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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

In this work, the saturation physics of ion temperature gradient (ITG) turbulence is probed by studying how amplitudes and scalings with key parameters vary across a hierarchy of reduced models. The models derive from nonlinear fluid equations for toroidal ITG turbulence under approximations to the mode coupling interactions in wavenumber space and the representation of turbulent decorrelation. Mode coupling approximations include local-in-wavenumber treatments like the spectral density of flux in quasilinear theory, a truncation to three nonlinearly interacting waves, and the interactions in a cascade to high radial wavenumber mediated by a single zonal flow. Turbulent decorrelation treatments are based on the triplet correlation time with and without eddy damping. Model fidelity is assessed by the scalings and magnitudes of the squared amplitudes of unstable mode, stable mode, and zonal flow with respect to the flow-damping rate and temperature gradient. It is shown that all models reproduce fundamental scalings, provided they incorporate the coupling of unstable mode, stable mode, and zonal flow. Accurate amplitude prediction requires eddy damping in the triplet correlation time and proper representation of the zonal-flow drive by interactions associated with the radial wavenumber cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Improved prescription for winding an electromagnet

We describe an improvement on the magnetic scalar potential approach to design an electromagnet, which incorporates the need to wind the coil as a helix. Any magnetic field that can be described by a magnetic scalar potential is produced with high fidelity within a Target region; all fields are confined within a larger Return. The helical winding only affects the field in the Return.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Coulomb expansion of a thin dust cloud observed experimentally under afterglow plasma conditions

The Coulomb expansion of a thin cloud of charged dust particles was observed experimentally, in a plasma afterglow. This expansion occurs due to mutual repulsion among positively charged dust particles, after electrons and ions have escaped the chamber volume. In the experiment, a two-dimensional cloud of dust particles was initially levitated in a glow-discharge plasma. The power was then switched off to produce afterglow conditions. The subsequent fall of the dust cloud was slowed by reversing the electric force, to an upward direction, allowing an extended observation. At early time, measurements of the Coulomb expansion in the horizontal direction are found to be accurately modeled by the equation of state for a uniformly charged thin disk. Finally, bouncing from the lower electrode was found to be avoided by lowering the impact velocity <100 mm/s.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
DOE OSTI2021

Consistent coupling algorithms for coupled core-edge simulations of plasma turbulence

Two schemes for coupling gyrokinetic simulations of microturbulence in tokamaks are proposed. The first scheme is based on an additive Schwarz domain decomposition. In this work, we show that, because the goal of turbulence is long-time averages of the dynamics rather than temporal accuracy, the iteration to self-consistency across domains, which is typically required by Schwarz schemes, can be avoided, thereby accelerating the computation. Second, we propose a coupling scheme that relies entirely on the addition of source terms, leaving the boundary conditions arbitrary. The practical motivations for such a scheme are discussed, and forms of the source terms that ensure consistency and stability are derived. The schemes are tested on a nonlinear, one-dimensional model problem, and the first scheme is further tested on the Hasegawa–Wakatani model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Machine learning changes the rules for flux limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock capturing methods. Focusing on flux limiters provides a specific plug-and-play component for existing numerical methods. Since their introduction, an array of flux limiters has been designed. Using the coarse-grained Burgers' equation, we show that flux-limiters may be rank-ordered in terms of their log-error relative to high-resolution data. We then develop a theory to find an optimal flux-limiter and present flux-limiters that outperform others tested for integrating Burgers' equation on lattices with [Formula: see text], and 2x, 3x, 4x, and 8x coarse-grainings. We train a continuous piecewise linear limiter by minimizing the mean-squared misfit to six-grid point segments of high-resolution data, averaged over all segments. While flux limiters are generally designed to have an output of φ(r) = 1 at a flux ratio of r = 1, our limiters are not bound by this rule and yet produce a smaller error than standard limiters. Here we find that our machine learned limiters have distinctive features that may provide new rules-of-thumb for the development of improved limiters. Additionally, we use our theory to learn flux-limiters that outperform standard limiters across a range of values (as opposed to at a specific fixed value) of coarse-graining, number of discretized bins, and diffusion parameter. This demonstrates the ability to produce flux limiters that should be more broadly useful than standard limiters for general applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Slow manifold reduction as a systematic tool for revealing the geometry of phase space

Many non-dissipative reduced plasma models can be derived from more fundamental non-dissipative models by restricting to an approximate invariant manifold. I present a general systematic procedure for finding the Hamiltonian formulation of a plasma model that can be derived in this manner. Several illustrative examples are considered in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗
DOE OSTI2023

A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations

Here, we introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions verify the energy cascade phenomenon. To our knowledge, this is the first numerical scheme that can capture the long time asymptotic behavior of solutions to those isotropic 3-wave kinetic equations, where the energy cascade can be observed. Our numerical energy cascade rates are in good agreement with previously obtained theoretical results. The finite volume scheme given here relies on a new identity, allowing one to reduce the number of terms needed in the collision operators.

3-wave equation↗
DOE OSTI2022

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing equations of motion are used: (1) a quasistatic formulation that effectively describes smooth deformations, and (2) a fully dynamic formulation that captures large changes in the sheet's velocity. The former is a differential-algebraic system of equations integrated implicitly in time, while the latter is a set of ordinary differential equations (ODEs) integrated explicitly. We adopt a hybrid integration scheme to adaptively alternate between the quasistatic and dynamic representations as appropriate. Further, we demonstrate the capacity of this method to effectively simulate a variety of crumpling phenomena. Finally, we show that statistical properties, notably the accumulation of creases under repeated loading, as well as the area distribution of facets, are consistent with experimental observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Spatial coupling of gyrokinetic simulations, a generalized scheme based on first-principles

In this paper, we present a scheme that spatially couples two gyrokinetic codes using first-principles. Coupled equations are presented and a necessary and sufficient condition for ensuring accuracy is derived. This new scheme couples both the field and the particle distribution function. The coupling of the distribution function is only performed once every few time-steps, using a five-dimensional (5D) grid to communicate the distribution function between the two codes. This 5D grid interface enables the coupling of different types of codes and models, such as particle and continuum codes, or delta-f and total-f models. Transferring information from the 5D grid to the marker particle weights is achieved using a new resampling technique. Demonstration of the coupling scheme is shown using two XGC gyrokinetic simulations for both the core and edge. We also apply the coupling scheme to two continuum simulations for a one-dimensional advection–diffusion problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗
DOE OSTI2021

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ 2 ) in the L∞(Ω) norm, which is optimal considering the O(δ 2 ) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Finally, based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ 2 ) convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Divergence of Velocity Fields in Electrochemical Systems

The passage of current through electrochemical systems results in the development of concentration gradients in the electrolytic phase that can be modeled using concentrated solution theory. Application of this theory requires knowledge of three concentration-dependent transport coefficients, which are often taken to be conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity. The governing diffusion equation for molar concentration contains two additional terms - the thermodynamic factor which is related to activity of the electrolytic species and the solvent velocity. The main advance in this paper is the derivation of an expression for the divergence of the solvent velocity. Solving this equation requires knowledge of the partial molar volume of the electrolyte. Analogous expressions are derived for the mass average and molar average velocities. These velocities occur naturally in the diffusion equation if concentration is expressed as weight fraction and mole fraction of the electrolytic species, respectively.

diffusion↗
DOE OSTI2021

Differentiating densities on smooth manifolds

Lebesgue integration of derivatives of strongly-oscillatory functions is a recurring challenge in computational science and engineering. Integration by parts is an effective remedy for huge computational costs associated with Monte Carlo integration schemes. In case of Lebesgue integrals over a smooth manifold, however, integration by parts gives rise to a derivative of the density implied by charts describing the domain manifold. This paper focuses on the computation of that derivative, which we call the density gradient function, on general smooth manifolds. We analytically derive formulas for the density gradient and present examples of manifolds determined by popular differential equation-driven systems. Furthermore, we highlight the significance of the density gradient by demonstrating a numerical example of Monte Carlo integration involving oscillatory integrands.

97 MATHEMATICS AND COMPUTING↗