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At least 1,369 records · Page 76

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DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2002

Computation of Turbulent Heat Transfer on the Walls of a 180 Degree Turn Channel With a Low Reynolds Number Reynolds Stress Model

The Low Reynolds number version of the Stress-omega model and the two equation k-omega model of Wilcox were used for the calculation of turbulent heat transfer in a 180 degree turn simulating an internal coolant passage. The Stress-omega model was chosen for its robustness. The turbulent thermal fluxes were calculated by modifying and using the Generalized Gradient Diffusion Hypothesis. The results showed that using this Reynolds Stress model allowed better prediction of heat transfer compared to the k-omega two equation model. This improvement however required a finer grid and commensurately more CPU time.

Ameri, A. A.↗

NASA NTRS2011

Analysis of the Radiative Transfer Equation with Highly Asymmetric Phase Function

This paper considers a scalar radiative transfer problem with high scattering anisotropy, Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal. which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2 + is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.

Korkin, Sergey V.↗

DOE OSTI2023

Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

In this work, we present a phase-field model that captures the evolution of ionic concentrations and phase fractions during solid-state metathesis (SSM) reactions where diffusion limits the rate of transformation. The evolution of the mole fraction of each ion is obtained via governing equations that describe the reduction of a free energy, which includes an energy landscape with local minima located at compositions corresponding to stable products. We utilized two Lagrange multipliers to impose constraints of electroneutrality as well as on the sum of mole fractions, which were then eliminated to derive set of two partial differential equations that describe the dynamics of the mole fraction evolution. From these governing equations, the expressions for effective mobilities for the cations and the anions were obtained. We first study the effect of mobilities of ions on the reaction kinetics, using a simple model considering the ions with an identical absolute value of charge numbers. The simulation results show that the overall characteristic mobility, defined as the sum of the two effective ionic mobilities, provides an excellent measure of the rate at which reaction progresses and that the ratio of the effective mobilities of the anions and the cations signifies the manner by which the reaction progresses. We then generalize the model to consider ions with different charge numbers and tuned the mobility of ions based on their diffusion coefficients reported in the literature and experimental data from a thin-film experiment for the synthesis of FeS 2 to demonstrate the capability of the model to predict the phase evolution during SSM reactions. In particular, the simulation predicts nonplanar phase evolution, which is recently observed in thin-film reactions for the synthesis of FeS 2 via transmission electron microscopy. The approach can serve as a basis for models for phase transformations in other multiphase ionic mixtures, such as in all-solid-state batteries and in ionic liquids.

36 MATERIALS SCIENCE↗

DOE OSTI2025

The origin of the Stokes–Einstein relation in simple dense liquids

Here, we investigate the origin of the universal relation between structural relaxation and diffusion in simple dense liquids, known as the Stokes–Einstein (SE) relation. The fact that this relation, originally derived from a hydrodynamic model of a macroscopic particle in a viscous medium, can describe the microscopic-scale liquid dynamics still eludes understanding. We introduce a new universal measure of structural relaxation in a system of N identical particles based on an explicit decomposition of the configuration space into N! congruent convex polyhedra. This measure makes it possible to quantify the correlation between two distinct particle configurations in terms of their minimal Euclidean distance, optimized with respect to particle permutations. Using this measure alongside a model of independent random walkers under the single-occupancy constraint, we derive a master equation that quantifies the SE relation. It allows us to demonstrate that the universal relation between structural relaxation and diffusion in simple dense liquids is caused by two conditions: (a) the confinement of the dominant density fluctuations to the first coordination shell, manifested by de Gennes narrowing, and (b) Gaussianity of the diffusion process; the former is shown to be violated in low-density fluids, and the latter is known to be violated in supercooled liquids.

Physics - Condensed matter physics↗

NASA NTRS2005

Ring Current Dynamic in the Presence of EMIC Waves

The effect of EMIC waves, generated by a positive ion temperature anisotropy on Earth s RC ions is one of the best known examples of wave-particle interaction in the magnetosphere and the most controversial mechanism of RC losses. Under certain conditions, relativistic electrons with energy 21 MeV can be removed from the outer RB by EMIC wave scattering during a magnetic storm much faster than by any other loss mechanisms. That is why the calculation of EMIC waves is a very critical part of the NASA LWS program. The new RC model that we have developed and present for the first time has several new features that we have combine together in a one single model: (a) several lower frequency cold plasma wave modes are taken into account; (b) wave tracing of these wave has been incorporated in the energy EMIC wave equation; (c) no assumptions regarding wave shape spectra have been made; (d) no assumptions regarding the shape of particle distribution have been made to calculate the growth rate; (e) pitch- angle, energy, and mix diffusions are taken into account together for the first time; (f) the exact loss-cone RC analytical solution has been found and coupled with bounce-averaged numerical solution of kinetic equation; (g) LHW are included as an additional factor that contributes to saturation process of EMIC waves; and (h) the hot ions were included in the real part of dielectric permittivity tensor. We compare our theoretical results with the different EMIC waves models as well as RC experimental data.

Khazanov, G. V.↗

NASA NTRS1989

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Przekwas, A. J.↗

NASA NTRS1977

SAS-2 observations of the diffuse gamma radiation in the galactic latitude interval from 10 to 90 deg in both hemispheres

An analysis of all the second Small Astronomy Satellite (SAS-2) gamma-ray data for galactic latitudes higher than 10 deg in both hemispheres has shown that the intensity varies with galactic latitude, being larger near 10 deg than 90 deg. For energies above 100 MeV the gamma-ray data are consistent with a latitude distribution of the form I(b) = C1 + C2/sin b, with the second term being dominant. This result suggests that the radiation above 100 MeV is coming largely from local regions of the galactic disk. Between 35 and 100 MeV, a similar equation is also a good representation of the data, but here the two terms are comparable. These results indicate that the diffuse radiation above 35 MeV consists of two parts, one with a relatively hard galactic component and the other an isotropic steep spectral component which extrapolates back well to the low-energy (less than 10 MeV) diffuse radiation. The steepness of the diffuse isotropic component places significant constraints on possible theoretical models of this radiation.

Fichtel, C. E.↗

DOE OSTI2021

Analysis of a New Implicit Solver for a Semiconductor Model

Here, we present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann--Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov--Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann--Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, against a recently developed nested iterative solver.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2005

Ring Current-Electromagnetic Ion Cyclotron Waves Coupling

The effect of Electromagnetic Ion Cyclotron (EMIC) waves, generated by ion temperature anisotropy in Earth s ring current (RC), is the best known example of wave- particle interaction in the magnetosphere. Also, there is much controversy over the importance of EMIC waves on RC depletion. Under certain conditions, relativistic electrons, with energies 21 MeV, can be removed from the outer radiation belt (RB) by EMIC wave scattering during a magnetic storm. That is why the calculation of EMIC waves must be a very critical part of the space weather studies. The new RC model that we have developed and present for the first time has several new features that we have combine together in a one single model: (a) several lower frequency cold plasma wave modes are taken into account; (b) wave tracing of these wave has been incorporated in the energy EMIC wave equation; (c) no assumptions regarding wave shape spectra have been made; (d) no assumptions regarding the shape of particle distribution have been made to calculate the growth rate; (e) pitch-angle, energy, and mix diffusions are taken into account together for the first time; (f) the exact loss-cone RC analytical solution has been found and coupled with bounce-averaged numerical solution of kinetic equation; (g) the EMIC waves saturation due to their modulation instability and LHW generation are included as an additional factor that contributes to this process; and (h) the hot ions were included in the real part of dielectric permittivity tensor. We compare our theoretical results with the different EMIC waves models as well as RC experimental data.

Khazanov, G. V.↗

NASA NTRS1982

Analytical modeling of operating characteristics of premixing-prevaporizing fuel-air mixing passages. Volume 1: Analysis and results

A model for predicting the distribution of liquid fuel droplets and fuel vapor in premixing-prevaporizing fuel-air mixing passages of the direct injection type is reported. This model consists of three computer programs; a calculation of the two dimensional or axisymmetric air flow field neglecting the effects of fuel; a calculation of the three dimensional fuel droplet trajectories and evaporation rates in a known, moving air flow; a calculation of fuel vapor diffusing into a moving three dimensional air flow with source terms dependent on the droplet evaporation rates. The fuel droplets are treated as individual particle classes each satisfying Newton's law, a heat transfer, and a mass transfer equation. This fuel droplet model treats multicomponent fuels and incorporates the physics required for the treatment of elastic droplet collisions, droplet shattering, droplet coalescence and droplet wall interactions. The vapor diffusion calculation treats three dimensional, gas phase, turbulent diffusion processes. The analysis includes a model for the autoignition of the fuel air mixture based upon the rate of formation of an important intermediate chemical species during the preignition period.

Anderson, O. L.↗

NASA NTRS1977

SAS-2 observations of the diffuse gamma radiation in the galactic latitude interval 10 deg absolute b or equal to 90 deg

An analysis of all of the second small astronomy satellite gamma-ray data for galactic latitudes with the absolute value of b 10 deg has shown that the intensity varies with galactic latitude, being larger near 10 deg than 90 deg. For energies above 100 MeV the gamma-ray data are consistent with a latitude distribution of the form I(b) = C sub 1 + C sub 2/sin b, with the second term being dominant. This result suggests that the radiation above 100 MeV is coming largely from local regions of the galactic disk. Between 35 and 100 MeV, a similar equation is also a good representation of the data, but here the two terms are comparable. These results indicate that the diffuse radiation above 35 MeV consists of two parts, one with a relatively hard galactic component and the other an isotropic, steep spectral component which extrapolates back well to the low energy diffuse radiation. The steepness of the diffuse isotropic component places significant constraints on possible theoretical models of this radiation.

Fichtel, C. E.↗

DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Higher order methods for convection-diffusion problems

This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.

Murphy, J. D.↗

DOE OSTI2026

Nonlinear causality of Israel-Stewart theory with diffusion

We present the first fully nonlinear causality constraints in D = 3 + 1 dimensions for Israel-Stewart theory in the presence of energy and number diffusion in the Eckart and Landau hydrodynamic frames, respectively. These constraints are algebraic inequalities that make no assumption on the underlying geometry of the spacetime or the equation of state. In order to highlight the distinct physical and structural behavior of the two hydrodynamic frames, we discuss the special ultrarelativistic ideal gas equation of state considered in earlier literature in D = 1 + 1 dimensions, and show that our general D = 3 + 1 constraints reduce to their results upon an appropriate choice of angles. For this equation of state in both D = 1 + 1 and D = 3 + 1 dimensions one can show that: (i) there exists a region allowed by nonlinear causality in which the baryon current transitions into a spacelike vector in the Landau frame, and (ii) an analogous argument shows that the solutions of the Eckart frame equations of motion never violate the dominant energy condition, assuming nonlinear causality holds. Furthermore, we then compare our results with those from linearized Israel-Stewart theory and show that the linear causality bounds fail to capture the new physical constraints on energy and number diffusion that are successfully obtained through our nonlinear causality approach.

Quark-gluon plasma↗

NASA NTRS1972

Diffusive and radiative effects on vaporization times of drops in film boiling

Diffusive and radiative effects are incorporated into an analysis for the vaporization time of drops in film boiling. The momentum, energy, and continuity equations are solved with some appropriate simplifications so as to obtain a simple closed form solution for the overall film boiling heat transfer coefficient. Next, a theoretical expression for the droplet vaporization time is developed and compared to the measured vaporization times of water droplets vaporizing into air, argon, nitrogen, and helium. The agreement between experiment and theory is good. Under the helium blanket, the diffusive evaporative component is significant in comparison to the film boiling component.

Baumeister, K. J.↗

DOE OSTI2019

A computational model for nanosecond pulse laser-plasma interactions

A multi-physics numerical model for laser-induced optical breakdown and laser-plasma interaction in a non-equilibrium gas is presented, accounting for: production of priming electrons via multi-photon ionization, energy absorption, cascade ionization, induced hydrodynamic response, and shock formation and propagation. The gas is governed by the Navier-Stokes equations, with non-equilibrium effects taken into account by means of a two-temperature model. The space-time dependence of the laser beam is modeled with a flux-tube formulation for the Radiative Transfer Equation. The flow governing equations are discretized in space using a second-order finite volume method. The semi-discrete equations are marched in time using an implicit-explicit (IMEX) dual time-stepping strategy, where diffusion and chemistry are solved implicitly, whereas convection is explicit. Application to a 20 ns long 50 mJ pulse laser-induced breakdown in quiescent O 2 shows the advantages of this temporal discretization during and just after the laser pulse, while a less-expensive symmetric Strang splitting (with implicit chemistry) is sufficient for the post-breakdown gas dynamics after ≃ 0.1 μs. The integrated model is shown to reproduce key features of corresponding experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Isotope effects on the high pressure viscosity of liquid water measured by differential dynamic microscopy

In this paper, differential dynamic microscopy is performed in diamond anvil cells to measure the viscosity of water along the 24 °C isotherm to high-pressure by determination of the tracer diffusion coefficient of monodisperse silica spheres of known diameter and application of the Stokes-Einstein-Sutherland equation. This technique allows liquid samples to be compressed to greater pressure prior to freezing than with other viscometry methods. The highest-pressure measurement was made at 1.67 GPa, considerably deeper into the supercompressed regime than previously reported. The effect of isotopic composition is investigated with samples of normal water, heavy water, and partially deuterated water. When data below 0.25 GPa are excluded a free volume model fits the observed viscosities well yielding a theoretical glass transition density close to that observed in very-high-density amorphous ice. The improved fit above 0.25 GPa coincides with the loss of other anomalous behaviors in liquid water caused by hydrogen bonding and represents a transition to properties closer to those of a simple liquid.

74 ATOMIC AND MOLECULAR PHYSICS↗