Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical diffusion”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2017

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

We develop a numerical model to study the time-dependent modulation of galactic cosmic rays in the inner heliosphere. In the model, a time-delayed modified Parker heliospheric magnetic field (HMF) and a new diffusion coefficient model, NLGCE-F, from Qin and Zhang, are adopted. In addition, the latitudinal dependence of magnetic turbulence magnitude is assumed to be ∼(1+sin{sup 2}θ)/2 from the observations of Ulysses, and the radial dependence is assumed to be ∼r{sup S}, where we choose an expression of S as a function of the heliospheric current sheet tilt angle. We show that the analytical expression used to describe the spatial variation of HMF turbulence magnitude agrees well with the Ulysses, Voyager 1, and Voyager 2 observations. By numerically calculating the modulation code, we get the proton energy spectra as a function of time during the recent solar minimum, it is shown that the modulation results are consistent with the Payload for Antimatter-Matter Exploration and Light-nuclei Astrophysics measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

The quasi-linear diffusion of particles from resonant interactions with a spectrum of electrostatic waves is investigated theoretically, extending results obtained for no magnetic field and for strong magnetic fields to cases where the ambient magnetic field which organizes azimuthally symmetric wave and particle distributions does not have to be taken into consideration in evaluating the local interaction. The derivation of the governing equations is explained, and numerical results are presented in extensive graphs and characterized in detail. Slow-mode ion-acoustic waves are shown to be unstable under the plasma conditions studied, and the dependence of resonant-ion diffusion rates with pitch angle, speed, and the distribution of wave energy in wavenumber space is explored. The implications of the present findings for theoretical models of the earth bow shock and plasma-sheet boundary layer are indicated.

Dusenbery, P. B.↗
NASA NTRS1992

Effects of training on muscle O2 transport at VO2max

To quantify the relative contributions of convective and peripheral diffusive components of O2 transport to the increase in leg O2 uptake (VO2leg) at maximum O2 uptake (VO2max) after 9 wk of endurance training, 12 sedentary subjects (age 21.8 +/- 3.4 yr, VO2max 36.9 +/- 5.9 ml.min-1.kg-1) were studied. VO2max, leg blood flow (Qleg), and arterial and femoral venous PO2, and thus VO2leg, were measured while the subjects breathed room air, 15% O2, and 12% O2. The sequence of the three inspirates was balanced. After training, VO2max and VO2leg increased at each inspired O2 concentration [FIO2; mean over the 3 FIO2 values 25.2 +/- 17.8 and 36.5 +/- 33% (SD), respectively]. Before training, VO2leg and mean capillary PO2 were linearly related through the origin during hypoxia but not during room air breathing, suggesting that, at 21% O2, VO2max was not limited by O2 supply. After training, VO2leg and mean capillary PO2 at each FIO2 fell along a straight line with zero intercept, just as in athletes (Roca et al. J. Appl. Physiol. 67: 291-299, 1989). Calculated muscle O2 diffusing capacity (DO2) rose 34% while Qleg increased 19%. The relatively greater rise in DO2 increased the DO2/Qleg, which led to 9.9% greater O2 extraction. By numerical analysis, the increase in Qleg alone (constant DO2) would have raised VO2leg by 35 ml/min (mean), but that of DO2 (constant Qleg) would have increased VO2leg by 85 ml/min, more than twice as much. The sum of these individual effects (120 ml/min) was less (P = 0.013) than the observed rise of 164 ml/min (mean). This synergism (explained by the increase in DO2/Qleg) seems to be an important contribution to increases in VO2max with training.

NASA Discipline Musculoskeletal↗
NASA NTRS2001

Concentration Field of Reactants and Products Species in a Reacting Vortex Ring

The proposed paper will present experimental and numerical results on the concentration fields of both reactants and products species in a reacting vortex ring that is generated from the interaction between a diffusion flame and a laminar vortex ring. Flame-vortex interactions are canonical configurations used to study the underlying processes occurring in complicated turbulent reacting flows. This type of configuration contains many of the fundamental aspects of the coupling between fluid dynamics and combustion that could be investigated with more controllable conditions than are possible under direct investigations of turbulent flames. The current configuration has been studied experimentally by Chen and Dahm and Chen et al. under microgravity conditions, and by Park and Shin, and You et al. under normal gravity conditions. This configuration is similar to that used in the analyses of Karagozian and Manda of their 2-D vortex pair in which both fuel and entrained oxidizer are present. The vortex ring used in this study is generated by issuing methane into an air environment through the exit of an axisymmetric nozzle. The experiments were conducted under microgravity conditions in order to remove the undesirable effects of buoyancy that can affect both the flame structure and ring dynamics resulting in possibly asymmetric and nonrepeatable interactions. The experimental technique of diode laser wavelength modulation spectroscopy (WMS) is used to measure concentration fields of reactants, CH4 and O2, products, H2O, CO2, OH, and temperature fields which can be inferred from either line pairs of O2 or OH lines. This technique has been investigated previously by Silver and Bomse et al. This is the first time that the technique has been applied to reacting vortex rings under microgravity conditions. The effect of ring circulation and fuel volume on the species concentration fields will be investigated. The experimental results will be compared to the current numerical results, and used to validate the numerical studies. In addition, the existence of burned cores during the interactions will be determined, and the increase in reactant consumption with increased ring circulation will be examined. Numerical studies were also conducted by solving the Navier-Stokes and mixture fraction equations with the assumptions of unity Lewis and Schmidt numbers. Equilibrium chemistry and flamelet libraries were used to obtain the temperature and species mass fraction fields. The numerical results will serve as guidelines in conducting the experimental studies. Ring circulation and fuel volume effects on the interactions and species concentration fields will be investigated and compared to experimental results.

Chen, Shin-Juh↗
DOE OSTI2019

Beyond the effectiveness factor: Multi-step reactions with intraparticle diffusion limitations

Though common in many industrial chemical processes, multi-step reactions occurring within porous catalyst particles provide significant challenges to previously established modeling frameworks. In this work, a system of reaction-diffusion equations is solved analytically via eigenanalysis. The intraparticle concentration profiles are integrated over the particle volume to obtain effectiveness factors for each reacting species, referred to herein as a multi-step effectiveness vector (MEV). The MEV solution is tested for the case of uniform flow past a stationary catalyst particle with a state-of-the-art, multi-step reaction scheme for fluid catalytic cracking (FCC). Outputs from particle-resolved direct numerical simulation (DNS) are compared to outputs from ordinary differentials with effective reaction closures coming from the MEV solution, the classic single-step effectiveness factor (SEF) (R. Aris, 'The mathematical theory of diffusion and reaction in permeable catalysts: The theory of the steady state,' Oxford University Press, 1975), and utilizing the intrinsic rates as-is. When compared to DNS, the MEV solution shows excellent agreement for the formation of all species and quantitatively captures the intraparticle concentration profiles. By contrast, the intrinsic treatment shows an over-prediction for product formation and the SEF treatment shows mixed levels of accuracy that depend upon the reaction coupling. Specifically, the SEF treatment accurately characterizes product formation if the kinetic scheme is weakly coupled but shows significant departure if stronger coupling is present. The computational cost associated with the MEV solution is associated with eigendecomposition of the Thiele matrix, an N x N matrix where N is the number of reacting components. Overall, the method is shown to be relatively easy to implement and may significantly enhance the fidelity of chemical reactor simulations that employ multi-step reaction schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The Role of Kinetic Instabilities and Waves in Collisionless Magnetic Reconnection

Magnetic reconnection converts magnetic field energy into particle energy by breaking and reconnecting magnetic field lines. Magnetic reconnection is a kinetic process that generates a wide variety of kinetic waves via wave-particle interactions. Kinetic waves have been proposed to play an important role in magnetic reconnection in collisionless plasmas by, for example, contributing to anomalous resistivity and diffusion, particle heating, and transfer of energy between different particle populations. These waves range from below the ion cyclotron frequency to above the electron plasma frequency and from ion kinetic scales down to electron Debye length scales. This review aims to describe the progress made in understanding the relationship between magnetic reconnection and kinetic waves. We focus on the waves in different parts of the reconnection region, namely, the diffusion region, separatrices, outflow regions, and jet fronts. Particular emphasis is placed on the recent observations from the Magnetospheric Multiscale (MMS) spacecraft and numerical simulations, which have substantially increased the understanding of the interplay between kinetic waves and reconnection. Some of the ongoing questions related to waves and reconnection are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Uncovering grain and subgrain microstructure at the scale of additive manufacturing melt tracks with a scalable cellular automaton solidification model

Metal additive manufacturing, characterized by rapid solidification, yields refined grains with a distinctive cellular subgrain microstructure that plays a pivotal role in determining material properties. Due to the significant computational expense demanded to simulate the required physics with submicron spatial resolution, their numerical simulations have been limited to proof-of-concept studies to either 2D or small subregions of a melt pool. In this study, an open-source, scalable, solidification code, muMatScale, based on the cellular automaton method, has been developed to predict the grain and the underlying subgrain microstructure over an entire melt pool. The model incorporates flexible parallelization schemes, utilizing MPI and OpenMP GPU Offloading, in addition to appropriate multi-physics specific to non-equilibrium rapid solidification in AM. The impact of nucleation parameters on grain microstructures was investigated with a focus on grain size variations and morphology transitions. With selected nucleation parameters, the simulation predicted the grain size, subgrain morphology, crystallographic orientation, and microsegregation aligned with experimental measurements. The model demonstrates that epitaxial grain growth is a dominant factor at the melt pool boundary, influencing grain size variation under different grain sizes in the build plate while maintaining consistent primary dendrite arm spacing under identical thermal conditions. Here, the highly efficient numerical model enables large-scale simulations with a spatial resolution of 100 nm or less, unveiling unprecedented insights into thermal and solutal diffusion driven grain growth, and the subgrains with microsegregation within grains in 3D across scales. muMatScale will enable the linking of submicron length-scale microstructure to part-level material behavior by investigating fundamental solidification problems at the intercellular scale in many-track and many-layer builds.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Exponential time differencing for the tracer equations appearing in primitive equation ocean models

The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several equations may be added to and coupled to the dynamics system. In many relevant situations, the time-step requirements of explicit methods imposed by the transport and mixing in the vertical direction are more restrictive than those for the horizontal, and this may cause the need to use very small time steps if a fully explicit method is employed. To overcome this issue, we propose an exponential time differencing (ETD) solver where the vertical terms (transport and diffusion) are treated with a matrix exponential, whereas the horizontal terms are dealt with in an explicit way. In this work, we investigate numerically the computational speed-ups that can be obtained over other semi-implicit methods, and we analyze the advantages of the method in the case of multiple tracers.

42 ENGINEERING↗
DOE OSTI2023

Toward DMC Accuracy Across Chemical Space with Scalable Δ-QML

In the past decade, quantum diffusion Monte Carlo (DMC) has been demonstrated to successfully predict the energetics and properties of a wide range of molecules and solids by numerically solving the electronic many-body Schrödinger equation. With O(N 3 ) scaling with the number of electrons N, DMC has the potential to be a reference method for larger systems that are not accessible to more traditional methods such as CCSD(T). Assessing the accuracy of DMC for smaller molecules becomes the stepping stone in making the method a reference for larger systems. We show that when coupled with quantum machine learning (QML)-based surrogate methods, the computational burden can be alleviated such that quantum Monte Carlo (QMC) shows clear potential to undergird the formation of high-quality descriptions across chemical space. We discuss three crucial approximations necessary to accomplish this: the fixed-node approximation, universal and accurate references for chemical bond dissociation energies, and scalable minimal amons-set-based QML (AQML) models. Numerical evidence presented includes converged DMC results for over 1000 small organic molecules with up to five heavy atoms used as amons and 50 medium-sized organic molecules with nine heavy atoms to validate the AQML predictions. Finally, numerical evidence collected for Δ-AQML models suggests that already modestly sized QMC training data sets of amons suffice to predict total energies with near chemical accuracy throughout chemical space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1972

Composition dependence of ion diffusion coefficients in gas mixtures at arbitrary field strengths

Expressions for the diffusion coefficient of ions in gas mixtures are obtained from momentum transfer theory, and are given in terms of the diffusion coefficients and drift velocities of the ions in the pure component gases. Blanc's law holds exactly at all field strengths if the mean free time between collisions is independent of velocity (Maxwell model), but otherwise there may be either positive or negative deviations from Blanc's law at high fields. Such deviations are of comparable magnitude for the diffusion coefficients and the mobility, but are not identical. Specific cases of inverse-power potentials are treated in further detail, and some numerical examples are given for rigid-sphere interactions.

Whealton, J. H.↗
NASA NTRS1974

Quasi-three-dimensional flow solution by meridional plane analysis

A computer program has been developed to obtain subsonic or shockfree transonic, nonviscous flow analysis on the hub-shroud mid-channel flow surface of a turbomachine. The analysis may be for any annular passage, with or without blades. The blades may be fixed or rotating and may be twisted and leaned. The flow may be axial, radial or mixed. Blade surface velocities over the entire blade are approximated based on the rate of change of angular momentum. This gives a 3-D flow picture based on a 2-D analysis. The paper discusses the method used for the program and shows examples of the type of passages and blade rows which can be analyzed. Also, some numerical examples are given to show how the program can be used for practical assistance in design of blading, annular passages, and annular diffusers.

Katsanis, T.↗
NASA NTRS1975

Investigation B: Laminar confined coaxial entrance flow with heat generation

The results of a parametric study on the entrance flow region in a gas core nuclear reactor are presented. The physical system is modeled as laminar confined, coaxial flow with heat generation in the inner fluid. The governing equations include the boundary layer approximations and the assumptions of only radial radiative transport of energy represented as an energy diffusion term. The Von Mises transformation and a zeta transformation are used to transform the equations into nonlinear nonhomogeneous convective-diffusion equations. A unique combination of forward and backward difference equations which yields accurate results at moderate computational times, is used in the numerical method. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

Bobba, G. K. M.↗
NASA NTRS1974

Quasi-three-dimensional flow solution by meridional plane analysis

A computer program has been developed to obtain subsonic or shock-free transonic, nonviscous flow analysis on the hub-shroud midchannel flow surface of a turbomachine. The analysis may be for any annular passage, with or without blades. The blades may be fixed or rotating and may be twisted and leaned. The flow may be axial, radial, or mixed. Blade surface velocities over the entire blade are approximated, based on the rate of change of angular momentum. This gives a three-dimensional flow picture based on a two-dimensional analysis. This paper discusses the method used for the program and shows examples of the type of passages and blade rows which can be analyzed. Also, some numerical examples are given to show how the program can be used for practical assistance in design of blading, annular passages, and annular diffusers.

Katsanis, T.↗
NASA NTRS1979

Warm/cold cloud processes

Technical assistance continued in support of the Atmospheric Cloud Physics Laboratory is discussed. A study of factors affecting warm cloud formation showed that the time of formation during an arbitrary expansion is independent of carrier gas composition for ideal gases and independent of aerosol concentration for low concentrations of very small aerosols. Equipment and procedures for gravimetric evaluation of a precision saturator were laboratory tested. A numerical feasibility study was conducted for the stable levitation of charged solution droplets by an electric field in a one-g static diffusion chamber. The concept, operating principles, applications, limits, and sensitivity of the levitation technique are discussed.

Bowdle, D. A.↗
NASA NTRS1982

Features of a reattaching turbulent shear layer subject to an adverse pressure gradient

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step with superimposed adverse pressure gradient. Mean velocities, Reynolds stresses and triple-products measured by a laser Doppler velocimeter are presented for two cases of adverse pressure gradient. Mixing lengths, eddy viscosities, production, convection, turbulent diffusion, and dissipation terms are extracted from the data. These data are compared with various mixing length and eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and the algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model

Driver, D. M.↗
NASA NTRS1985

The anisotropic radiative transfer problem in optically thick, strongly magnetized plasma - A comparison of results

The accuracy of four different methods for solving the coherent radiative transfer problem in a strongly magnetized plasma is compared. Specific attention is given to the case of a semi-infinite homogeneous plasma with a magnetic field perpendicular to the surface. The four approaches evaluated were: diffusion approximation schemes; the generalized H-function method of Silant'ev (1982) the Feautrier method of Nagel (1981) and the integral equation approach of Meszares and Bonazzola (1981). It is found that the coupled diffusion approximation schemes of Nagel (1981) and Kaminker et al. (1982) provided satisfactory results and were more efficient in many cases than direct numerical methods.

Pavlov, G. G.↗