49 Search Results

Machine-learned slope limiters adopt strange forms but work well. These slope-limiters performed as well as commonly used limiters for the range of test cases shown. The computational cost of evaluating a B-Spline limiter tractable.

Abstract not provided.

We propose to adopt statistical regression as the projection operator to enable data-driven learning of the operators in the Mori–Zwanzig formalism. We present a principled method to extract the Markov and memory operators for any regression models. We show that the choice of linear regression results in a recently proposed data-driven learning algorithm based on Mori’s projection operator, which is a higher-order approximate Koopman learning method. We show that more expressive nonlinear regression models naturally fill in the gap between the highly idealized and computationally efficient Mori’s projection operator and the most optimal yet computationally infeasible Zwanzig’s projection operator. Wemore » performed numerical experiments and extracted the operators for an array of regression-based projections, including linear, polynomial, spline, and neural network–based regressions, showing a progressive improvement as the complexity of the regression model increased. In conclusion, our proposition provides a general framework to extract memory-dependent corrections and can be readily applied to an array of data-driven learning methods for stationary dynamical systems in the literature.« less

The effect of compressibility on the single-mode Rayleigh–Taylor instability is examined using two (2D) and three-dimensional (3D) direct numerical simulations. To isolate compressibility from background stratification effects, this work employs a constant density profile on each side of the interface. The numerical simulations are performed at various Reynolds numbers using the gas kinetic method for static Mach numbers up to M = 0.4. The most important finding is that compressibility acting in isolation enhances the instability and perturbations grows faster with increasing Mach number, unlike previous results with background isothermal state, which show suppression of the instability at higher staticmore » Mach numbers. In addition, compressibility is also shown to increase the bubble-spike asymmetry. While the instability grows faster for the 3D case, the findings are qualitatively similar in 2D and 3D. Furthermore, the dynamical reasons underlying the effect of compressibility are elucidated by examining the evolution of vorticity and turbulent kinetic energy transport equations.« less

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consistmore » of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.« less

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particlesmore » moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.« less

In this work, we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data were generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws andmore » symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.« less

The structure of collisional plasma shocks has been subject to an extensive, multi-decadal investigation—in the hydrodynamic, hybrid kinetic ion/electron fluid, and fully kinetic ion/electron limits. Despite this thoroughness, all of these studies apply exclusively to classical, weakly coupled plasmas. Here, we report the first results for a planar hydrodynamic simulation of a strong, steady-state shock in a subspace of the warm dense matter (WDM) regime. Specifically, we consider a plasma of fully degenerate electrons with moderate-to-strongly coupled ions. Since the WDM ion and electron transport coefficients and equation of state differ markedly from their non-degenerate, weak-coupling equivalents, we find thatmore » the structure of a WDM plasma shock notably deviates from the ideal plasma picture.« less

Proper scales for the mean flow and Reynolds shear stress in planar turbulent mixing layers are determined from a scaling patch analysis of the mean continuity and momentum equations. By seeking an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is determined as V_ref=(dδ/dx)U_ref, where dδ/dx is the growth rate of the mixing layer width and U_ref=U_h–U_l is the difference between the velocity of the high speed stream U_h and the velocity of the low speed stream U_l. By seeking an admissible scaling for the mean momentum equation, a proper scale for themore » kinematic Reynolds shear stress is determined as R_uv,ref=U_avgV_ref=[$$\frac{1}{2A_u}$$$$\frac{dδ}{dx}$$]$$U^{2}_{ref}$$ where A_u $$_{=}^{def}$$(U_h–U_l)/(U_h+U_l) is the normalized velocity difference that emerges naturally in the admissible scaling of the mean momentum equation. Self-similar equations for the scaled mean transverse flow V* and Reynolds shear stress $$R^{*}_{uv}$$=R_uv/R_uv,ref are derived from the mean continuity and mean momentum equations. Finally, approximate equations for V* and $$R^{*}_{uv}$$ are developed and found to agree well with experimental data.« less

The identification of processes that locally and approximately dominate dynamical system behavior has enabled significant advances in understanding and modeling nonlinear differential dynamical systems. Conventional methods of dominant process identification involve piecemeal and ad hoc (non-rigorous, informal) scaling analyses to identify dominant balances of governing equation terms and to delineate the spatiotemporal boundaries (boundaries in space and/or time) of each dominant balance. For the first time, we present an objective global measure of the fit of dominant balances to observations, which is desirable for automation, and was previously undefined. Furthermore, we propose a formal definition of the dominant balance identificationmore » problem in the form of an optimization problem. Here, we show that the optimization can be performed by various machine learning algorithms, enabling the automatic identification of dominant balances. Our method is algorithm agnostic and it eliminates reliance upon expert knowledge to identify dominant balances which are not known beforehand.« less