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Morel, Jim E.

Publications and source records attributed to Morel, Jim E..

At least 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2024

A New Galerkin Quadrature Method Not Requiring a Matrix Inverse

We derive a new Galerkin quadrature (GQ) method for S 𝑛 calculations that differs from the two methods preceding it in that a matrix inverse for an 𝑁 𝑑 × 𝑁 𝑑 matrix, where 𝑁𝑑 is the number of directions in the quadrature set, is no longer required. Galerkin quadrature methods are designed for calculations with highly anisotropic scattering. Such methods are not simply special angular quadratures but also are methods for representing the S 𝑛 scattering source that offers several advantages relative to the standard scattering source representation when highly truncated Legendre cross-section expansions must be used. Galerkin quadrature methods are also useful when the scattering is moderately anisotropic, but the quadrature being used is not sufficiently accurate for the order of the scattering source expansion that is required. Furthermore, we derive the new method and present computational results showing that its performance for two challenging problems is comparable to those of the two GQ methods that preceded it.

Galerkin quadrature↗
DOE OSTI2024

Neutron source reconstruction using a generalized expectation–maximization algorithm on one-dimensional neutron images from the Z facility

Magnetized Liner Inertial Fusion experiments have been performed at the Z facility at Sandia National Laboratories. These experiments use deuterium fuel, which produces 2.45 MeV neutrons on reaching thermonuclear conditions. To study the spatial structure of neutron production, the one-dimensional imager of neutrons diagnostic was fielded to record axial resolved neutron images. In this diagnostic, neutrons passing through a rolled edge aperture form an image on a CR-39-based solid state nuclear track detector. In this report we present a modified generalized expectation–maximization algorithm to reconstruct an axial neutron emission profile of the stagnated fusion plasma. We validate the approach by comparing the reconstructed neutron emission profile to an x-ray emission profile provided by a time-integrated pinhole camera.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Anomalous Behavior of Newtonian Hydrodynamics Coupled with Radiation Transport

This study shows that Newtonian hydrodynamics coupled with radiation transport, using a wide range of methods for treating the material-motion corrections, results in anomalous behavior. In particular, the flow of infinite-medium equilibration will accelerate whenever viewed moving past an observer in the laboratory frame. The acceleration may cause the velocity to increase exponentially in time. An exact fully-relativistic solution is derived to show that there is no acceleration, independent of the reference frame. This solution is analytic and may be used as a validation problem for the simulation of fully-relativistic radiation hydrodynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Transport error estimation using residual Monte Carlo

The residual Monte Carlo (RMC) method is also known in the literature as sequential Monte Carlo and reduced-source Monte Carlo. Given a Monte Carlo method for solving a linear equation and an approximate solution to that system, the residual method enables use of essentially the same Monte Carlo algorithm to directly compute the additive error or “defect” associated with the approximate solution. As the size of the defect decreases relative to the size of the solution, the residual Monte Carlo method becomes increasingly efficient relative to the standard Monte Carlo (SMC) method. Here we present a new RMC algorithm for evaluating the space-angle error in S n radiation transport solutions, and provide computational examples demonstrating that it can be far more efficient than SMC for this purpose. Herein we also describe a particular pitfall that must be avoided if RMC is to be efficient, and explain why the performance of RMC can significantly differ between different transport problems and different quantities of interest for the same problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Massively parallel transport sweeps on meshes with cyclic dependencies

When solving the first-order form of the linear Boltzmann equation, a common misconception is that the matrix-free computational method of “sweeping the mesh”, used in conjunction with the Discrete Ordinates method, is too complex or does not scale well enough to be implemented in modern high performance computing codes. This has led to considerable efforts in the development of matrix-based methods that are computationally expensive and is partly driven by the requirements placed on modern spatial discretizations. In particular, modern transport codes are required to support higher order elements, a concept that invariably adds a lot of complexity to sweeps because of the introduction of cyclic dependencies with curved mesh cells. In this article we will present a comprehensive implementation of sweeping, to a piecewise-linear DFEM spatial discretization with particular focus on handling cyclic dependencies and possible extensions to higher order spatial discretizations. We find that these methods are implemented in a new C++ simulation framework called Chi-Tech (). We present some typical simulation results with some performance aspects that one can expect during real world simulations, we also present a scaling study to >100k processes where Chi-Tech maintains greater than 80% efficiency solving a total of 87.7 trillion angular flux unknowns for a 116 group simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing

The purpose of this paper is to present a Variable Eddington Factor (VEF) method for the 1-D grey radiative transfer equations that uses a lumped linear discontinuous Galerkin spatial discretization for the Sequations together with a constant-linear mixed finite-element discretization for the VEF moment and material temperature equations. The use of independent discretizations can be particularly useful for multiphysics applications such as radiation-hydrodynamics. The VEF method is quite old, but to our knowledge, this particular combination of differencing schemes has not been previously investigated for radiative transfer. We define the scheme and present computational results. As expected, the scheme exhibits second-order accuracy for the directionally-integrated intensity and material temperature, and behaves well in the thick diffusion limit. An important focus of this study is the treatment of the strong temperature dependence of the opacities and the spatial dependence of the opacities within each cell, which are not explicitly defined by the basic discretization schemes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Nonlinear Diffusion Acceleration of the Least-Squares Transport Equation in Geometries with Voids

In this paper we show the extension of the Nonlinear-Diffusion Acceleration (NDA) to geometries containing small voids using a weighted least-squares (WLS) high order equation. Even though the WLS equation is well defined in voids, the low-order drift diffusion equation was not defined in materials with a zero cross section. This paper derives the necessary modifications to the NDA algorithm. We show that a small change to the NDA closure term and a non-local definition of the diffusion coefficient solve the problems for voids regions. These changes do not affect the algorithm for optical thick material regions, while making the algorithm well defined in optically thin ones. We use a Fourier analysis to perform an iterative analysis to confirm that the modifications result in a stable and efficient algorithm. Numerical results of our method will be presented in the second part of the paper. We test this formulation with a small, one-dimensional test problem. Additionally we present results for a modified version of the C5G7 benchmark containing voids as a more complex, reactor like problem. We compared our results to PDT, Texas A&M’s transport code, utilizing a first order discontinuous formulation as reference and the self-adjoint angular flux equation with void treatment (SAAFτ ), a different second order form. The results indicate, that the NDA WLS performed comparably or slightly worse then the asymmetric SAAFτ , while maintaining a symmetric discretization matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Comparison of two Galerkin quadrature methods

Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard S N method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard S N method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwise sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly set negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

High-order solution methods for grey discrete ordinates thermal radiative transfer

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗