Accelerating Eulerian Fluid Simulation With Convolutional Networks

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations. Our method solves the incompressible Euler equations using the standard operator splitting method, in which a large sparse linear system with many free parameters must be solved. We use a Convolutional Network with a highly tailored architecture, trained using a novel unsupervised learning framework to solve the linear system. We present real-time 2D and 3D simulations that outperform recently proposed data-driven methods; the obtained results are realistic and show good generalization properties.Comment: Significant revisio

Cumulant expansions for atmospheric flows

The equations governing atmospheric flows are nonlinear. Consequently, the hierarchy of cumulant equations is not closed. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly through interactions of mean fields with disturbances such as thermals or eddies. In such situations, truncations of the hierarchy of cumulant equations hold promise as a closure strategy. We review how truncations at second order can be used to model and elucidate the dynamics of atmospheric flows. Two examples are considered. First, we study the growth of a dry convective boundary layer, which is heated from below, leading to turbulent upward energy transport and growth of the boundary layer. We demonstrate that a quasilinear truncation of the equations of motion, in which interactions of disturbances among each other are neglected but interactions with mean fields are taken into account, can capture the growth of the convective boundary layer even if it does not capture important turbulent transport terms. Second, we study the evolution of two-dimensional large-scale waves representing waves in Earth's upper atmosphere. We demonstrate that a cumulant expansion truncated at second order (CE2) can capture the evolution of such waves and their nonlinear interaction with the mean flow in some circumstances, for example, when the wave amplitude is small enough or the planetary rotation rate is large enough. However, CE2 fails to capture the flow evolution when nonlinear eddy--eddy interactions in surf zones become important. Higher-order closures can capture these missing interactions. The results point to new ways in which the dynamics of turbulent boundary layers may be represented in climate models, and they illustrate different classes of nonlinear processes that can control wave dissipation and momentum fluxes in the troposphere.Comment: 43 pages, 10 figures, accepted for publication in the New Journal of Physic

Simulation of transition dynamics to high confinement in fusion plasmas

The transition dynamics from the low (L) to the high (H) confinement mode in magnetically confined plasmas is investigated using a first-principles four-field fluid model. Numerical results are in close agreement with measurements from the Experimental Advanced Superconducting Tokamak - EAST. Particularly, the slow transition with an intermediate dithering phase is well reproduced by the numerical solutions. Additionally, the model reproduces the experimentally determined L-H transition power threshold scaling that the ion power threshold increases with increasing particle density. The results hold promise for developing predictive models of the transition, essential for understanding and optimizing future fusion power reactors

Self-solidifying active droplets showing memory-induced chirality

Most synthetic microswimmers do not reach the autonomy of their biological counterparts in terms of energy supply and diversity of motion. Here we report the first all-aqueous droplet swimmer powered by self-generated polyelectrolyte gradients, which shows memory-induced chirality while self-solidifying. An aqueous solution of surface tension-lowering polyelectrolytes self-solidifies on the surface of acidic water, during which polyelectrolytes are gradually emitted into the surrounding water and induce linear self-propulsion via spontaneous symmetry breaking. The low diffusion coefficient of the polyelectrolytes leads to long-lived chemical trails which cause memory effects that drive a transition from linear to chiral motion without requiring any imposed symmetry breaking. The droplet swimmer is capable of highly efficient removal (up to 85%) of uranium from aqueous solutions within 90 min, benefiting from self-propulsion and flow-induced mixing. Our results provide a route to fueling self-propelled agents which can autonomously perform chiral motion and collect toxins

Nature of complex singularities for the 2D Euler equation

A detailed study of complex-space singularities of the two-dimensional incompressible Euler equation is performed in the short-time asymptotic r\'egime when such singularities are very far from the real domain; this allows an exact recursive determination of arbitrarily many spatial Fourier coefficients. Using high-precision arithmetic we find that the Fourier coefficients of the stream function are given over more than two decades of wavenumbers by \hat F(\k) = C(\theta) k^{-\alpha} \ue ^ {-k \delta(\theta)}, where \k = k(\cos \theta, \sin \theta). The prefactor exponent $\alpha$, typically between 5/2 and 8/3, is determined with an accuracy better than 0.01. It depends on the initial condition but not on $\theta$. The vorticity diverges as $s^{-\beta}$, where $\alpha+\beta= 7/2$ and $s$ is the distance to the (complex) singular manifold. This new type of non-universal singularity is permitted by the strong reduction of nonlinearity (depletion) which is associated to incompressibility. Spectral calculations show that the scaling reported above persists well beyond the time of validity of the short-time asymptotics. A simple model in which the vorticity is treated as a passive scalar is shown analytically to have universal singularities with exponent $\alpha =5/2$.Comment: 22 pages, 24 figures, published version; a version of the paper with higher-quality figures is available at http://www.obs-nice.fr/etc7/euler.pd

CHARACTERIZATION AND FLOW PHYSICS OF PLASMA SYNTHETIC JET ACTUATORS

Plasma synthetic jet actuators are investigated experimentally, in which the geometrical design of single dielectric barrier discharge (SDBD) plasma actuators is modified to produce zero-mass flux jets similar to those created by mechanical devices. The SDBD plasma actuator consists of two rectangular electrodes oriented asymmetrically and separated by a layer of dielectric material. Under an input of high voltage, high frequency AC or pulsed DC, a region of plasma is created in the interfacial air gap on account of electrical breakdown of the ambient air. A coupling between the electric field in the plasma and the neutral air near the actuator is introduced, such that the latter experiences a net force which results in a horizontal wall jet. This effect of the actuator has been demonstrated to be useful in mitigating boundary layer separation in aerodynamic flows. To increase the impact that a plasma actuator may have on the flow field, this research investigates the development and characterization of a novel flow control device, the plasma synthetic jet actuator, which tailors the residual air in the form of a vertical jet resembling conventional continuous and synthetic jets. This jet can be either three dimensional using annular electrode arrays, or nearly two dimensional using two rectangular strip exposed electrodes and one embedded electrode. Detailed measurements on the isolated plasma synthetic jet reveal that pulsed operation of the actuator results in the formation of multiple counterrotating vortical structures in the flow field. The output jet velocity and momentum are found to be higher for unsteady pulsing as compared to steady operation. In the case of flow over a flat plate, the actuator is observed to create a localized interaction region within which the baseline flow direction and boundary layer characteristics are modified. The efficiency of the actuator in coupling momentum to the neutral air is found to be related to the plasma morphology, pulsing frequency, actuator dimension, and input power. An analytical scaling model is proposed to describe the effects of varying the above variables on the output jet characteristics and actuator efficiency, and the experimental data is used for model validation