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DOE OSTI2018

Progress toward a new implementation of the mortar finite element method in MOOSE

The mortar finite element method has been used for many years in a variety of applications, including the enforcement of continuity conditions across decomposed domains, the implementation of Dirichlet boundary conditions, obtaining improved estimates of surface fluxes, and for solving large deformation contact mechanics problems. There is a currently great deal of interest in developing more robust mechanical and thermal contact solution strategies in the MOOSE framework and physics modules, and schemes based on the mortar finite element approach appear to be a promising avenue of development. There are a number of challenges associated with the development of a robust Lagrange multiplier based formulation of the mortar finite element method which can be tackled using the relatively simple framework of thermal contact problems, before tackling more complicated applications such as thermomechanical contact. In this report, we describe several aspects of our mortar finite element method implementation for solving thermal contact problems. The approach and notation used are based primarily based on the work of Bin Yang et al. ("Two dimensional mortar contact methods for large deformation frictional sliding," International Journal for Numerical Methods in Engineering 62(9), 2005).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

High Order Discontinuous Galerkin Method and Applications (Final Technical Report)

This project aims at the developments and improvements of high order accurate discontinuous Galerkin finite element methods for solving partial differential equations arising from DOE applications. Algorithm development, improvement, analysis, implementation and applications aspects are addressed. The partial differential equations under study involve solutions with shocks or other discontinuities, rapidly changing regions, or multiscale solutions. These include the so-called convection dominated cases, such as the hyperbolic equations (e.g. Euler equations of gas dynamics), parabolic equations with small viscosities (e.g. high Reynolds number Navier-Stokes equations), KdV type equations with small dispersion describing water waves (small third derivative terms), time-dependent bi-harmonic equations and equations with hyper-viscosity (small fourth or higher even derivative terms), problems with highly oscillatory coefficients, or problems for which the macro-scale PDE models may not be correct in localized regions and a micro-scale model must be used instead. Furthermore, we are interested in the long time solutions of such equations with waves traveling a long distance, such as the electromagnetic waves. The requirement on numerical methods is thus high order accuracy, low dissipation/dispersion errors over long time, and a clean and sharp discontinuity resolution. It would also be highly desirable to have the numerical methods to be flexible for complicated geometry and boundary conditions, and to be easy in an adaptive and massively parallel environment. The discontinuous Galerkin finite element method has this potential, however the design and analysis of the discontinuous Galerkin method for each specific class of partial differential equations would require detailed research.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Analytical Radiochemical Method Development for Mark 18A Program

The Savannah River National Laboratory Nuclear Measurements Group was tasked by the Mark 18A Program team with developing three analytical characterization methods. These methods will support process and waste characterization of the Mark 18A program material. While methods already existed for most analytes of interest to the Mark 18A program team, the Nuclear Measurements Group developed and refined methods to quantify the Cf isotopes, 107 Pd, and 121m Sn. The results of that effort are presented in this work. Methods were successfully developed to characterize the Mark 18A samples for the needed isotopes and the NMG is ready to receive Mark 18A program samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements

In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.

17 WIND ENERGY↗

DOE OSTI2021

thornado-hydro: A Discontinuous Galerkin Method for Supernova Hydrodynamics with Nuclear Equations of State

This paper describes algorithms for non-relativistic hydrodynamics in the toolkit for high-order neutrino radiation hydrodynamics (thornado), which is being developed for multiphysics simulations of core-collapse supernovae (CCSNe) and related problems with Runge–Kutta discontinuous Galerkin (RKDG) methods. More specifically, thornado employs a spectral type nodal collocation approximation, and we have extended limiters — a slope limiter to prevent non-physical oscillations and a bound-enforcing limiter to prevent non-physical states — from the standard RKDG framework to be able to accommodate a tabulated nuclear equation of state (EoS). To demonstrate the efficacy of the algorithms with a nuclear EoS, we first present numerical results from basic test problems in idealized settings in one and two spatial dimensions, employing Cartesian, spherical-polar, and cylindrical coordinates. Then, we apply the RKDG method to the problem of adiabatic collapse, shock formation, and shock propagation in spherical symmetry, initiated with a 15 M ⊙ progenitor. Herein, we find that the extended limiters improve the fidelity and robustness of the RKDG method in idealized settings. The bound-enforcing limiter improves robustness of the RKDG method in the adiabatic collapse application, while we find that slope limiting in characteristic fields is vulnerable to structures in the EoS — more specifically, in the phase transition from nuclei and nucleons to bulk nuclear matter. The success of these applications marks an important step toward applying RKDG methods to more realistic CCSN simulations with thornado in the future.

Nuclear astrophysics (1129)↗

DOE OSTI2018

Convergence Analysis of a Locally Accelerated Preconditioned Steepest Descent Method for Hermitian-Definite Generalized Eigenvalue Problems

By extending the classical analysis techniques due to Samokish, Faddeev and Faddeeva, and Longsine and McCormick among others, we prove the convergence of preconditioned steepest descent with implicit deflation (PSD-id) method for solving Hermitian-definite generalized eigenvalue problems. Moreover, we derive a nonasymptotic estimate of the rate of convergence of the PSD-id method. We show that with a proper choice of the shift, the indefinite shift-and-invert preconditioner is a locally accelerated preconditioner, and is asymptotically optimal that leads to superlinear convergence. Numerical examples are presented to verify the theoretical results on the convergence behavior of the PSDid method for solving ill-conditioned Hermitian-definite generalized eigenvalue problems arising from electronic structure calculations. While rigorous and full-scale convergence proofs of preconditioned block steepest descent methods in practical use still largely eludes us, we postulate that the theoretical results introduced in this paper sheds light on an improved understanding of the convergence behavior of these block methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1952

A simple numerical method for the calculation of the laminar boundary layer

An iteration difference method for the calculation of the incompressible laminar boundary layer is described. The method uses Prandtl's boundary layer equation and the boundary conditions directly and permits the attainment of an arbitrary accuracy. The method has been tested successfully in the continuation of the Blasius profile on the flat plate, on the circular cylinder investigated by Heimenz and on an elliptical cylinder of fineness ratio 1:4. The method makes possible the testing of previously developed methods, all of which contain important assumptions.

BOUNDARY LAYER, LAMINAR - CALCULATIONS - SCHRODER ↗

NASA NTRS2015

A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method

The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.

Fluid Dynamics↗

NASA NTRS2016

Towards a Viscous Wall Model for Immersed Boundary Methods

Immersed boundary methods are frequently employed for simulating flows at low Reynolds numbers or for applications where viscous boundary layer effects can be neglected. The primary shortcoming of Cartesian mesh immersed boundary methods is the inability of efficiently resolving thin turbulent boundary layers in high-Reynolds number flow application. The inefficiency of resolving the thin boundary is associated with the use of constant aspect ratio Cartesian grid cells. Conventional CFD approaches can efficiently resolve the large wall normal gradients by utilizing large aspect ratio cells near the wall. This paper presents different approaches for immersed boundary methods to account for the viscous boundary layer interaction with the flow-field away from the walls. Different wall modeling approaches proposed in previous research studies are addressed and compared to a new integral boundary layer based approach. In contrast to common wall-modeling approaches that usually only utilize local flow information, the integral boundary layer based approach keeps the streamwise history of the boundary layer. This allows the method to remain effective at much larger y+ values than local wall modeling approaches. After a theoretical discussion of the different approaches, the method is applied to increasingly more challenging flow fields including fully attached, separated, and shock-induced separated (laminar and turbulent) flows.

Immersed↗

NASA NTRS2020

Spectral Spherical Harmonics Discrete Ordinate Method

A new method for modeling the radiative transfer in inhomogeneous three-dimensional media illuminated by a Gaussian beam is described. This approach, called the Spectral Spherical Harmonics Discrete Ordinate Method (SSHDOM), uses the Fourier expansion method to transform the three-dimensional radiative transfer into an one-dimensional equation in the spectral domain, and the Spherical Harmonics Discrete Ordinate Method (SHDOM) for its solution. Specifically, (i) the source function is represented in the spectral domain through a spherical harmonic expansion, (ii) the spectral one-dimensional radiative transfer equation is integrated along discrete ordinates through a spatial grid, and (iii) the solution method is based on the Picard iteration. Both SSHDOM and SHDOM algorithms are implemented in a common computer code.

Gaussian beam↗

NASA NTRS2021

An Evaluation of Timely Communications Access Methods Using NASA Space Network

There is a growing interest among scientists to coordinate diverse and temporally responsive measurements from multiple space and ground-based observatories in order to obtain greater insights into transient scientific events than would otherwise be possible. Many transient scientific events of interest occur randomly and the scientific value of follow-up observations decays with time. As a result, transient science operations among distributed observatories require timely access to communications network services. This paper develops two complimentary methods to improve users’ network access timeliness using the NASA Space Network (SN). Descriptive models of each method are developed using Systems Modeling Language. Pathfinder experiments are designed and executed. Suitability of the methods is discussed in light of the experimental results. Innovative applications of the methods are presented. This research establishes that the as-built SN systems have adequate capabilities and capacity to support infusion of the methods to current and future users with emergent time-sensitive service needs. The minimum service access wait time was determined to be approximately 10 min and is achievable 84% of the time. An average access wait time of approximately 14 min is expected when SN resource blocking occurs. A roadmap to improve SN access timeliness is presented.

Space Communications and Navigation↗

NASA NTRSDate not supplied

Comparing Acoustic Prediction Methods for Additively Manufactured Porous Strutures

While macroscale methods for predicting the acoustic properties of porous structures have been popular in the past, they often require time-consuming manufacturing and testing workflows. Meanwhile, microscale approaches allow the prediction of transport parameters based exclusively on a periodic structure’s unit cell geometry. Here, we compare these methods to predict the characteristic impedance of additively manufactured porous structures. We use the microscale approach to estimate the geometry’s transport parameters, then predict the characteristic properties using the Johnson-Champoux-Allard (JCA) model. We measure the acoustic properties of the printed structures using a normal incidence impedance tube and estimate the transport parameters using an inverse characterization approach. We use the two-thickness method as a macroscale approach to predict the characteristic properties from the measured surface impedances of two sample thicknesses. Finally, we compare these characteristic prediction methods. Our results show that the inverse characterization and two-thickness methods offer the closest match to the measured values at low frequencies.

impedance↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

A highly efficient, edge-based viscous (EBV) discretization method has been recently implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver and evaluated for Reynolds-averaged Navier-Stokes (RANS) formulations. In comparison to a well-established cell-based viscous (CBV) method, the EBV method has demonstrated multifold acceleration of all viscous-kernel computations on general unstructured mixed-element grids. The viscous kernels include evaluation of viscous fluxes, diffusion terms in turbulence models, and the corresponding Jacobian terms. In this paper, an EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Previously reported EBV computations have been conducted on traditional computing architectures based on central processing units (CPU). This paper assesses benefits of the EBV method on modern high-performance computing architectures based on graphics processing units (GPU). The GPU implementations of the CBV and EBV methods are verified by comparing solutions and iterative convergence with those observed in CPU computations on the same grids. A comprehensive assessment of the EBV speedup on CPU and GPU architectures is presented for established benchmark corner flows, namely, a supersonic flow through a long square duct and a subsonic flow around a NASA juncture flow model.

CFD↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

CFD↗

DOE OSTI2023

Simulation of Reverse Osmosis Membrane Compaction Using Material Point Method (MPM)

Access to fresh drinking water in the future requires effective management of industrial wastewater and water purification from available resources. In this study, we present the simulation methodology and the analysis of a Reverse Osmosis (RO) membrane under various pressure conditions using the Material Point Method (MPM). In contrast to other numerical methods, MPM solves the continuum governing equations on material points in a Lagrangian framework. The method does not require a grid connecting the material points hence making it suitable to simulate large deformations during membrane compaction. The time integration is carried out using the explicit Euler method, while the spatial discretization is performed using linear or cubic-spline shape functions. A series of planar images containing detailed pore structures obtained from X-ray tomography experiments is converted to a three-dimensional collection of material points to simulate the membrane. Compressive loads are applied to the top layer of the membrane to simulate the experiments. The membrane deformation and pore size distribution before and after load application are reported and compared with the experimental measurements. The presentation discusses the numerical methods used, the performance of the solver on high-performance computing machines, and the results of membrane compaction in detail.

ENGINEERING,MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Determining Physical Parameters of Shielded Uranium using Gamma Spectroscopy and the Differential Evolution Adaptive Metropolis (DREAM) Method

Inverse radiation transport is a well-established method for determining unknown parameters within a system that exhibits particle leakage. Two significant challenges of solving inverse transport problems are (1) to determine multiple unknowns without false convergence on local minima and (2) to be able to quantify uncertainty. It was recently demonstrated that the Differential Evolution Adaptive Metropolis (DREAM) method effectively meets both of these challenges. In Bledsoe's 2014 article, the DREAM method was only applied to numerical test cases in which measured data were simulated using MCNP. This paper provides results of research conducted at Oak Ridge National Laboratory (ORNL) in which DREAM was applied to two-dimensional inverse transport problems using real-world measurements. The DREAM method uses a Markov chain Monte Carlo (MCMC) method to obtain a posterior distribution of unknown parameters. In this application, the posterior distribution is determined by using a uniform prior distribution and a likelihood function. The goal of the inverse problem is to find the regions in which the likelihood function is at or near its maximum. In the traditional MCMC approach, a single Markov chain is employed. In practice, MCMC approaches have a high acceptance rate to solutions that are near the current point of sampling, but they exhibit slow convergence to solutions far from the sampling point. The DREAM algorithm was designed to alleviate this issue by initiating multiple Markov chains and using the differential evolution algorithm to generate trial points for each chain. Solving for the mass of radioactive material within a voluminous source is a challenging problem for gamma-ray spectroscopy. Inverse gamma-ray transport can supply a range of possible material compositions, but reducing the differences between predicted and actual measurements can lead to false results. DREAM is a rapid technique for determining the most likely solution for several unknown parameters in an inverse transport problem. This work applies DREAM to a series of gamma spectroscopy experiments performed at ORNL.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

The Half Monte Carlo Method: Combining Total Monte Carlo with Nuclear Data Sensitivity Profiles

Both Total Monte Carlo (TMC) and Generalized Linear Least Squares (GLLS) algorithms have been used extensively to perform nuclear uncertainty propagation. Both methods have strengths and weaknesses, for example, the time required to perform TMC limits its attractiveness, while GLLS cannot generate higher order moments of output distributions and also has trouble dealing with nonlinear distributions. This work uses a new method that overcomes many of the aforementioned limitations of TMC and GLLS, while at the same time reasonably reproduces the TMC result. The concept is a simple combination of the two methods i.e., generate the random nuclear data files using the TMC approach, and then propagate the effect on the integral parameters like k{sub eff} using sensitivity coefficients, as opposed to cumbersome neutron transport calculations. Agreement is demonstrated for the Jezebel sphere ICSBEP benchmark. Since the method is part TMC part GLLS, the term Half Monte Method (HMM) will be used.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Global variance reduction method applied to HBR-2 benchmark - 25144

It is a great challenge to obtain reliable results in reasonable time by the Monte Carlo (MC) method in solving deep-penetration shielding problems. Global variance reduction (GVR) method uses biased source and weight window to decrease MC calculation tally error for deep-penetration problems. However, excessive splitting of large weight particles out of the source region is time-consuming for problems with significant fluence rate variation. A new GVR method, which performs space and energy splitting/roulette based on the importance of the phase space, is proposed in this paper to avoid excessive splitting of large weight particles. The improved GVR method is applied to HBR-2 benchmark. Numerical results show that the new GVR method achieves good corresponding results to those of references. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗