of the neural network output is made in terms of the alignment statistics of the predicted pressure-Hessian eigenvectors with the strain-rate eigenvectors for turbulent isotropic flow as well as channel flow. Our analysis of the predicted solution leads to the discovery of ten unique coefficients of the tensor basis of strain-rate and rotation-rate tensors, the linear combination over which accurately captures key alignment statistics of the pressure-Hessian tensor.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
GP-FL: Model-Based Hessian Estimation for Second-Order Over-the-Air Federated Learning
Second-order methods are widely adopted to improve the convergence rate of learning algorithms. In federated learning (FL), these methods require the clients to share their local Hessian matrices with the parameter serve…
Federated LearningSecond-order methodsPredicting the wall-shear stress and wall pressure through convolutional neural networks
The objective of this study is to assess the capability of convolution-based neural networks to predict wall quantities in a turbulent open channel flow. The first tests are performed by training a fully-convolutional ne…
Reproducing the Acoustic Velocity Vectors in a Circular Listening Area
Acoustic velocity vectors are important for human's localization of sound at low frequencies. This paper proposes a sound field reproduction algorithm, which matches the acoustic velocity vectors in a circular listening …
Multi-agent reinforcement learning for wall modeling in LES of flow over periodic hills
We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning (MARL). The model is trained using low-Reynolds-number flow over …
Multi-agent Reinforcement LearningAppearance of Random Matrix Theory in Deep Learning
We investigate the local spectral statistics of the loss surface Hessians of artificial neural networks, where we discover excellent agreement with Gaussian Orthogonal Ensemble statistics across several network architect…
Deep Learning