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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A data-driven operational model for traffic at the Dallas Fort Worth International Airport

Airports are on the front line of significant innovations, allowing the movement of more people and goods faster, cheaper, and with greater convenience. As air travel continues to grow, airports will face challenges in responding to increasing passenger vehicle traffic, which leads to lower operational efficiency, poor air quality, and security concerns. This paper evaluates methods for traffic demand forecasting combined with traffic microsimulation, which will allow airport operations staff to accurately predict traffic and congestion. Using two years of detailed data describing individual vehicle arrivals and departures, aircraft movements, and weather at Dallas-Fort Worth (DFW) International Airport, we evaluate multiple prediction methods including the Auto Regressive Integrated Moving Average (ARIMA) family of models, traditional machine learning models, and DeepAR, a modern recurrent neural network (RNN). We find that these algorithms are able to capture the diurnal trends in the surface traffic, and all do very well when predicting the next 30 minutes of demand. Longer forecast horizons are moderately effective, demonstrating the challenge of this problem and highlighting promising techniques as well as potential areas for improvement. Traffic demand is not the only factor that contributes to terminal congestion, because temporary changes to the road network, such as a lane closure, can make benign traffic demand highly congested. Combining a demand forecast with a traffic microsimulation framework provides a complete picture of traffic and its consequences. The result is an operational intelligence platform for exploring policy changes, as well as infrastructure expansion and disruption scenarios. To demonstrate the value of this approach, we present results from a case study at DFW Airport assessing the impact of a policy change for vehicle routing in high demand scenarios. This framework can assist airports like DFW as they tackle daily operational challenges, as well as explore the integration of emerging technology and expansion of their services into long term plans.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties

Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However, the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator [W. K. Yeo (CUP, 1993)] and require no assumptions about the nature of the flow or magnetic field. Thus, the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvénic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular, the anisotropy of the flow. Their properties are a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

An Enhanced Virtual Crack Closure Technique for Stress Intensity Factor Calculation along Arbitrary Crack Fronts and the Application in Hydraulic Fracturing Simulation

The virtual crack closure technique (VCCT) is widely used for calculating energy release rates along crack fronts and modeling the propagation of cracks in solid materials. Although the VCCT formulation for smooth crack fronts has been sufficiently addressed in the literature, the application of VCCT to a nonsmoothed crack front with sharp corners warrants further investigation. In this study, we describe an enhanced VCCT to calculate energy release rates and stress intensity factors for cracks with arbitrary shapes in 3D domains discretized on structured grids. The formulations of the enhanced VCCT were developed and implemented into a multiphysics simulation environment capable of simulating crack propagation in the framework of linear elastic fracture mechanics. Comparisons with existing analytical/numerical solutions and other VCCT approaches were performed to verify the enhanced VCCT in terms of SIF calculation along nonsmoothed crack fronts. We then applied the enhanced VCCT to a hydraulically driven penny-shaped fracture problem to further demonstrate its capability to simulate nonsmoothed fracture propagation.

02 PETROLEUM↗
DOE OSTI2022

A simple improved low temperature correction for the hierarchical equations of motion

The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system–bath coupling strength. However, in its standard form, this method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here, we propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection, which alleviates this problem and restores consistency with the weak-coupling master equation with a minimal hierarchy. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna–Matthews–Olson complex. The new closure is found to improve convergence of the HEOM even beyond the weak-coupling limit and is very straightforward to implement in existing HEOM codes.

Fay, Thomas P. (ORCID:000000030625731X)↗
DOE OSTI2017

International Approaches for Nuclear Waste Disposal in Geological Formations: Geological Challenges in Radioactive Waste Isolation—Fifth Worldwide Review

The overall objective of the Fifth Worldwide Review (WWR-5) is to document the current state-of-the-art of major developments in a number of nations throughout the World pursuing geological disposal programs, and to summarize challenging problems and experience that have been obtained in siting, preparing and reviewing cases for the operational and long-term safety of proposed and operating nuclear waste repositories. The scope of the Review is to address current specific technical issues and challenges in safety case development along with the interplay of technical feasibility, siting, engineering design issues, and operational and post-closure safety. In particular, the chapters included in the report present the following types of information: the current status of the deep geological repository programs for high level nuclear waste and low- and intermediate level nuclear waste in each country, concepts of siting and radioactive waste and spent nuclear fuel management in different countries (with the emphasis of nuclear waste disposal under different climatic conditions and different geological formations), progress in repository site selection and site characterization, technology development, buffer/backfill materials studies and testing, support activities, programs, and projects, international cooperation, and future plans, as well as regulatory issues and transboundary problems.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

CTF: A modernized, production-level, thermal hydraulic solver for the solution of industry-relevant challenge problems in pressurized water reactors

CTF is a thermal hydraulic (T/H) subchannel tool that has been extensively developed over the past ten years as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL) program. The code was selected early in the CASL program for support of high-impact challenge problems that were found to be relevant to the nuclear industry and its currently operating fleet of pressurized water reactors (PWRs), including issues such as departure from nucleate boiling (DNB), crud-induced power shifts (CIPSs), and reactivity-insertion accidents (RIAs). By incorporating CTF into the multiphysics Virtual Environment for Reactor Application (VERA) core simulator software developed by CASL, CTF has become the primary means of providing fluid and fuel thermal feedback, as well as T/H figure-of-merits (FOMs) in large-scale reactor simulations. With the goal of solving industry challenge problems, CASL placed great emphasis on developing high-quality, high-performance, validated software tools that offer higher fidelity than what is currently possible with current industry methods. In support of this effort, CTF was developed from a research tool into an nuclear quality assurance (NQA-1)–compliant, production-level software tool that is capable of addressing the stated challenge problems and goals of CASL. This work presents a review of the major technological achievements that were realized in developing CTF over the past decade of the CASL program and presents an overview of the code solution approach and closure models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media

Empirical or theoretical extensions of Darcy’s law for immiscible two-phase flow have shown significant limitations in properly modeling the flow at the continuum scale. We tackle this problem by proposing a set of upscaled equations based on pore-scale flow regimes, that is, the topology of flowing phases. The incompressible Navier-Stokes equation is upscaled by means of multiple-scale expansions and its closures derived from the mechanical energy balance for different flow regimes at the pore scale. We also derive the applicability conditions of the upscaled equations based on the order of magnitude of relevant dimensionless numbers, that is, Eotvos, Reynolds, capillary, Froude numbers, and the viscosity and density ratio of the system, as well as a set of closures valid for the basic flow regimes of low Eotvos number systems, that is, core-annular and plug and drop traffic flows. We provide analytical expressions for the relative permeability of the wetting and nonwetting phases in different flow regimes and demonstrate that the effect of the flowing-phases topology on the relative permeabilities is significant. Finally, we show that the classical two-phase Darcy law is recovered for a limited range of operative conditions, while specific terms accounting for interfacial and wall interactions should be incorporated to accurately model ganglia or drop traffic flow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Collaborative Research: Enabling multi-scale studies of magnetic reconnection with interpretable data-driven models

The development of accurate reduced descriptions and improved closures for magnetic reconnection is an important and a long‐standing challenge in plasma physics. The four‐fluid approach, and associated closures, that were investigated have the potential to improve the accuracy of plasma fluid models, capturing physical effects which would otherwise require a kinetic description. If successful, this approach could have an important impact for the modeling of laboratory and space plasmas. The major goals of this project were to develop new machine learning (ML) tools based on sparse and symbolic regression techniques, and to extract interpretable and generalizable reduced models (e.g., in the form of partial differential equations - PDEs) from data generated by first principles plasma simulations. Preserving interpretability of such data‐driven models is key to addressing the long‐standing theoretical and numerical challenges. Prior proof‐of‐principle studies have demonstrated the enormous potential of this approach, by recovering the well‐established hierarchy of plasma equations (from Vlasov to MHD) from data produced by particle‐in‐cell (PIC) simulations. Our goal in this project was to extend and apply these new tools to construct better kinetic closures for magnetic reconnection; to derive better models of particle injection and acceleration by this fundamental plasma process; and to use this understanding to accelerate the development of multi‐scale plasma algorithms. While our immediate focus was on the problem of magnetic reconnection, the tools that were will developed are general and applicable to other areas of plasma physics, and more broadly to many‐body phenomena. We anticipate that the development of these multi‐scale models will have a significant impact across different areas of plasma science, from fusion to space and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

High performance double-null plasmas under radiating divertor and mantle scenarios on DIII-D

Experiments to combine a radiating divertor or mantle with high power, high βN plasma operation have successfully reduced the divertor heat flux by 40% but have also encountered several challenging problems. For example, injecting either neon or argon seed impurities have led both to significant fuel dilution of the core plasma and to the emergence of harmful tearing mode activity which compromised plasma beta and energy confinement time. Increased divertor closure ended in more effective control over the injected seed impurity inventory, although it was also observed that small radial variations in the placement of the outer separatrix strike point within the DIII-D ‘closed’ divertor could lead to clear differences in the impurity build-up inside the core plasma. Active particle pumping of argon seed impurities through the divertor leg on the high-field side of a double-null divertor configuration showed little effect on seed impurity inventory and only modest control over the deuterium fuel inventory. Normally, 80% or greater of injected argon was removed by the corresponding cryo-pump on the low-field (outboard) side of that divertor, with the remaining argon being removed by the outboard cryo-pump from the opposite divertor. For single-null divertor cases, the contribution of the inner (high-field) cryo-pump to impurity and main-ion control appears to be complicated by the levels of divertor recycling and degree of divertor detachment. In general, divertor design that impedes the escape of seed impurities, plasma shaping that allows a higher stability limit, and electron cyclotron deposition profiles that prevent tearing mode onset and impede impurity accumulation in the core are under consideration for addressing the issues presented in our work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

The Functor system: a new on-the-fly take on Material Properties based on C++ functions

In the context of solving multiphysics problems, the discretization of the partial differential equations (PDE) at hand often takes the spotlight. However, for most engineering users and even application developers, the discretization of the equations has already been performed. Instead, they are tasked with implementing specific closure relations and material properties. MOOSE has long enabled this using the Materials system. This system relied on the pre-computation of all properties before they are used in the PDE or in postprocessing. In this talk we will introduce the Functor system, which was deployed in MOOSE in 2021, then present a few applications of functors in flow modeling simulations by the NEAMS program. Functors first offer great flexibility in their evaluation. Rather than storing various arrays for material properties, they are evaluated on the fly at the location and state, e.g. current or old value, requested. Unlike regular material properties, several operations such as the time derivative, the divergence and the curl can be requested from a functor. Similar to material properties, functors can be made to depend on arbitrary combinations of variables, functions, postprocessors and other properties. However, unlike material properties, any of these can be substituted for a functor material property. Thanks to this, objects no longer need to be duplicated based on the types of their parameters.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Constrained optimization framework for interface-aware sub-scale dynamics discrete closure model for multimaterial cells in Lagrangian cell-centered hydrodynamics

In this paper, we present the new discrete optimization-based interface-aware sub-scale dynamics (IA-SSD) closure model for multimaterial cells for Lagrangian cell-centered hydrodynamics. For the multimaterial cell, the kinematic and thermodynamic properties (e.g., velocity, density, pressure and internal energy) will typically vary between the materials. The discrete closure model is responsible for an accurate update of the thermodynamic states of the individual material components in the multimaterial cell, and for determining the nodal forces that move the vertices of the cell. The IA-SSD closure model consists of two stages — a bulk stage followed by a sub-scale stage. During the bulk stage, the total change in the volume of the cell, total force applied to the cell, and total work done on the cell are distributed between the materials to update their volume, velocity and total energy. This distribution is performed using volume fractions of the materials. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is used, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and are limited using physically justified constraints: positivity of volume, positivity of internal energy, and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. It is a first-of-its kind application of constrained optimization to develop discrete closure models in a more rigorous fashion. The pair-wise interaction between materials is essentially one dimensional in the direction that is normal to interface. Finally, for this reason, we demonstrate in this paper the performance of our new model on one dimensional numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.

58 GEOSCIENCES↗
DOE OSTI2026

Machine learning method for enforcing variable independence in background estimation with LHC data: ABCDisCoTEC

A novel solution is presented for the problem of estimating the backgrounds of a signal search using observed data while simultaneously maximizing the sensitivity of the search to the signal. The 'ABCD method' provides a reliable framework for background estimation by partitioning events into one signal-enhanced region (A) and three background-enhanced control regions (B, C, and D) via two smoothly varying, statistically independent variables. In practice, even slight correlations between the two variables can significantly undermine the method's performance. Thus, choosing appropriate variables by hand can present a formidable challenge, especially when background and signal differ only subtly. To address this issue, the ABCD with distance correlation (ABCDisCo) method was developed to construct two learned variables via a neural network trained to provide strong signal-background discrimination with small values of the distance correlation (DisCo) measure between the two learned variables. However, relying solely on minimizing the DisCo can result in learned variables that may not have distributions of background events that are smoothly varying and localized at extreme values, as necessary for the validity of the background estimation. The ABCDisCo training enhanced with closure (ABCDisCoTEC) method is introduced to solve this issue by directly minimizing the nonclosure, expressed as a dedicated differentiable loss term. This extended method is applied to a data set of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the CMS detector at the CERN Large Hadron Collider. Additionally, given the complexity of the minimization problem with constraints on multiple loss terms, the modified differential method of multipliers is applied and shown to greatly improve the stability and robustness of the ABCDisCoTEC method, compared to grid search hyperparameter optimization procedures.

Hayrapetyan, Aram [Yerevan Phys. Inst.]↗
DOE OSTI2024

A Second Moment Method for k -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

The second moment method is a linear acceleration technique that couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasidiffusion. While this method has been shown to be comparable to quasidiffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to the belief that the resulting inhomogeneous source makes the problem ill posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasidiffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Finally, the results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

CTF Parallel Performance Improvements

CTF is a modernized version of COBRA-TF (Coolant Boiling in Rod Arrays-Two Fluid), which is a thermal hydraulic (T/H) sub-channel code based on a two-phase, two-fluid model that formulates the conservation equations of mass, energy, and momentum for three fields of vapor, continuous liquid, and entrained liquid droplets. Under the Consortium for Advanced Simulation of Light Water Reactors (CASL) program sponsored by the U.S. Department of Energy, CTF is being further developed and improved for modeling and simulation of light water reactors. The code improvements for predicting T/H responses of pressurized water reactor (PWR) cores are focused on its applications to specific challenge problems deemed significant to the industry, such as departure from nucleate boiling (DNB) and crud-induced power shift. The code is also being used for T/H feedback in normal operating condition depletions in PWR and boiling water reactor designs in the reactor core simulator, Virtual Environment for Reactor Applications Core Simulator (VERA-CS), being developed by CASL. CTF modifications under the CASL program include software optimization, new closure models, and parallelization for modeling full reactor core T/H responses. The purpose of this work was to improve the parallel performance of CTF. CTF was originally parallelized via a domain-decomposition strategy using the Message Passing Interface (MPI), in which the basis of a solution domain was a physical assembly in the model. In other words, a user who wanted to perform a parallel solution with CTF had to provide the code one processor per assembly in the model (e.g., 56 cores for a 56 assembly quarter-core model, or 193 cores for a 193 assembly full-core model). This design was rigid, demanding a very specific number of processors for a model; furthermore, when CTF was run in VERA-CS-which typically uses thousands of processors- many processors sat idle during the CTF solve because CTF was unable to use any more processors than there are physical assemblies. This was not necessarily a problem if the CTF execution speed was very fast, but the average time spent in a CTF solve for prototypical PWR operating conditions was significant (i.e., over 20 % of the simulation wall time was being spent in CTF for a standard core depletion simulation). Larger, more computationally intensive simulations performed in support of the CASL DNB challenge problem demonstrated a need for improvements in this original parallelization approach. The specific goal of this work was to allow CTF to use more processors than there are physical assemblies in the model, which would not only speed up CTF and improve the overall efficiency of VERA-CS but also give users more-flexible options for executing their simulations. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Uncertainty quantification tools for multiphase gas-solid flow simulations using MFIX

Computational fluid dynamics (CFD) has been widely studied and used in the scientific community and in the industry. Various models were proposed to solve problems in different areas. However, all models deviate from reality. Uncertainty quantification (UQ) process evaluates the overall uncertainties associated with the prediction of quantities of interest. In particular it studies the propagation of input uncertainties to the outputs of the models so that confidence intervals can be provided for the simulation results. In the present work, a non-intrusive quadrature-based uncertainty quantification (QBUQ) approach is proposed. The probability distribution function (PDF) of the system response can be then reconstructed using extended quadrature method of moments (EQMOM) and extended conditional quadrature method of moments (ECQMOM). The report first explains the theory of QBUQ approach, including methods to generate samples for problems with single or multiple uncertain input parameters, low order statistics, and required number of samples. Then methods for univariate PDF reconstruction (EQMOM) and multivariate PDF reconstruction (ECQMOM) are explained. The implementation of QBUQ approach into the open-source CFD code MFIX is discussed next. At last, QBUQ approach is demonstrated in several applications. The method is first applied to two examples: a developing flow in a channel with uncertain viscosity, and an oblique shock problem with uncertain upstream Mach number. The error in the prediction of the moment response is studied as a function of the number of samples, and the accuracy of the moments required to reconstruct the PDF of the system response is discussed. The QBUQ approach is then demonstrated by considering a bubbling fluidized bed as example application. The mean particle size is assumed to be the uncertain input parameter. The system is simulated with a standard two-fluid model with kinetic theory closures for the particulate phase implemented into MFIX. The effect of uncertainty on the disperse-phase volume fraction, on the phase velocities and on the pressure drop inside the fluidized bed are examined, and the reconstructed PDFs are provided for the three quantities studied. Then the approach is applied to a bubbling fluidized bed with two uncertain parameters, particle-particle and particle-wall restitution coefficients. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities and gas pressure are provided. The PDFs of the response are reconstructed using EQMOM with appropriate kernel density functions. The simulation results are compared to experimental data provided by the 2013 NETL small-scale challenge problem. Lastly, the proposed procedure is demonstrated by considering a riser of a circulating fluidized bed as an example application. The mean particle size is considered to be the uncertain input parameter. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities, and granular temperature are provided. Mean values and confidence intervals of the quantities of interest are compared to the experiment results. The univariate and bivariate PDF reconstructions of the system response are performed using EQMOM and ECQMOM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multi-frequency General Relativistic Radiation-hydrodynamics with M 1 Closure

We report on recent upgrades to our general relativistic radiation-magnetohydrodynamics code, Cosmos++ , which expands the two-moment, M 1 , radiation treatment from gray to multi-frequency transport, including Doppler and gravitational frequency shifts. The solver accommodates either photon (Bose–Einstein) or neutrino (Fermi–Dirac) statistical distribution functions with absorption, emission, and elastic scattering processes. An implicit scheme is implemented to simultaneously solve the primitive inversion problem together with the radiation–matter coupling source terms, providing stability over a broad range of opacities and optical depths where the interaction terms can be stiff. We discuss our formulations and numerical methods, and validate our methods against a wide variety of test problems spanning optically thin to thick regimes in flat, weakly curved, and strongly curved spacetimes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗