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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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Compact finite volume methods for the diffusion equation

An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.

Rose, Milton E.↗
DOE OSTI2019

fPINNs: Fractional Physics-Informed Neural Networks

Physics-informed neural networks (PINNs), introduced, are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly encoded into the NN using automatic differentiation, while the sum of the mean-squared PDE residuals and the mean-squared error in initial-boundary conditions is minimized with respect to the NN parameters. Here we extend PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and we study systematically their convergence, hence explaining both fPINNs and PINNs for the first time. Specifically, we demonstrate their accuracy and effectiveness in solving multidimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box (BB) forcing terms). A novel element of the fPINNs is the hybrid approach that we introduce for constructing the residual in the loss function using both automatic differentiation for the integer-order operators and numerical discretization for the fractional operators. This approach bypasses the difficulties stemming from the fact that automatic differentiation is not applicable to fractional operators because the standard chain rule in integer calculus is not valid in fractional calculus. To discretize the fractional operators, we employ the Grünwald--Letnikov (GL) formula in one-dimensional fractional ADEs and the vector GL formula in conjunction with the directional fractional Laplacian in two- and three-dimensional fractional ADEs. We first consider the one-dimensional fractional Poisson equation and compare the convergence of the fPINNs against the finite difference method (FDM). We present the solution convergence using both the mean L 2 error as well as the standard deviation due to sensitivity to NN parameter initializations. Using different GL formulas we observe first-, second-, and third-order convergence rates for small size training sets but the error saturates for larger training sets. We explain these results by analyzing the four sources of numerical errors due to discretization, sampling, NN approximation, and optimization. The total error decays monotonically (below 10 –5 for a third-order GL formula) but it saturates beyond that point due to the optimization error. We also analyze the relative balance between discretization and sampling errors and observe that the sampling size and the number of discretization points (auxiliary points) should be comparable to achieve the highest accuracy. As we increase the depth of the NN up to certain value, the mean error decreases and the standard deviation increases, whereas the width has essentially no effect unless its value is either too small or too large. We next consider time-dependent fractional ADEs and compare white-box (WB) and BB forcing. We observe that for the WB forcing, our results are similar to the aforementioned cases; however, for the BB forcing fPINNs outperform FDM. Subsequently, we consider multidimensional time-, space-, and space-time-fractional ADEs using the directional fractional Laplacian and we observe relative errors of 10 –3 ~ 10 –4 . Lastly, we solve several inverse problems in one, two, and three dimensions to identify the fractional orders, diffusion coefficients, and transport velocities and obtain accurate results given proper initializations even in the presence of significant noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (N u ), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Finally, our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Stability of the Tonks–Langmuir discharge pre-sheath

The article formulates the stability problem of the plasma sheath in the Tonks–Langmuir discharge. Using the kinetic description of the ion gas, i.e., the stability of the potential shape in the quasi-neutral pre-sheath regarding the high and low frequency, the perturbations are investigated. The electrons are assumed to be Maxwell–Boltzmann distributed. Regarding high-frequency perturbations, the pre-sheath is shown to be stable. The stability problem regarding low-frequency perturbations can be reduced to an analysis of the “diffusion like” equation, which results in the instability of the potential distribution in the pre-sheath. By means of the Particle in Cell simulations, also the nonlinear stage of low frequency oscillations is investigated. Comparing the figure obtained with the figure for linear stage, one can find obvious similarity in the spatial-temporal behavior of the potential.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

Supersonic wind tunnel optimization

Attention is given to major problems arising in the course of definition studies for an optimum supersonic wind tunnel facility that incorporates advanced technologies. The issues identified encompass (1) large amplitude stream disturbances due to acoustic radiation from nozzle wall boundary layers; (2) flow field and model shape distortion caused by sting supports and their installation; (3) lack of sufficient three-dimensional flow visualizaton and diagnostic capabilities that allow ready identification of 'Reynolds number effects'; (4) lack of aerodynamic/propulsion facilities for investigation of the requisite range of vehicle attitudes and transient propulsion behavior; and (5) inordinately large energy usage, primarily due to diffuser inefficiency. Remedies are offered for these problems.

Bushnell, D. M.↗
DOE OSTI2014

The iterative thermal emission method: A more implicit modification of IMC

For over 40 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems typically contain regions that are optically thick and diffusive, as a consequence of the high degree of “pseudo-scattering” introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features that could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be nonphysical, in that they violate a maximum principle, where IMC-calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called iterative thermal emission IMC, which is designed to have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit version of IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time step material temperature during a time step. A better estimate of the end of time step material temperature allows for a more implicit estimate of other temperature-dependent quantities: opacity, heat capacity, Fleck factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. We have verified the ITE IMC method against 0-D and 1-D analytic solutions and problems from the literature. These results are compared with traditional IMC. We perform an infinite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. The ITE IMC method does however yield solutions with larger variance because each sub-step uses a different Fleck factor (even at equilibrium)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A New Method for the Solution of Group Diffusion Equations

Here, the diffusion equations associated with the multigroup, multiregion problem are solved by expansions in eigenfunctions which are solutions of the Helmholtz equation. A determinantal criticality equation is exhibited in which the order of the determinant is independent of the number of groups and which can be solved without recourse to complicated computational procedures. Moreover, the need to fulfill explicitly the requirements that the flux and current associated with each neutron group be continuous across interfaces is eliminated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Stable low diffusion flux splitting schemes on unstructured meshes

Shock instabilities are shown to manifest in modern low-diffusion flux-vector splitting (FVS) schemes when used on unstructured meshes, or situations where shocks do not align with the mesh lines. These instabilities occur irrespective of the Mach number of the shock. Three types of dissipative mechanisms that suppress these instabilities are presented. These mechanisms are carefully designed in order to affect only problematic regions of the flux-splittings. The AUSM + and LDFSS schemes are stabilized using the proposed modifications. It is shown that the added dissipation improves the shock behavior of AUSM and LDFSS on unstructured meshes. It is also shown that the AUSM + -up scheme is prone to the “carbuncle” instability, a specific type of shock instability, when used on unstructured meshes. The modifications proposed in this work do not lead to carbuncle instabilities for the problems considered here. Furthermore, the modified schemes are shown to satisfy certain properties that are crucial for accurate shear layer computations, such as stationary contact preservation. Using benchmark problems, it is demonstrated that despite the diffusion added for stabilization, these schemes are not overly diffusive. Furthermore, due to these advantages, the modified FVS schemes presented here are promising candidates for high-speed compressible flow computations on unstructured meshes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Ho, Lee-Wing↗
DOE OSTI2020

Thermochemically-Informed Mass Transport Model for Zr in U-Zr Fuel

Recent improvements to the coupled Thermochimica-MOOSE/BISON code system have enabled efficient calculations of species transport based on direct evaluation of composition and temperature dependent chemical potentials of the species. This presents an alternative to the traditional approach to species transport in nuclear fuels, which has been to employ a diffusion formulation that combines concentration-gradient driven Fickian diffusion with a Soret term based on a heat of transport fit to experimental data. Here we describe the application of the coupled code system to the diffusion of Zr in U-Zr metallic fuel. New classes implemented in BISON to solve this problem are documented. The Zr concentration profile after 50 years of diffusion is found to be strongly dependent on the assumptions made pertaining how to mobility is calculated in multi-phase regions of the fuel element. Two assumptions are compared (simple averaging of mobilities and using the majority phase mobility), and good qualitative agreement with experimental measurements is obtained using the majority phase assumption.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Demonstration of Full Core Reactor Depletion with MPACT

MPACT is a three-dimensional (3-D) whole core transport code capable of generating sub-pin level power distributions. This feature is accomplished by obtaining the integral transport solutions to the heterogeneous reactor problem in which the actual detailed geometrical configuration of fuel components such as the pellet and cladding is modelled explicitly.. The cross section data needed for the neutron transport calculation are obtained directly from a multigroup microscopic cross section library similar to those used in lattice physics codes. Hence MPACT involves neither a priori homogenization nor group condensation for the core spatial solution. The integral transport solution is obtained by means of the method of characteristics (MOC) that employs discrete ray tracing. Since the direct application of the 3-D MOC capability in MPACT to 3-D core configuration requires considerable amounts of memory and computing time for practical reactor applications, an alternative approximate 3-D solution method was implemented in MPACT based on a 2D-1D approach which employs planar MOC solutions in the framework of the 3-D coarse mesh finite difference (CMFD) formulation. The axial coupling is resolved by one-dimensional (1-D) diffusion solutions and the planar and axial problems are coupled through the transverse leakage. The use of a lower order 1-D solution in the axial direction is justified by the fact that most heterogeneity in the core occurs in the radial direction rather than the axial. However, it is possible to use one of the higher order methods in MPACT such as the 1-D SN kernel if improved solution accuracy is desired. The CMFD formulation which originally served as an efficient nodal formulation is used in MPACT to accelerate the whole core transport calculation. The basic mesh in the CMFD formulation is a pin cell which is much coarser than the flat source regions defined for MOC calculations. The concept of dynamic homogenization of group constants for the pin cells provides the basis of the CMFD formulation in whole core transport calculation. The intra-cell flux distribution determined from the MOC calculation is used to generate the homogenized cell constants while the MOC cell surface averaged currents are used to determine the radial nodal coupling coefficients. This dynamic implementation of the equivalence theory formulation ensures the same transport solution is obtained with CMFD as the one obtained using unaccelerated MOC calculations alone. The ability of MPACT to predict the Hot, Zero Power (HZP) condition of a reactor was reported in CASL-U-2014-0045-000. The purpose of this report is to demonstrate the capability of MPACT to simulate the operation of a reactor at Hot, Full Power (HFP) conditions during normal operation throughout a full operating cycle. The time scale for a reactor burnup cycle is typically one to two years and therefore short time phenomena such as the effect of delayed neutrons can be neglected. Instead the time dependence can be treated quasi-statically using the depletion algorithm presented in CASL-U-2013-0276-001. The full power operation requires thermal hydraulic feedback to be present during the entire simulation which will utilize the work in CASL-U-2014-0051-000. However, due to the significant computational burden of the coupled physics simulation, a simplified thermal hydraulic model is used for the analysis reported here which is principally intended to demonstrate the full core neutronics depletion. In addition to the thermal hydraulic feedback, the effect of Boron 10 depletion should be modeled in cases where major boron additions are not performed for extended periods of time. Each of these capabilities will be described in the following sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

A high-order staggered meshless method for elliptic problems

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attains $O(h^{m})$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An information diffusion technique to assess integrated hazard risks

An integrated risk is a scene in the future associated with some adverse incident caused by multiple hazards. An integrated probability risk is the expected value of disaster. Due to the difficulty of assessing an integrated probability risk with a small sample, weighting methods and copulas are employed to avoid this obstacle. To resolve the problem, in this paper, we develop the information diffusion technique to construct a joint probability distribution and a vulnerability surface. Then, an integrated risk can be directly assessed by using a small sample. A case of an integrated risk caused by flood and earthquake is given to show how the suggested technique is used to assess the integrated risk of annual property loss.

58 GEOSCIENCES↗
NASA NTRS1987

Numerical solution of the radiation transport equation in disk geometry

An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

Spagna, George F., Jr.↗
NASA NTRS1980

Application of finite-element-techniques to the interaction of conduction and radiation in an absorbing, scattering and emitting medium

In this paper, the authors demonstrate that a Galerkin finite element method of analysis, utilizing isoparametric elements, offers a viable means of solving continuum thermal radiation problems with conduction in a participating medium. The participating medium was considered to be a gray radiation medium exhibiting isotropic absorption, emission, and scattering characteristics and optical properties that are independent of temperature. The medium was considered to be bounded by infinite parallel opaque, gray surfaces with diffuse emission and reflection characteristics. In solving this problem, a finite element formulation was developed to describe a system in radiative equilibrium. Then the results of this first analysis were linked with a second finite element model which incorporated conduction into the analysis. The results of this study were found to be in good agreement with existing published data. The model offers the following advantageous features: geometric generality, a computational algorithm which is 'convenient' and 'computable', and a functional basis for extension of the radiation model to higher order approximation.

Wu, S. T.↗
DOE OSTI2019

ICAT: A numerical scheme to minimize numerical diffusion in advection-dispersion modeling and its application in identifying flow channeling

The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. We report discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.

15 GEOTHERMAL ENERGY↗