Search NASA⌕ Search

SEARCH · Search NASA

Results for “diffusion equation”

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 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Broadband light sources based on InAs/InGaAs metamorphic quantum dots

We propose a design for a semiconductor structure emitting broadband light in the infrared, based on InAs quantum dots (QDs) embedded into a metamorphic step-graded In{sub x}Ga{sub 1−x}As buffer. We developed a model to calculate the metamorphic QD energy levels based on the realistic QD parameters and on the strain-dependent material properties; we validated the results of simulations by comparison with the experimental values. On this basis, we designed a p-i-n heterostructure with a graded index profile toward the realization of an electrically pumped guided wave device. This has been done by adding layers where QDs are embedded in In{sub x}Al{sub y}Ga{sub 1−x−y}As layers, to obtain a symmetric structure from a band profile point of view. To assess the room temperature electro-luminescence emission spectrum under realistic electrical injection conditions, we performed device-level simulations based on a coupled drift-diffusion and QD rate equation model. On the basis of the device simulation results, we conclude that the present proposal is a viable option to realize broadband light-emitting devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Improved analytic modeling of the linear Rayleigh–Taylor instability with plasma transport

The Rayleigh–Taylor (R–T) instability with transport effects has long been studied analytically in the neutral fluid regime. How this picture may differ in plasmas has been given less consideration, however. Leveraging previous numerical simulations with plasma viscosity and diffusion of R–T at a binary plasma interface, we show how plasma transport and kinetic effects alter the linear R–T dispersion relation. Our insight informs a much improved analytical dispersion relation, which better matches the simulation data than previously established models. Additionally, we demonstrate the importance of employing asymptotically correct viscosity coefficients in fluid codes for accurately capturing plasma R–T growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Conforming and nonconforming virtual element methods for elliptic problems

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1 - and L 2 -error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Anharmonic phonon damping enhances the T c of BCS-type superconductors

In this study, a theory of superconductivity is presented where the effect of anharmonicity, as entailed in the acoustic, or optical, phonon damping, is explicitly considered in the pairing mechanism. The gap equation is solved including diffusive Akhiezer damping for longitudinal acoustic phonons or Klemens damping for optical phonons, with a damping coefficient which, in either case, can be directly related to the Grüneisen parameter and hence to the anharmonic coefficients in the interatomic potential. The results show that the increase of anharmonicity has a strikingly nonmonotonic effect on the critical temperature T c . The optimal damping coefficient yielding maximum T c is set by the velocity of the bosonic mediator. This theory may open up unprecedented opportunities for material design where T c may be tuned via the anharmonicity of the interatomic potential, and presents implications for the superconductivity in the recently discovered hydrides, where anharmonicity is very strong and for which the anharmonic damping is especially relevant.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Electrochemical Reactivity of Hydrogen Storage Materials: Exploring Borohydride and Hydrazinium Salt Mixtures

Electrochemical characterization of hydrogen storage materials was conducted in a non-aqueous environment to investigate the direct electrochemical release and consumption of hydrogen and the potential for regeneration. We first address the challenge of minimal solubility of the synthetic precursors, sodium borohydride (NaBH 4 ) and hydrazinium bromide (N 2 H 5 Br), in both organic and inorganic solvents. We next determine and calibrate a reference electrode formulation compatible with our non-aqueous media and analytes that demonstrates a stable reference potential. We employ cyclic voltammetry (CV) to characterize the precursors and mixtures thereof. Each CV peak is assigned to a corresponding electrochemical reaction. Using the rate-dependent CV method and Randles–Ševčík equation, we calculate the diffusion coefficient of each chemical (NaBH 4 and N 2 H 5 Br). Analysis of the CVs, coupled with 11B NMR analysis, reveals a room temperature chemical transformation of NaBH 4 and N 2 H 5 Br mixtures into hydrazine borane (N 2 H 4 BH 3 ). These results are particularly significant, considering the limited information available on the electrochemical characterization of metal borohydride and hydrazinium salt in non-aqueous media. This work establishes a foundation for adapting a non-aqueous electrochemical system to further study the borohydride family of chemistries and to design and develop electrochemical devices for direct electrical and chemical energy interconversion with hydrogen storage materials.

08 HYDROGEN↗
DOE OSTI2021

TMAP7

TMAP7 was developed by the Fusion Safety Program at INL primarily as a safety analysis code, to analyze tritium retention and loss in fusion reactor structures and systems during normal operation and accident conditions. TMAP7 solves one-dimensional thermal- and mass-diffusive transport and trapping equations for transport through structures, across the interface between enclosures and structures, and zero dimensional fluid transport between enclosures.

Humrickhouse, PaulW.↗
DOE OSTI2021

TMAP4

TMAP4 was developed by the Fusion Safety Program at INL primarily as a safety analysis code, to analyze tritium retention and loss in fusion reactor structures and systems during normal operation and accident conditions. TMAP4 solves one-dimensional thermal- and mass-diffusive transport and trapping equations for transport through structures, across the interface between enclosures and structures, and zero dimensional fluid transport between enclosures.

Humrickhouse, PaulW.↗
DOE OSTI2020

The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers

The design and implementation of a new framework for adaptive mesh refinement calculations are described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list" that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both nonrelativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Abstract. Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics.

58 GEOSCIENCES↗
NASA NTRS1973

The neutral-atmosphere temperature instrument.

The determination of the temperature of the neutral gas at the location of the satellite is based on measurement of the velocity distribution of the molecular nitrogen. Measurement of the thermal-velocity component in the presence of the free-stream velocity will be obtained through application of the velocity-scan technique and, independently, through use of a baffle technique. A 3-cm diameter spherical sampling chamber with a 0.5-cm diameter precisely knife-edged orifice is located at the satellite equator to permit free diffusion of atmosphere gases between the chamber interior and the atmosphere. The spherical chamber is connected through a high-conductance tube to a quadrupole mass-spectrometer sensor to permit accurate quantitative evaluation of the density of the gas.

Spencer, N. W.↗
NASA NTRS1977

Model for premixed turbulent flames

Flame speed and mean degree of reaction profiles are determined for an ensemble mean one-dimensional premixed turbulent flame. Elementary closure models are employed to treat turbulence closure problems arising from the nonlinear convective and chemical reaction rate terms in the time-dependent fuel conservation equation; a constant eddy diffusivity is useed to model correlation terms derived from the convective term. An expression developed for fuel consumption is solved to obtain the turbulent flame speed and the variation of mean fuel mass fraction across the flame. Comparison of the numerical analysis with experimental data indicates the importance of the quenching of the combustion reaction in high-wavenumber eddies.

Gouldin, F. C.↗
NASA NTRS1978

A three-dimensional turbulent compressible flow model for ejector and fluted mixers

A three dimensional finite element computer code was developed to analyze ejector and axisymmetric fluted mixer systems whose flow fields are not significantly influenced by streamwise diffusion effects. A two equation turbulence model was used to make comparisons between theory and data for various flow fields which are components of the ejector system, i.e., (1) turbulent boundary layer in a duct; (2) rectangular nozzle (free jet); (3) axisymmetric nozzle (free jet); (4) hypermixing nozzle (free jet); and (5) plane wall jet. Likewise, comparisons of the code with analytical results and/or other numerical solutions were made for components of the axisymmetric fluted mixer system. These included: (1) developing pipe flow; (2) developing flow in an annular pipe; (3) developing flow in an axisymmetric pipe with conical center body and no fluting and (4) developing fluted pipe flow. Finally, two demonstration cases are presented which show the code's ability to analyze both the ejector and axisymmetric fluted mixers.

Rushmore, W. L.↗
NASA NTRS1977

Evolution of weak disturbances in inert binary mixtures

The evolution of weak disturbances in inert binary mixtures is determined for the one-dimensional piston problem. The interaction of the dissipative and nonlinear mechanisms is described by Burgers' equation. The binary mixture diffusion mechanisms enter as an additive term in an effective diffusivity. Results for the impulsive motion of a piston moving into an ambient medium and the sinusoidally oscillating piston are used to illustrate the results and elucidate the incorrect behavior pertaining to the associated linear theory.

Rasmussen, M. L.↗
NASA NTRS1983

Numerical study of a ramjet dump combustor flow field

Increased interest in ramjet propulsion systems with higher performance requirements and tighter constraints on system size and weight has lead to the need for improved techniques for analyzing and designing such systems. A computer program has been developed to analyze the turbulent reacting flow field in a ramjet dump combustor configuration. The program solves the axisymmetric Navier-Stokes and species equations throughout the engine diffuser and combustor providing a unified analysis of the complete engine flow field, including flow separation, fuel-air mixing, and preliminary results with chemical reaction. Details of the program development are given, along with a comparison of program results with data from a dump combustor simulation experiment, to allow assessment of the flow field modeling that is employed.

Drummond, J. P.↗
NASA NTRS1982

A basic code for the prediction of transient three-dimensional turbulent flowfields

A primitive pressure-velocity finite difference code has been developed to predict transient three-dimensional turbulent flow. The code is a simplified yet effective prediction procedure for use by persons with little experience in computational fluid dynamics, and into which user-oriented complexities can easily be added. The method is based on the transient two-dimensional Los Alamos SOLA prediction technique for laminar flows. Turbulence is simulated by means of a two-equation turbulence model; species diffusion and buoyancy are also included. Two applications of the code are presented to local destratification near the release structure of a reservoir and to the deflection of a jet entering normally into a uniform cross-flow. Predicted results exhibit good agreement with experimental data, showing that a useful characterization of fully three-dimensional flows is now available.

Busnaina, A. A.↗