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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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Simultaneous numerical representation of soil microsite production and consumption of carbon dioxide, methane, and nitrous oxide using probability distribution functions

Production and consumption of nitrous oxide (N 2 O), methane (CH 4 ), and carbon dioxide (CO 2 ) are affected by complex interactions of temperature, moisture, and substrate supply, which are further complicated by spatial heterogeneity of the soil matrix. This microsite heterogeneity is often invoked to explain non-normal distributions of greenhouse gas (GHG) fluxes, also known as hot spots and hot moments. To advance numerical simulation of these belowground processes, we expanded the Dual Arrhenius and Michaelis-Menten (DAMM) model, to apply it consistently for all three GHGs with respect to the biophysical processes of production, consumption, and diffusion within the soil, including the contrasting effects of oxygen (O 2 ) as substrate or inhibitor for each process. High-frequency chamber-based measurements of all three GHGs at the Howland Forest (ME, USA) were used to parameterize the model using a multiple constraint approach. The area under a soil chamber is partitioned according to a bivariate lognormal probability distribution function (PDF) of carbon (C) and water content across a range of microsites, which leads to a PDF of heterotrophic respiration and O 2 consumption among microsites. Linking microsite consumption of O 2 with a diffusion model generates a broad range of microsite concentrations of O 2 , which then determines the PDF of microsites that produce or consume CH 4 and N 2 O, such that a range of microsites occurs with both positive and negative signs for net CH 4 and N 2 O flux. Results demonstrate that it is numerically feasible for microsites of N 2 O reduction and CH 4 oxidation to co-occur under a single chamber, thus explaining occasional measurement of simultaneous uptake of both gases. Simultaneous simulation of all three GHGs in a parsimonious modeling framework is challenging, however it increases confidence that agreement between simulations and measurements is based on skillful numerical representation of processes across a heterogeneous environment.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

A GENERALIZED TWO-COMPONENT MODEL OF SOLAR WIND TURBULENCE AND AB INITIO DIFFUSION MEAN-FREE PATHS AND DRIFT LENGTHSCALES OF COSMIC RAYS

We extend a two-component model for the evolution of fluctuations in the solar wind plasma so that it is fully three-dimensional (3D) and also coupled self-consistently to the large-scale magnetohydrodynamic equations describing the background solar wind. The two classes of fluctuations considered are a high-frequency parallel-propagating wave-like piece and a low-frequency quasi-two-dimensional component. For both components, the nonlinear dynamics is dominanted by quasi-perpendicular spectral cascades of energy. Driving of the fluctuations by, for example, velocity shear and pickup ions is included. Numerical solutions to the new model are obtained using the Cronos framework, and validated against previous simpler models. Comparing results from the new model with spacecraft measurements, we find improved agreement relative to earlier models that employ prescribed background solar wind fields. Finally, the new results for the wave-like and quasi-two-dimensional fluctuations are used to calculate ab initio diffusion mean-free paths and drift lengthscales for the transport of cosmic rays in the turbulent solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A thermodynamic study of shear banding in polymer solutions

Although shear banding is a ubiquitous phenomenon observed in soft materials, the mechanisms that give rise to shear-band formation are not always the same. In this work, we develop a new two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics. The model is based on the hypothesis that the direct coupling between polymer stress and concentration is the driving mechanism of steady shear-band formation. To obtain smooth banded profiles in the two-fluid framework, a new stress-diffusive term is added to the time evolution equation for the conformation tensor. The advantage of the new model is that the differential velocity is treated as a state variable. This allows a straightforward implementation of the additional boundary conditions arising from the derivative diffusive terms with respect to this new state variable. To capture the overshoot of the shear stress during the start of a simple shear flow, we utilize a nonlinear Giesekus relaxation. Moreover, we include an additional relaxation term that resembles the term used in the Rouse linear entangled polymer model to account for convective constraint release and chain stretch to generate the upturn of the flow curve at large shear rates. Numerical calculations performed for cylindrical Couette flow confirm the independency of the solution from the deformation history and initial conditions. Furthermore, we find that stress-induced migration is the responsible diffusive term for steady-state shear banding. Because of its simplicity, the new model is an ideal candidate for the use in the simulation of more complex flows.

42 ENGINEERING↗
DOE OSTI2017

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Pan, Wenxiao↗
DOE OSTI2016

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng–Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young–Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young–Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young–Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Application of Dislocation Theory to Minimize Defects in Artificial Solids Built with Nanocrystal Building Blocks

Conspectus. Oriented atomic attachment of colloidal inorganic nanocrystals represents a powerful synthetic method for preparing complex inorganic superstructures. Examples include fusion of nanocrystals into dimer and superlattice structures. If the attachment were perfect throughout, then the resulting materials would have single crystal-like alignment of the individual nanocrystals' atomic lattices. While individual colloidal nanocrystals typically are free of many defects, there are a multitude of pathways that can generate defects upon nanocrystal attachment. These attachment generated defects are typically undesirable, and thus developing strategies to favor defect-free attachment or heal defective interfaces are essential. There may also be some cases where attachment-derived defects are desirable. In this Account, we summarize our current understanding of how these defects arise, in order to offer guidance to those who are designing nanocrystal derived solids. The small size of inorganic nanocrystals means short diffusion lengths to the surface, which favor the formation of nanocrystal building blocks with pristine atomic structures. Upon attachment, however, there are numerous pathways that can lead to atomic scale defects, and bulk crystal dislocation theory provides an invaluable guide to understanding these phenomena. As an example, an atomic step edge can be incorporated into the interface leading to an extra half-plane of atoms, known as an edge dislocation. These dislocations can be well described by the Burgers vector description of dislocations, which geometrically identifies planes in which a dislocation can move. Our in situ measurements have verified that bulk dislocation theory predictions for 1D defects hold true at few-nanometer length scales in PbTe and CdSe nanocrystal interfaces. Ultimately, the applicability of dislocation theory to nanocrystal attachment enables the predictive design of attachment to prevent or facilitate healing of defects upon nanocrystal attachment. We applied similar logic to understand formation of planar (2D) defects such as stacking faults upon nanocrystal attachment. Again concepts from bulk crystal defect crystallography can identify attachment pathways that can prevent or deterministically form planar defects upon nanocrystal attachment. The concepts we discuss work well for identifying favorable attachment geometries for nanocrystal pairs ; however it is currently unclear how to translate these ideas to near-simultaneous multiparticle attachment. Geometric frustration, which prevents nanocrystal rotation, and yet-to-be considered defect generation pathways unique to multiparticle attachment complicate defect-free superlattice attachment. New imaging methods now allow for the direct observation of local attachment trajectories and may enable improved understanding of such multiparticle phenomena. With further refinement, a unified framework for understanding and ultimately eliminating structural defects in fused nanocrystal superstructures may well be achievable in coming years.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Grid resolution requirement of chemical explosive mode analysis for large eddy simulations of premixed turbulent combustion

Full Article Figures & data References Citations Metrics Reprints & Permissions Read this article Abstract The grid resolution requirement for trustworthy Chemical Explosive Mode Analysis (CEMA) in Large Eddy Simulation (LES) of premixed turbulent combustion is proposed. Explicit filtering, to emulate the effect of the LES filter, is applied to one-dimensional laminar flame and three-dimensional planar turbulent flames across a wide range of Karlovitz numbers (5 - 239). The identification of the flame front by CEMA is found relatively insensitive to the cell size (Δ), while the combustion mode identification shows more significant sensitivity. Specifically, increasing Δ falsely enhances the auto-ignition and local extinction modes and suppresses the diffusion-assisted mode. Limited dependence of the CEMA performance on the turbulent combustion regime (Karlovitz number) is observed. A simple grid size criterion for reliable CEMA mode identification in LES is proposed as Δ ≲ δ L /2; The criterion can be relaxed to Δ ≲ δ L in the laminar flame limit. Furthermore, theoretical analysis is conducted on an idealised chemistry-diffusion system. The effects of the filtering process and turbulence on the local combustion mode are demonstrated, which is consistent with the numerical observations. Further, by incorporating turbulent combustion models in CEMA, potential improvement in identifying local combustion modes can be expected.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗
DOE OSTI2018

A Fast and Accurate Method of Radiation Hydrodynamics Calculation in Spherical Symmetry

We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation, and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A front-fixing finite element method for pricing American options under regime-switching jump-diffusion models

A front-fixing finite element method is applied to solve the partial integro-differential equations (PIDEs) arising in pricing American options under Markov-modulated jump-diffusion models with the free boundaries feature. For this purpose, we used a front-fixing method to transform the pricing problem into a nonlinear parabolic integro-differential equation on a fixed domain. Then the variational form of the resulting problem is solved by a finite element method. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence of the proposed method for the pricing problem and compare its accuracy to some recent works on pricing American options under regime-switching jump-diffusion models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

79 ASTRONOMY AND ASTROPHYSICS↗
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

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The effects of phase decorrelation on the dynamics of the bump-on-tail instability

The dynamics of the bump-on-tail instability has been studied. The novelty of the work is the analysis of how the bump-on-tail dynamics is affected by an extrinsic stochastisation of the phase of the wave-particle interaction; here referred to as phase decorrelation. For this purpose, a nonlinear Monte Carlo model has been developed. When the characteristic time scale for macroscopic phase decorrelation becomes shorter than time scales of nonlinear wave-particle dynamics, the system may be described quasilinearly, with the phase decorrelation being replaced by a quasilinear diffusion coefficient in particle energy. A purely quasilinear Monte Carlo model, which is typically less computationally demanding than the fully nonlinear description due to the reduced dimensionality of phase space, has been developed for comparison. In this paper, parameter regimes, where the nonlinear and the quasilinear descriptions quantitatively agree on a macroscopic level, have been investigated, using combined theoretical and numerical analyses. Qualitative effects on the macroscopic dynamics by the presence of phase decorrelation and/or by structures of the energy distribution function in the proximity of the wave-particle resonance are also studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bound-preserving finite element approximations of the Keller–Segel equations

We report this paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the L ∞ (Ω)-norm to the L 1 (Ω)-norm limiting the growth of the singularity when supported on a macroelement.

97 MATHEMATICS AND COMPUTING↗