Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStatistical Learning for Fluid Flows: Sparse Fourier divergence-free approximations
334
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. In the Fourier setting, the incompressibility (divergence-free) constraint becomes a finite set of linear algebraic equations. We couple our spatial approximation with the truncated Singular Value Decomposition (SVD) of the flow measurements for temporal compression. Our computational framework thus combines supervised and unsupervised learning techniques. We assess the capabilities of our method in various numerical examples arising in fluid mechanics.
rate research
Read More
We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for canonical flow problems. We consider the estimation of force coefficients and wakes from a limited number of sensors on the surface for flows over a cylinder and NACA0012 airfoil with a Gurney flap. The influence of the temporal density of the training data is also examined. Furthermore, we consider the use of convolutional neural network in the context of super-resolution analysis of two-dimensional cylinder wake, two-dimensional decaying isotropic turbulence, and three-dimensional turbulent channel flow. In the concluding remarks, we summarize on findings from a range of regression type problems considered herein.
A two-fluid Discrete Boltzmann Model(DBM) for compressible flows based on Ellipsoidal Statistical Bhatnagar-Gross-Krook(ES-BGK) is presented. The model has flexible Prandtl number or specific heat ratio. Mathematically, the model is composed of two coupled Discrete Boltzmann Equations(DBE). Each DBE describes one component of the fluid. Physically, the model is equivalent to a macroscopic fluid model based on Navier-Stokes(NS) equations, and supplemented by a coarse-grained model for thermodynamic non-equilibrium behaviors. To obtain a flexible Prandtl number, a coefficient is introduced in the ellipsoidal statistical distribution function to control the viscosity. To obtain a flexible specific heat ratio, a parameter is introduced in the energy kinetic moments to control the extra degree of freedom. For binary mixture, the correspondence between the macroscopic fluid model and the DBM may be several-to-one. Five typical benchmark tests are used to verify and validate the model. Some interesting non-equilibrium results, which are not available in the NS model or the single-fluid DBM, are presented.
Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are usually performed in an Eulerian (fixed) frame of reference with snapshots from measurements or evolution equations. The Eulerian description poses some difficulties, however, when the domain or the mesh deforms with time as, for example, in fluid-structure interactions. For such cases, we first formulate a Lagrangian modal analysis (LMA) ansatz by a posteriori transforming the Eulerian flow fields into Lagrangian flow maps through an orientation and measure-preserving domain diffeomorphism. The development is then verified for Lagrangian variants of POD and DMD using direct numerical simulations (DNS) of two canonical flow configurations at Mach 0.5, the lid-driven cavity and flow past a cylinder, representing internal and external flows, respectively, at pre- and post-bifurcation Reynolds numbers. The LMA is demonstrated for several situations encompassing unsteady flow without and with boundary and mesh deformation as well as non-uniform base flows that are steady in Eulerian but not in Lagrangian frames. We show that LMA application to steady nonuniform base flow yields insights into flow stability and post-bifurcation dynamics. LMA naturally leads to Lagrangian coherent flow structures and connections with finite-time Lyapunov exponents (FTLE). We examine the mathematical link between FTLE and LMA by considering a double-gyre flow pattern. Dynamically important flow features in the Lagrangian sense are recovered by performing LMA with forward and backward (adjoint) time procedures.
In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the interpretability of neural networks. This has contributed to the hasty characterization of most NN methods as black boxes and hindering wider acceptance of more powerful machine learning algorithms for physics. In an effort to address such issues in fluid flow modeling, we use a probabilistic neural network (PNN) that provide confidence intervals for its predictions in a computationally effective manner. The model is first assessed considering the estimation of proper orthogonal decomposition (POD) coefficients from local sensor measurements of solution of the shallow water equation. We find that the present model outperforms a well-known linear method with regard to estimation. This model is then applied to the estimation of the temporal evolution of POD coefficients with considering the wake of a NACA0012 airfoil with a Gurney flap and the NOAA sea surface temperature. The present model can accurately estimate the POD coefficients over time in addition to providing confidence intervals thereby quantifying the uncertainty in the output given a particular training data set.
We present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble emph{Bacillus subtilis} bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into $xy$-space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
