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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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Three-dimensional radiative transfer on a massively parallel computer

We perform 3D radiative transfer calculations in non-local thermodynamic equilibrium (NLTE) in the simple two-level atom approximation on the Mas-Par MP-1, which contains 8192 processors and is a single instruction multiple data (SIMD) machine, an example of the new generation of massively parallel computers. On such a machine, all processors execute the same command at a given time, but on different data. To make radiative transfer calculations efficient, we must re-consider the numerical methods and storage of data. To solve the transfer equation, we adopt the short characteristic method and examine different acceleration methods to obtain the source function. We use the ALI method and test local and non-local operators. Furthermore, we compare the Ng and the orthomin methods of acceleration. We also investigate the use of multi-grid methods to get fast solutions for the NLTE case. In order to test these numerical methods, we apply them to two problems with and without periodic boundary conditions.

Vath, H. M.↗
NASA NTRS2004

Hybrid Particle-Element Simulation of Impact on Composite Orbital Debris Shields

This report describes the development of new numerical methods and new constitutive models for the simulation of hypervelocity impact effects on spacecraft. The research has included parallel implementation of the numerical methods and material models developed under the project. Validation work has included both one dimensional simulations, for comparison with exact solutions, and three dimensional simulations of published hypervelocity impact experiments. The validated formulations have been applied to simulate impact effects in a velocity and kinetic energy regime outside the capabilities of current experimental methods. The research results presented here allow for the expanded use of numerical simulation, as a complement to experimental work, in future design of spacecraft for hypervelocity impact effects.

Fahrenthold, Eric P.↗
NASA NTRS1994

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Yee, H. C.↗
DOE OSTI2018

On One Numerical-Analytic Method for the Solution of One-Dimensional Quasistatic Problems of Thermoelasticity for Thermosensitive Bodies of Simple Geometry

We propose a procedure for the numerical-analytic solution of one-dimensional problems of thermoelasticity for bodies of simple geometry based on the representation of temperature dependences of the physicomechanical characteristics of materials in the form of piecewise constant functions of temperature and the application of the Kirchhoff substitution and the methods of generalized functions. This procedure enables us to study one-dimensional nonstationary thermal and quasistatic stress-strain states under the combined thermal and force action with controlled reliability.

36 MATERIALS SCIENCE↗
NASA NTRS2009

Coupled Neutron Transport for HZETRN

Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light particle transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Slaba, Tony C.↗
DOE OSTI2014

TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4

Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

The analysis of nonequilibrium, chemically reacting, supersonic flow in three dimensions using a bicharacteristics method.

A second-order numerical method of characteristics based on a bicharacteristics scheme was developed for the evaluation of steady, supersonic, nonequilibrium, chemically reacting flows. The absolute accuracy and order of accuracy of the method was shown by comparisons with spherical source flow and axisymmetric, nonequilibrium flows. Numerical results were obtained for elliptical and super-elliptical nozzles. These results illustrate the complex nature of three-dimensional flows and the inadequacy of quasi-three-dimensional methods which neglect cross flows.

Cline, M. C.↗
NASA NTRS1979

Development of analytical orbit propagation technique with drag

Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.

Source record↗
NASA NTRS1977

Calculation of laminar and turbulent boundary layers for two-dimensional time-dependent flows

A general method for computing laminar and turbulent boundary layers for two-dimensional time-dependent flows is presented. The method uses an eddy-viscosity formulation to model the Reynolds shear-stress term and a very efficient numerical method to solve the governing equations. The model was applied to steady two-dimensional and three-dimensional flows and was shown to give good results. A discussion of the numerical method and the results obtained by the present method for both laminar and turbulent flows are discussed. Based on these results, the method is efficient and suitable for solving time-dependent laminar and turbulent boundary layers.

Cebeci, T.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-16659-DND

Heat transfer is best understood through theory and application of principles in thermal analysis. Modern thermal analysis leverages the power of computers and numerical methods to simulate heat transfer in networks representing a physical system. This lesson is an introduction to numerical methods in heat transfer.

Steven L Rickman↗
DOE OSTI2016

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3D code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.

42 ENGINEERING↗
NASA NTRS1991

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Cerro, J. A.↗
DOE OSTI2015

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

58 GEOSCIENCES↗
NASA NTRS1984

Shock capturing finite difference algorithms for supersonic flow past fighter and missile type configurations

The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.

Osher, S.↗
DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1981

Trends and pacing items in computational aerodynamics

A perspective is presented of trends in computational aerodynamics, and of important technology development items that pace future advanced applications. From a survey of AIAA Journal papers published during the past two decades, the growth trends and the progressively increasing emphasis on code development for viscous, compressible, turbulent flow are illustrated. These trends are reflected in the chronology of introduction by the aerospace industry of new computational methods in aircraft design. Key pacing items outlined are: automatic grid generation for nonlinear inviscid computations; advanced computers, improved efficiency of numerical methods, and improved turbulence models for Reynolds-averaged Navier-Stokes computations; advanced computers, time-dependent three-dimensional law-of-the-wall, code development, improved efficiency of numerical methods, and improved subgrid-scale turbulence modeling for large eddy simulations.

Chapman, D. R.↗
NASA NTRS1990

A parallel iterative solution method for systems of nonlinear hyperbolic equations

An iterative algorithm suitable for the solution of a system of nonlinear hyperbolic partial differentiation equations in multiple dimensions is discussed. Current numerical methods for systems of nonlinear PDEs have limited parallelism due to strong coupling between the equations. This method decouples the PDEs by linearizing the convention coefficient for a space-time domain. This provides large grain parallelism. The linearization also allows the treatment of some terms in the equations as source terms, providing more freedom to choose from a wider variety of numerical methods. Smaller grain parallelism may be exploited within the solves for each equation. Thus, the method has potential for parallelism at several levels.

Scroggs, Jeffrey S.↗
DOE OSTI2023

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

Here, in this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open-source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT . This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open-source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase.

97 MATHEMATICS AND COMPUTING↗