SEARCH · Search NASA

Results for “Diffusion equations”

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.

SourceResearch connectionFrom yearThrough year

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

At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Uncoupling Electrokinetic Flow Solutions

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.

58 GEOSCIENCES↗

DOE OSTI2025

TRANSP integrated modeling code for interpretive and predictive analysis of tokamak plasmas

This paper provides a comprehensive review of the TRANSP code, a sophisticated tool for interpretive and predictive analysis of tokamak plasmas, detailing its major capabilities and features. It describes the equations for particle, power, and momentum balance analysis, as well as the poloidal field diffusion equations. The paper outlines the spatial and time grids used in TRANSP and details the equilibrium assumptions and solvers. Various models for heating and current drive and radiation, including updates to the NUBEAM model, are discussed. The handling of large-scale events such as sawtooth crashes and pellet injections is examined, along with the predictive capabilities for advancing plasma profiles. The integration of TRANSP with the ITER Integrated Modeling and Analysis Suite (IMAS) is highlighted, demonstrating enhanced data access and analysis capabilities. Additionally, the paper discusses best practices and continuous integration techniques to enhance TRANSP's robustness. The suite of TRANSP tools, designed for efficient data analysis and simulation, further supports the optimization of tokamak operations and coupling with other tokamak codes. Continuous development and support ensure that TRANSP remains a major code for the analysis of experimental data for controlled thermonuclear fusion, maintaining its critical role in supporting the optimization of tokamak operations and advancing fusion research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Uptake of N 2 O 5 by aqueous aerosol unveiled using chemically accurate many-body potentials

The reactive uptake of N 2 O 5 to aqueous aerosol is a major loss channel for nitrogen oxides in the troposphere. Despite its importance, a quantitative picture of the uptake mechanism is missing. Here we use molecular dynamics simulations with a data-driven many-body model of coupled-cluster accuracy to quantify thermodynamics and kinetics of solvation and adsorption of N 2 O 5 in water. The free energy profile highlights that N 2 O 5 is selectively adsorbed to the liquid–vapor interface and weakly solvated. Accommodation into bulk water occurs slowly, competing with evaporation upon adsorption from gas phase. Leveraging the quantitative accuracy of the model, we parameterize and solve a reaction–diffusion equation to determine hydrolysis rates consistent with experimental observations. We find a short reaction–diffusion length, indicating that the uptake is dominated by interfacial features. The parameters deduced here, including solubility, accommodation coefficient, and hydrolysis rate, afford a foundation for which to consider the reactive loss of N 2 O 5 in more complex solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1986

Pseudo-time algorithms for the Navier-Stokes equations

A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

Swanson, R. C.↗

NASA NTRS1992

Comparison of diffusion and particle drift descriptions of radial transport in the earth's inner magnetosphere

The paper compares two approaches for describing the radial motion of charged particles in the equatorial plane of the earth's magnetosphere: the radial diffusion and the guiding-center drift. For this purpose, a time-dependent observation-based model electrostatic field is computed for the August 1990 storm event, and this field is used to (1) calculate the guiding-center drift of a ring of monoenergetic test particles and (2) compute the specific radial diffusion coefficient and solve the relevant diffusion equation. Generally, only fair agreement was found between the guiding-center and the diffusion calculation approaches. The best agreement could be obtained for the case of a series of small storms rather than for one substantial storm.

Riley, Pete↗

DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

42 ENGINEERING↗

NASA NTRS2000

A Self-Consistent Plasma-Sheath Model for the Inductively Coupled Plasma Reactor

Accurate determination of ion flux on a wafer requires a self-consistent, multidimensional modeling of plasma reactor that adequately resolves the sheath region adjoining the wafer. This level of modeling is difficult to achieve since non-collisional sheath lengths are usually 3-4 orders of magnitude smaller than the reactor scale. Also, the drift-diffusion equations used for ion transport becomes invalid in the sheath since the ion frictional force is no longer in equilibrium with drift and diffusion forces. The alternative is to use a full momentum equation for each ionic species. In this work we will present results from a self-consistent reactor scale-sheath scale model for 2D inductively coupled plasmas. The goal of this study is to improve the modeling capabilities and assess the importance of additional physics in determining important reactor performance features, such as the ion flux uniformity, coil frequency and configuration effects, etc. Effect of numerical dissipation on the solution quality will also be discussed.

Bose, Deepak↗

DOE OSTI2023

A New Analytical Expression for Estimating the Adiabatic Temperature Rise in Lithium-Ion Batteries During High-Power Pulses

A coupled, thermal-electrochemical model is used to explain why the Joule heating assumption (i.e., I 2 R) does not provide a good representation of the temperature rise during high power pulses in lithium-ion batteries, even in cases where the reversible heat generation can be neglected. The poor agreement occurs because the internal resistance changes during the pulse due to the opposing effects of mass transport in the electrolyte, which raises the resistance, and heat generation (temperature rise), which lowers the resistance. These insights are used to propose a new analytical expression for predicting the temperature rise during adiabatic pulses with limited experimental and physical data. The expression accounts for thermal effects using a Taylor series expansion of an Arrhenius-type equation. It accounts for transport effects using an approximate solution to the one-dimensional diffusion equation. The new expression is shown to accurately estimate the simulated, adiabatic temperature rise across a range of loadings (1 to 4 mAh cm -2 ) and C-rates (1C to 10C) for cells containing LiNi 0.5 Mn 0.3 Co 0.2 O 2 positive electrodes and graphite negative electrodes. In conclusion, it is also shown to accurately estimate the experimental, adiabatic temperature rise measured for cells with LiFePO 4 positive electrodes and mesocarbon negative electrodes with minimal changes to the fitted parameters.

25 ENERGY STORAGE↗

NASA NTRS1992

Shadowing and the role of small diffusivity in the chaotic advection of scalars

Using techniques from shadowing theory, the solution of the scalar advection-diffusion equation is studied. It is shown that, under certain circumstances, the effect of small scalar diffusivity is to smooth the zero-diffusivity solution by averaging local fine-scaled structure against a Gaussian. The method of study depends on shadowing and thus fails for nonuniformly stretching systems, its failure suggesting the ways in which the effects of asymptotically small molecular diffusion can become nonlocal in chaotic fluid flows.

Klapper, I.↗

NASA NTRS1985

Nonstationary modulation of galactic cosmic rays in a nonlinear model

An automdel equation for the solar wind velocity is obtained in the self-consistent model. The solution of the convection-diffusion equation is obtained for the density of galactic cosmic rays at a definite dependence of the diffusion coefficient and solar wind velocity on the rigidity and distance.

Babayan, V. K.↗

NASA NTRS2004

Computations of Wall Distances Based on Differential Equations

The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

Tucker, Paul G.↗

NASA NTRS2013

Conductance of Ion Channels - Theory vs. Experiment

Transmembrane ion channels mediate a number of essential physiological processes in a cell ranging from regulating osmotic pressure to transmission of neural signals. Kinetics and selectivity of ion transport is of critical importance to a cell and, not surprisingly, it is a subject of numerous experimental and theoretical studies. In this presentation we will analyze in detail computer simulations of two simple channels from fungi - antiamoebin and trichotoxin. Each of these channels is made of an alpha-helical bundle of small, nongenomically synthesized peptides containing a number of rare amino acids and exhibits strong antimicrobial activity. We will focus on calculating ionic conductance defined as the ratio of ionic current through the channel to applied voltage. From molecular dynamics simulations, conductance can be calculated in at least two ways, each involving different approximations. Specifically, the current, given as the number of charges transferred through the channel per unit of time, can be obtained from the number of events in which ions cross the channel during the simulation. This method works well for large currents (high conductance values and/or applied voltages). If the number of crossing events is small, reliable estimates of current are difficult to achieve. Alternatively, conductance can be estimated assuming that ion transport can be well approximated as diffusion in the external potential given by the free energy profile. Then, the current can be calculated by solving the one-dimensional diffusion equation in this external potential and applied voltage (the generalized Nernst-Planck equation). To do so three ingredients are needed: the free energy profile, the position-dependent diffusion coefficient and the diffusive flux of ions into the channel. All these quantities can be obtained from molecular dynamics simulations. An important advantage of this method is that it can be used equally well to estimating large and small currents. In addition, once the free energy profile becomes available the full current-voltage dependence can be readily obtained. For both channels we carried out calculations using both approaches. We also tested the main assumptions underlying the diffusive model, such as uncorrelated nature of individual crossing events and Fickian diffusion. The accuracy and consistency of different methods will be discussed. Finally we will discuss how comparisons between calculated and measured ionic conductance and selectivity of transport can be used for determining structural models of the channels.

Pohorille, Andrew↗

DOE OSTI2017

Hydrophilic domain structure in polymer exchange membranes: Simulations of NMR spin diffusion experiments to address ability for model discrimination

Here, we detail the development of a flexible simulation program (NMR_DIFFSIM) that solves the nuclear magnetic resonance (NMR) spin diffusion equation for arbitrary polymer architectures. The program was used to explore the proton ( 1 H) NMR spin diffusion behavior predicted for a range of geometrical models describing polymer exchange membranes. These results were also directly compared with the NMR spin diffusion behavior predicted for more complex domain structures obtained from molecular dynamics (MD) simulations. The numerical implementation and capabilities of NMR_DIFFSIM were demonstrated by evaluating the experimental NMR spin diffusion behavior for the hydrophilic domain structure in sulfonated Diels-Alder Poly(Phenylene) (SDAPP) polymer membranes. The impact of morphology variations as a function of sulfonation and hydration level on the resulting NMR spin diffusion behavior were determined. These simulations allowed us to critically address the ability of NMR spin diffusion to discriminate between different structural models, and to highlight the extremely high fidelity experimental data required to accomplish this. A direct comparison of experimental double-quantum-filtered 1 H NMR spin diffusion in SDAPP membranes to the spin diffusion behavior predicted for MD-proposed morphologies revealed excellent agreement, providing experimental support for the MD structures at low to moderate hydration levels.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Tricoupled hybrid lattice Boltzmann model for nonisothermal drying of colloidal suspensions in micropore structures

A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K ( 70°C ), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Because the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1975

On the convergence of certain finite-difference schemes by an inverse-matrix method

The inverse-matrix method of analyzing the convergence of the solution of a given system of finite-difference equations to the solution of the corresponding system of partial-differential equations is discussed and generalized. The convergence properties of a time- and space-centered differencing of the diffusion equation are analyzed as well as a staggered grid differencing of the Cauchy-Riemann equations. These two schemes are significant since they serve as simplified model algorithms for two recently developed methods used to calculate nonlinear aerodynamic flows.

Steger, J. L.↗

NASA NTRS1991

Combined energy and pitch angle diffusion of pickup ions at Comet Halley

It is well known that cometary pickup ions, e.g., H2O(+), OH(+), O(+), CO(+), H(+), initially form a ring-beam distribution in the solar wind reference frame, which is highly unstable to the growth of MHD waves (such as ion-cyclotron waves). The low-frequency magnetic fluctuations (or waves), which were observed upstream of Comet Halley, cannot only pitch-angle-scatter the pickup ions so that the distribution becomes at least partially isotropized, but also stochastically accelerate the ions, resulting in the energetic ion populations observed in the vicinity of Comet Halley. Here, numerical solutions of the quasi-linear diffusion equation were used to investigate the cometary ion pickup process at Comet Halley. Both pitch angle and energy diffusion are taken into account. Many quasi-linear models of cometary pickup ions exist which involve one type of diffusion or the other but not both types at once. It is found that the pitch angle scattering occurs faster than the energy diffusion, as expected. Moreover, the results demonstrate that the distribution of accelerated energetic ions is more isotropic than that of ions which have just been picked up. In fact, the ion distribution function on the initial pickup shell is quite anisotropic, even close to the Comet-Halley bow shock.

Ye, Gang↗

NASA NTRS1994

Radial diffusion of relativistic electrons in Neptune's magnetosphere

Measurements of greater than or = 1 MeV electrons in Neptune's magnetosphere from L approximately = 4 to 14 are well represented by solutions of a model radial diffusion equation that includes losses due to absorption by the satellite Proteus. The model provides estimates of the radial diffusion coefficient, which is 5 x 10(exp -8) (L/5)(exp 8)/s, and the outer boundary energy spectrum, which is an exponential with an e-folding energy of 0.1 MeV. The diffusion coefficient is consistent with theoretical estimates based on the assumption that diffusion is driven by atmospheric neutral winds.

Selesnick, R. S.↗