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At least 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

The Multilevel in Space and Energy Diffusion (MSED) method accelerates the iterative convergence of multigroup diffusion eigenvalue problems by performing work on lower-order equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a one-dimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarse-mesh finite difference (CMFD) system in the three-dimensional Michigan Parallel Characteristics Transport (MPACT) code. In this paper, the results from the implementation of MSED in MPACT are introduced, and the changes needed to make MSED more suitable for MPACT are described. For problems without feedback, the conclusions in this paper show that MSED can reduce the CMFD run time by an order of magnitude and the overall run time by a factor of 2 to 3 compared to the default CMFD solver in MPACT [PI with the generalized minimal residual (GMRES) method]. For problems with feedback, the convergence of the outer Picard iteration scheme is worsened by the well-converged CMFD solutions produced by the standard MSED method. To overcome this unintuitive deficiency, MSED may be run with looser convergence criteria (a modified version of the MSED method called MSED-L) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSED-L can reduce the CMFD run time in MPACT by an order of magnitude, without negatively impacting the outer Picard iteration scheme.

3-D↗
NASA NTRS1986

Diffuser investigation for advanced multi-megawatt MPD engine development

Steady-state testing of advanced, multimegawatt MPD engines requires vacuum facilities with pumping speeds which are not presently available. Gas dynamic diffusers have been proposed as a possible solution to this problem. An analytical investigation into the feasibility of using a diffuser for pumping the MPD engine exhaust is presented here. This analysis uses a detailed equation of state based on the partition function for the high temperature argon exhaust. On the basis of the electron-ion momentum exchange collision frequency in the exhaust plasma, it was concluded that the diffuser gas dynamics could be modeled to a first approximation with ordinary continuum equations. Calculations of the stagnation pressure in the diffuser, downstream of a strong normal shock, yielded pressures on the order of 10 torr suggesting that the diffuser is feasible for pumping the MPD engine exhaust.

Brophy, J. R.↗
DOE OSTI2015

Dynamic of charged planar geometry in tilted and non-tilted frames

We investigate the dynamics of charged planar symmetry with an anisotropic matter field subject to a radially moving observer called a tilted observer. The Einstein-Maxwell field equations are used to obtain a relation between non-tilted and tilted frames and between kinematical and dynamical quantities. Using the Taub mass formalism and conservation laws, two evolution equations are developed to analyze the inhomogeneities in the tilted congruence. It is found that the radial velocity (due to the tilted observer) and the electric charge have a crucial effect on the inhomogeneity factor. Finally, we discuss the stability in the non-tilted frame in the pure diffusion case and examine the effects of the electromagnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

Factors governing the ratio of inward to outward diffusing flux of satellite ions

The sensitivity of the flux ratio to the uncertainties in the boundary conditions and diffusion coefficient is analyzed. The principal result is that if the diffusion is driven externally, for example, by winds in Jupiter's ionosphere, the inward flux exceeds or is of the same order of magnitude as the outward flux. On the other hand, if the diffusion is driven locally by the centrifugal interchange instability, as suggested by one interpretation of Voyager plasma data, the outward flux can be one or two orders of magnitude greater than the inward flux. Fits to the Voyager in situ plasma torus data obtained through solutions to the transport equations appropriate to wind driven and centrifugally driven diffusion are compared.

Richardson, J. D.↗
NASA NTRS1994

Modification of the Two-equation Turbulence Model in NPARC to a Chien Low Reynolds Number K-epsilon Formulation

This report documents the changes that were made to the two-equation k-epsilon turbulence model in the NPARC (National-PARC) code. The previous model based on the low Reynolds number model of Speziale, was replaced with the low Reynolds number k-epsilon model of Chien. The most significant difference was in the turbulent Prandtl numbers appearing in the diffusion terms of the k and epsilon transport equations. A new inflow boundary condition and stability enhancements were also implemented into the turbulence model within NPARC. The report provides the rationale for making the change to the Chien model, code modifications required, and comparisons of the performances of the new model with the previous k-epsilon model and algebraic models used most often in PARC/NPARC. The comparisons show that the Chien k-epsilon model installed here improves the capability of NPARC to calculate turbulent flows.

Georgiadis, Nicholas J.↗
NASA NTRS1998

Comments on the Diffusive Behavior of Two Upwind Schemes

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Wood, William A.↗
NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗
NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗
NASA NTRS1998

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Wood, William A.↗
DOE OSTI2023

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density. In systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here, in this work, we study this problem using a model of coupled quantum dots with interactions decaying as 1/r α , where each dot hosts N degrees of freedom. The large-N limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by 1/N corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings previously found for N=1 and generic finite N. In order to reproduce these scalings, the fractional index μ in the FKPP equation needs to be shifted from the naïve value of μ=2⁢α–1 to a renormalized value μ=2⁢α–2. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

Abstract In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2023

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

Solar energetic particles↗
DOE OSTI2018

On the fractional Harry Dym equation

We present and discuss the general case of a fractional nonlinear partial differential equation using similarity reductions and recover results associated with Harry Dym-type equations. Particular cases are discussed and some plots illustrate the results. The fractional derivative is considered in the Caputo sense.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Hopf bifurcation in the driven cavity

Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two. The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the diffusion terms, and with an Adams-Bashforth scheme for the convection terms. A multigrid method is used to solve the linear implicit equations at each time step. Periodic asymptotic solutions have been found for Re = 10000 and for Re = 5000. The Re = 5000 results are validated by grid refinement calculations. The solutions are shown to be precisely periodic, and care is taken to demonstrate that asymptotic states were reached. A discussion is included about the indicators that are used to show that an asymptotic state was reached, and to show that the asymptotic state is indeed periodic.

Goodrich, John W.↗
DOE OSTI2023

High-Fidelity Simulations of Plasma-Assisted Oxidation of Hydrocarbon Fuels Using Nanosecond Pulsed Discharges

Next, a robust and efficient framework for simulating NSPD in multiple dimensions is developed. The reactive Navier-Stokes equations are extended to include a drift-diffusion plasma-fluid model with a local field approximation (LFA) in a finite-volume solver, which uses an adaptive mesh refinement (AMR) strategy to address the wide separation of length scales in the problem. A two-way coupling strategy is used whereby the plasma-fluid model and reactive Navier-Stokes equations are integrated simultaneously. The oxidation of ethylene/air mixtures mediated by NSPD is simulated in a pin-to-pin configuration. All phases of the plasma discharge are simulated explicitly (including streamer ignition, propagation, and connection, as well as the subsequent spark phase), along with the evolution of the plasma during the inter-pulse period. Temporally and spatially-resolved results are presented, with an emphasis on the analysis of heating and energy deposition, as well as of the evolution of the concentration of active particles generated during the NSPD and their influence on ignition.

adaptive mesh refinement↗
DOE OSTI2025

Simulation and generalized Langevin equation study of lipid subdiffusion in biomembrane phases

In biomembranes lipid mobility exhibits deviations from the classical diffusive behavior of Brownian particles, i.e. ‘anomalous’ diffusion. The question arises as to how this anomalous diffusive behavior varies in gel, ripple, and fluid biomembrane phases. Here, in this study, we perform all-atom molecular dynamics (MD) simulations of dimyristoylphosphatidylcholine (DMPC) bilayers in the three different phases and analyze the results using the framework of the Generalized Langevin Equation (GLE). This analysis emphasizes sub-diffusive behavior on the relatively short, picosecond-nanosecond timescales, capturing local molecular constraints and transient caging effects during the crossover of atomic dynamics from vibrational to incipient anharmonic motion. The ripple and gel phases are found to exhibit strong transient caging and prolonged memory effects resulting in distinct sub-diffusive behavior. The role of hydrogen bonding in lipid confinement is also examined, demonstrating its influence on phase-dependent molecular ordering and on short-time diffusional constraints. These findings demonstrate the GLE framework’s utility in characterizing molecular transport and lipid dynamics, with implications for longer timescale membrane dynamics.

Malik, Sheeba [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2016

Vertical dispersion in vegetated shear flows

Canopy layers control momentum and solute transport to and from the overlying water surface layer. These transfer mechanisms strongly dependent on canopy geometry, affect the amount of solute in the river, the hydrological retention and availability of dissolved solutes to organisms located in the vegetated layers, and are critical to improve water quality. In this work, we consider steady state transport in a vegetated channel under fully developed flow conditions. Under the hypothesis that the canopy layer can be described as an effective porous medium with prescribed properties, i.e., porosity and permeability, we model solute transport above and within the vegetated layer with an advection-dispersion equation with a spatially variable dispersion coefficient (diffusivity). By means of the Generalized Integral Transform Technique , we derive a semianalytical solution for the concentration field in submerged vegetated aquatic systems. We show that canopy layer’s permeability affects the asymmetry of the concentration profile, the effective vertical spreading behavior, and the magnitude of the peak concentration. Due to its analytical features, the model has a low computational cost. The proposed solution successfully reproduces previously published experimental data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Probabilistic learning and updating of a digital twin for composite material systems

This paper presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems. An example demonstrates the integration of experimental data with a computational database. The statistical approach is based on the probabilistic learning on manifolds recently developed by the authors. This approach leverages intrinsic structure detected through diffusion on graphs with projected stochastic differential equations to generate samples constrained to that structure.

42 ENGINEERING↗