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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.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Asymptotic Relaxation of Moment Equations for a Multi-species, Homogeneous BGK Model

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially nontrivial velocity distributions. Here, in this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large times.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonextensive hydrodynamics of boost-invariant plasmas

We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter q. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including q. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function (q → 1). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter q.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Competing ionization and dissociation in the H 2 gerade system

A numerically solvable two-dimensional (2D) model, employed by the authors to study the dissociative recombination of H$^+_2$ in the ungerade symmetry, is extended to describe the collision process in the gerade symmetry of H$_2$. In this symmetry, the ionization and dissociation processes are driven primarily by the direct, curve-crossing mechanism. The model is represented by a set of three coupled electronic channels in 2D, in the space of $\textit{s, p, d}$ partial waves of the colliding electron. In this work, we demonstrate that the Born-Oppenheimer properties of the H$_2$ molecule in the relevant range of internuclear distances can be described by such a model. The molecular rotational degrees of freedom are accounted for by the rotational frame transformation. The numerical solution of the model is discussed, and the resulting rovibrationally inelastic and dissociative recombination cross sections are compared with the available data.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water

H2OI95 is a stand-alone Fortran code for evaluating the IAPWS-95 equation-of-state model (Wagner and Pruss, 2002) for the thermodynamic properties of water. It further evaluates the corresponding thermochemical properties of water consistent with the CODATA recommendations (Cox et al., 1989). The IAPWS-95 model is based on a model equation for the dimensionless Helmholtz energy for which the primary variables are the inverse reduced temperature and reduced density. Here is the absolute temperature (K), is density (kg/m3), and the subscript refers to the critical point of water (647.096 K and 22.064 MPa pressure in this model, for which is 322 kg/m3). The code solves four basic types of problems, distinguished by the specified inputs: 1, Temperature (K) and density (kg/m3) or reduced density 2. Temperature (K) and pressure (MPa). 3. Temperature (K) on the saturation (liquid-vapor equilibrium) curve 4. Pressure (MPa) on the saturation curve Each type of problem is run using a corresponding input (text) file. All but the first type of problem require iteration. For example, to solve for desired temperature and pressure, the reduced density must be adjusted to give the desired pressure. Iteration is accomplished using the Newton-Raphson method, though the secant method is also used in solving the fourth type of problem. H2OI95 has been used to conduct numerical studies of convergence and the problem of multiple numerical solutions, only some of which correspond to valid results. Obtaining valid results depends mainly on appropriate choice of starting values. The default values in H2OI95 appear to consistently lead to generally desired results. With modification (not addressed here), H2OI95 can be used to support SUPCRT92 (Johnson et al., 1992) and similar codes that compute chemical thermodynamic properties of species and reactions over a wide range of temperature and pressure (273.16-1273K and 0-1000 MPa).

Wolery, ThomasJ.↗
DOE OSTI2024

pnnl/NEURALMIE

NeuralMie was developed to improve the representation of aerosol optical properties in E3SM, the DOE's Earth system model. NeuralMie is able to closely emulate numerical solutions to the problem at a fraction of the computational cost. TAMie was written to generate training data for NeuralMie.

Geiss, Andrew↗
DOE OSTI2025

AutoDiffSVDCompression [SWR-25-162]

This software contains the code and results for the paper Reducing Memory Usage of Reverse Mode AD by Compression. In particular, the code includes implementation of the necessary structures and functions for using the Singular Value Decomposition (SVD) to compress forward pass values needed for reverse mode AD as well as the necessary numerical solvers for Burgers’ Equation and numerical solution of a control problem. In addition to the code, the repository also contains the scripts, results, and logs used in the aforementioned publication. This repository is meant to enable the reproducibility of the results in the publication.

Maack, Jonathan [National Renewable Energy Laborat↗
DOE OSTI2022

CEFR simulation using diffusion code system RAST-F

In this study, the RAST-F code system, which is based on the two-step approach that couples a multi-group cross-section generation Monte-Carlo (MC) code and a multi-group nodal diffusion solver, was used for the neutronic simulation of the CEFR start-up experiments. The numerical solution of the RAST-F system was verified against the full core MC solution MCS at all control rods fully inserted and withdrawn states. The RAST-F solution of the selected experimental simulations was compared against the measurement data. A good agreement between RAST-F and MCS solutions was observed with less than 120 pcm discrepancies and 1.2% root-mean-square error in terms of k{sub eff} and power distribution, respectively. Meanwhile, the RAST-F result agreed well with the experimental data within two-sigma of experimental uncertainty. The good agreement of these results indicates that RAST-F can be used to neutronic steady-state simulations for small core-size SFR, which was challenged to deterministic code systems. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Asynchronous domain decomposition methods for nonlinear PDEs

One- and two-level parallel asynchronous methods for the numerical solution of nonlinear systems of equations, especially those arising from (nonlinear) partial differential equations, are studied. The proposed methods are based on domain decomposition techniques. Local convergence theorems are presented in several cases, with appropriate hypotheses. Computational results on a shared memory multiprocessor machine for various problems exhibiting nonlinearities are reported, illustrating the potential of these asynchronous methods, especially for heterogeneous clusters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Long-term impact of light- and elevated temperature-induced degradation on photovoltaic arrays

Low levelized cost of electricity (LCOE) has been identified as critical for widespread adoption of photovoltaics (PV) without subsidies. Maintaining decades-long high-energy production is often an under-recognized opportunity in meeting cost goals because component lifetimes are not fully quantified at the time of manufacture. Whereas certain standardized tests minimize risk of early failure, there is little guidance to quantitatively predict degradation (or lack thereof) over decades, based on accelerated tests. In this article, we move toward bridging the understanding between indoor accelerated tests and outdoor performance data, with the goal of predicting energy yield with enough accuracy to inform financial decisions. Light- and elevated temperature-induced degradation (LETID) in p-type Si modules is analyzed in terms of impact on long-term module performance and thus LCOE. A method to predict the progression of LETID, using fixed kinetic constants and a numerical solution to the basic reaction rate equations, is detailed. Predictions are compared against both published data and that new to this study. These data include both indoor accelerated tests and fielded modules. We use the results in financial models to derive LCOE of modules in different climates with varying amounts of LETID, including uncertainty. Cost models based on the predictions indicate that LETID has a significant and climate-dependent impact on LCOE. Finally, we show that - even given the uncertainties identified in the study - these financial calculations can provide useful guidance to quantify risk based on accelerated test results. The analysis serves as an example of developing a predictive approach to PV reliability using physics of failure.

14 SOLAR ENERGY↗
DOE OSTI2020

A GPU-based 2D shallow water quality model

In this paper, a 2D shallow water flow solver integrated with a water quality model is presented. The interaction between the main water quality constituents included is based on the Water Quality Analysis Simulation Program. Efficiency is achieved by computing with a combination of a Central Processing Unit (CPU) and a Graphics Processing Unit (GPU) device. This technique is intended to provide robust and accurate simulations with high computation speedups with respect to a single-core CPU in real events. The proposed numerical model is evaluated in cases that include the transport and reaction of water quality components over irregular bed topography and dry–wet fronts, verifying that the numerical solution in these situations conserves the required properties (C-property and positivity). The model can operate in any steady or unsteady form allowing an efficient assessment of the environmental impact of water flows. The field data from an unsteady river reach test case are used to show that the model is capable of predicting the measured temporal distribution of dissolved oxygen and water temperature, proving the robustness and computational efficiency of the model, even in the presence of noisy signals such as wind speed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

PETSc Users Manual (Rev. 3.13)

This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear solvers, nonlinear solvers, and time integrators that may be used in application codes written in Fortran, C, C++, and Python. PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than \rolling them" yourself.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water (Rev. 1)

H2OI95 is a stand-alone Fortran code for evaluating the IAPWS-95 equation-of-state model for the thermodynamic properties of water. It also evaluates the corresponding thermochemical properties of water consistent with the CODATA recommendations. The IAPWS-95 model is based on a model equation for the dimensionless Helmholtz energy for which the primary variables are the inverse reduced temperature (τ = T cr /T ) and reduced density (δ = ρ/ρ cr ). Here T is the absolute temperature (K), ρ is density (kg/m³), and the subscript “ cr ” refers to the critical point of water (647.096 K and 22.064 MPa pressure in this model, for which ρ cr is 322 kg/m³). The code solves four basic types of problems, distinguished by the specified inputs: 1. Temperature (K) and density (ρ kg/m³) or reduced density (δ) 2. Temperature (K) and pressure (MPa). 3. Temperature (K) on the saturation (liquid-vapor equilibrium) curve 4. Pressure (MPa) on the saturation curve. Each type of problem is run using a corresponding input (text) file. All but the first type of problem require iteration. For example, to solve for desired temperature and pressure, the reduced density must be adjusted to give the desired pressure. Iteration is accomplished using the Newton-Raphson method, though the secant method is also used in solving the fourth type of problem. For the last three types of problems, H2OI95 has been used to conduct numerical studies of convergence and the problem of multiple numerical solutions, some of which are not physically valid. Obtaining valid results depends mainly on appropriate choice of starting values for the density. The default values used in H2OI95 appear to consistently lead to generally desired results. With modification (not addressed here), H2OI95 can be used to support SUPCRT92 and similar codes that compute chemical thermodynamic properties of species and reactions over a wide range of temperature and pressure (273.16-1273K and 0-1000 MPa). Version 1.1 of this software calculates an extended set of water properties, including some derivable solely from IAPWS-95, such as the isobaric thermal expansivity and the isothermal compressibility, and still other properties based on supplementary models sanctioned by IAPWS, including the dynamic viscosity, thermal conductivity, surface tension, and static dielectric constant, and various other properties (notably Debye-Hückel parameters) derivable from the dielectric constant and its partial derivatives with respect to temperature and pressure. A coding error in Version 1.0 was identified while testing the implementation of the viscosity model. This error is described in Appendix C. It mainly affects calculation of “higher order” properties such as compressibility and heat capacity near the critical point.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Multigrid-Reduction-in-Time for the Rotating Shallow Water Equations

We consider multilevel time-parallel methods for the numerical solution of the rotating shallow water equations. In particular, the multigrid-reduction-in-time (MGRIT) algorithm is used for the parallel time integration. An asymptotic model is used at the coarse levels while the full model is employed at the finer levels. The asymptotic model is well-suited for highly oscillatory partial differential equations like the rotating shallow water equations because it can accurately and stably take the required large time-steps on coarse levels. Our work exploits the flexibility of the MGRIT algorithm in terms of the number of levels and relaxation schemes to show some computational benefits, especially with respect to FCF-relaxation and data reuse.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Understanding machine learning approaches for partial differential equations

Recent works in computational physics have been successful in the super-resolution of numerical solutions of partial differential equations (PDEs) via neural networks. In this paper we explore the possibilities and limitations of the data-driven discretization approach implemented by Bar-Sinai et. al., while contrasting it with a simpler yet weaker approach utilizing the nangs Python library. The results demonstrate what neural network parameters optimize accuracy and performance, as well as what conditions on PDEs are necessary to maintain convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Metric Type in the Target-matrix Mesh Optimization Paradigm

The Target Matrix Optimization Paradigm (TMOP) is a method for improving the accuracy, efficiency, and robustness of numerical solutions to partial differential equations by improving the geometric quality of the computational mesh, primarily through node movement. TMOP has been successfully applied to a number applications even though the paradigm was not fully understood at the time. With this work, TMOP can be seen to be a tightly woven fabric of interconnecting ideas and concepts that provides a powerful approach to mesh optimization. The central unifying concepts in TMOP are the concept of a Target Matrix and the concept of Metric Type. Target matrices are motivated by the desire to make mesh quality improvement application-specific and, when needed, solution-adaptive. Metric type plays an essential role because it provides, through the use of typed metrics, the bridge between application-specific quality and target construction. It is shown that there are eight theoretical metric types, including the shape and shape+size types used informally in the past. It is shown further that there exist well-posed metrics corresponding to six of the eight metric types. A well-posed metric is a metric that is typed and convex, polyconvex, or invex, and further, it is a metric that simplifies target construction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

PETSc Users Manual (Revision 3.15)

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

CTF Theory Manual (V.4.2)

Coolant-Boiling in Rod Arrays—Two Fluids (COBRA-TF) is a thermal/hydraulic (T/H) simulation code designed for light water reactor (LWR) vessel analysis. It uses a two-fluid, three-field (i.e. fluid film, fluid drops, and vapor) modeling approach. Both sub-channel and 3D Cartesian forms of 9 conservation equations are available for LWR modeling. The code was originally developed by Pacific Northwest Laboratory in 1980 and had been used and modified by several institutions over the last few decades. COBRA-TF also found use at the Pennsylvania State University (PSU) by the Reactor Dynamics and Fuel Modeling Group (RDFMG) and has been improved, updated, and subsequently re-branded as CTF. As part of the improvement process, it was necessary to generate sufficient documentation for the open-source code which had lacked such material upon being adopted by RDFMG. This document serves mainly as a theory manual for CTF, detailing the many two-phase heat transfer, drag, and important accident scenario models contained in the code as well as the numerical solution process utilized. Coding of the models is also discussed, all with consideration for updates that have been made when transitioning from COBRA-TF to CTF. Further documentation outside of this manual is also available at RDFMG which focus on code input deck generation and source code global variable and module listings

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Taylor wave solution for a general equation of state

This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.

97 MATHEMATICS AND COMPUTING↗