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DOE OSTI2021

FIERRO V.X

FIERRO is a modern C++ code intended to simulate quasi-static solid mechanics problems and transient, compressible material dynamic problems with Lagrangian methods, which have meshes with constant mass elements that move with the material. FIERRO is designed to aid a) material model research that has historically been done using commercial implicit and explicit finite element codes, b) numerical methods research, and c) computer science research. FIERRO supports user developed material models that adhere to several industry standard formats by using a C++ to Fortran interface to couple the model to the numerical solvers. FIERRO is built on the ELEMENTS library that supports a diverse suite of element types, including high-order elements, and quadrature rules. The mesh class within the ELEMENTS library is designed for efficient calculations on unstructured meshes and to minimize memory usage. FIERRO is designed to readily accommodate a range of numerical methods including continuous finite element, finite volume, and discontinuous Galerkin methods. FIERRO is designed to support explicit and implicit time integration methods. FIERRO only supports a single material in an element. No physical data exists within the code.

Morgan, Nathaniel↗

DOE OSTI2017

High temperature high velocity direct power extraction using an open-cycle oxy-combustion system

The implementation of oxy-fuel technology in fossil-fuel power plants may contribute to increased system efficiencies and a reduction of pollutant emissions. One technology that has potential to utilize the temperature of undiluted oxy-combustion flames is open-cycle magnetohydrodynamic (MHD) power generators. These systems can be configured as a topping cycle and provide high enthalpy, electrically conductive flows for direct conversion of electricity. This report presents the design and modeling strategies of a MHD combustor operating at temperatures exceeding 3000 K. Throughout the study, computational fluid dynamics (CFD) models were extensively used as a design and optimization tool. A lab-scale 60 kWth model was designed, manufactured and tested as part of this project. A fully-coupled numerical method was developed in ANSYS FLUENT to characterize the heat transfer in the system. This study revealed that nozzle heat transfer may be predicted through a 40% reduction of the semi-empirical Bartz correlation. Experimental results showed good agreement with the numerical evaluation, with the combustor exhibiting a favorable performance when tested during extended time periods. A transient numerical method was employed to analyze fuel injector geometries for the 60-kW combustor. The ANSYS FLUENT study revealed that counter-swirl inlets achieve a uniform pressure and velocity ratio when the ports of the injector length to diameter ratio (L/D) is 4. An angle of 115 degrees was found to increase distribution efficiency. The findings show that this oxy-combustion concept is capable of providing a high-enthalpy environment for seeding, in order to render the flow to be conductive. Based on previous findings, temperatures in the range of 2800-3000 K may enable magnetohydrodynamic power extraction. The heat loss fraction in this oxy-combustion system, based on CFD and analytical calculations, at optimal operating conditions, was estimated to be less than 10 percent. Furthermore, the heat transfer design removed approximately 7 MW/m2. The results observed in the lab-scale system were employed to develop a 1-MW scaled prototype. Scaling methods were based on critical design criteria found in similar systems, aimed at replicating combustion flow fields and reducing possible instabilities. A numerical simulation of the combustor wall was developed for a combined thermal steady model and static structural model. This combined model was developed predict combined stress parameters within the wall during testing conditions. Both models were developed within ANSYS FEA software package. The relative accuracy presented as well major performance parameters are discussed to assess the design's validity and ensure safety. The scaled prototype was manufactured through selective laser melting (SLM)-based additive manufacturing to reduce lead times and increase geometrical complexity. Additional CFD models were developed to optimize coolant manifold system parameters and perform a parametric study on channel geometry. An investigation on coolant manifold geometry demonstrated improvements in channel flow distribution when enlarging manifold lengths and increasing the number of tubes feeding into the flow. A three-dimensional model based on a single channel was developed to capture the effect of variable properties and thermal stratification. All cases in the simulation exhibited higher wall temperatures and lower convective coefficients than those determined through 1-D analytical equations. This implies that pressure and velocity safety factors must be implemented during system operation. Overall, the findings made in this investigation are thought to be of value to researchers and industrial practitioners when designing oxy-fuel direct power extraction systems operating at temperatures exceeding 3000 K. In addition to this, the implementation of the developed technology at pilot and commercial scales could result in a significant improvement in the efficiencies of heritage and next-generation power cycles.

03 NATURAL GAS↗

DOE OSTI2017

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

An interface capturing scheme for modeling atomization in compressible flows

The study of atomization in supersonic flow is critical to ensuring reliable ignition of scramjet combustors under startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both shocks and material interfaces with high density ratios. In this work, a shock and interface capturing scheme is developed that uses the Harten–Lax–van Leer–Contact (HLLC) Riemann solver while a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme retains the fluid immiscibility condition in the volume fraction and phasic densities in the context of the five equation model. The approach includes the effects of compressibility, surface tension, and molecular viscosity. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Simulations of secondary atomization of a cylindrical water column after its interaction with a shockwave show good qualitative agreement with experimentally observed behavior. Three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow demonstrate the robustness of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: Electrons moving at relativistic speeds, close lying states, and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules in which all the three effects are present. These are the heavier transition metal compounds, lanthanides, and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and the density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs as we demonstrate on the system of TlH, AsH, and SbH.

Brandejs, Jan (ORCID:0000000221073095)↗

DOE OSTI2022

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

A moist Boussinesq shallow water equations set for testing atmospheric models

The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allow the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics–physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. - Highlights: • Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations. • The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations. • This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy. • Like full models, temperature and moistures are advected as tracers that interact through a simplified yet realistic phase-change model. • This model is a unique tool to test numerical methods for atmospheric models, and physics–dynamics coupling, in a very realistic and simple way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Multi-layer hydrostatic equilibrium of planets and synchronous moons: theory and application to Ceres and to solar system moons

The hydrostatic equilibrium of multi-layer bodies lacks a satisfactory theoretical treatment despite its wide range of applicability. Here we show that by using the exact analytical potential of homogeneous ellipsoids we can obtain recursive analytical solutions and an exact numerical method for the hydrostatic equilibrium shape problem of multi-layer planets and synchronous moons. The recursive solutions rely on the series expansion of the potential in terms of the polar and equatorial shape eccentricities, while the numerical method uses the exact potential expression. These solutions can be used to infer the interior structure of planets and synchronous moons from their observed shape, rotation, and gravity. When applied to the dwarf planet Ceres, we show that it is most likely a differentiated body with an icy crust of equatorial thickness 30-90 km and a rocky core of density 2.4-3.1 g cm{sup –3}. For synchronous moons, we show that the J {sub 2}/C {sub 22} ≅ 10/3 and the (b – c)/(a – c) ≅ 1/4 ratios have significant corrections of order Ω{sup 2}/(πGρ), with important implications for how their gravitational coefficients are determined from fly-by radio science data and for how we assess their hydrostatic equilibrium state.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Application of the Most Likely Extreme Response Method for Wave Energy Converters: Preprint

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based on spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.

16 TIDAL AND WAVE POWER↗

DOE OSTI2015

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Expedited Real Time Processing for the NETL HYPER Cyber-Physical System (Final Report)

The primary objective of the proposed project was to provide the National Energy Technology Laboratory’s Hybrid Performance (Hyper) Facility the needed numerical methods algorithm(s), software development and implementation support to enact real time cyber-physical systems (CPSs) that simulate process dynamics on the order of five milliseconds or smaller. The proposed paths forward comprised three distinct approaches to hasten transient simulations. They fell under the numerical methods categorical options of: 1) optimizing key parameters within the facility’s pre-existing real time processing scheme; 2) introducing an “informed” processing approach wherein a priori computations expedite real time attempts; and 3) implementing alternatives to the employed explicit-implicit blended finite difference (spatio-temporal) approach. Each of these three classes were proposed independently as options for improvement, yet in some cases one class of approach could have complemented another.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2024

Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations

One of the most promising applications of machine learning in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective of machine-learning-based PDE solvers is to output a sufficiently accurate solution faster than standard numerical methods, which are used as a baseline comparison. Here, we first perform a systematic review of the ML-for-PDE-solving literature. Out of all of the articles that report using ML to solve a fluid-related PDE and claim to outperform a standard numerical method, we determine that 79% (60/76) make a comparison with a weak baseline. Second, we find evidence that reporting biases are widespread, especially outcome reporting and publication biases. We conclude that ML-for-PDE-solving research is overoptimistic: weak baselines lead to overly positive results, while reporting biases lead to under-reporting of negative results. To a large extent, these issues seem to be caused by factors similar to those of past reproducibility crises: researcher degrees of freedom and a bias towards positive results. We call for bottom-up cultural changes to minimize biased reporting as well as top-down structural reforms to reduce perverse incentives for doing so.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

SAM User's Guide

The System Analysis Module (SAM) is a modern system analysis tool being developed at Argonne National Laboratory for advanced non-LWR safety analysis. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for Sodium-cooled Fast Reactors (SFR), Lead-cooled Fast Reactors (LFR), and Molten Salt Reactors (MSR) or Fluoride-cooled High-temperature Reactors (FHR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage the modern advanced software environments and numerical methods. This document provides a user’s guide, which will help users understand the input description and core capabilities of the SAM code. A brief overview of the code is presented, as well as how to obtain and run it. The input syntax for various parts of the code is provided. Additionally, a number of example problems, starting with simple unit component problems to problems with increasing complexity, are provided. Because the code is still under active development, this SAM User’s Guide will evolve with periodic updates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2021

SAM User’s Guide

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

SAM User's Guide

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Density constrained TDHF [Book Chapter]

In this manuscript we provide an outline of the numerical methods used in implementing the density constrained time-dependent Hartree-Fock (DC-TDHF) method and provide a few examples of its application to nuclear fusion. In this approach, dynamic microscopic calculations are carried out on a three-dimensional lattice and there are no adjustable parameters, the only input is the Skyrme effective NN interaction. After a review of the DC-TDHF theory and the numerical methods, we present results for heavy-ion potentials V (R), coordinate-dependent mass parameters M(R), and precompound excitation energies E*(R) for a variety of heavy-ion reactions. Using fusion barrier penetrabilities, we calculate total fusion cross sections σ(E c.m. ) for reactions between both stable and neutron-rich nuclei. We also determine capture cross sections for hot fusion reactions leading to the formation of superheavy elements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Comparison of numerical weather prediction based deterministic and probabilistic wind resource assessment methods

Numerical weather prediction (NWP) models have been widely used for wind resource assessment. Model runs with higher spatial resolution are generally more accurate, yet extremely computational expensive. An alternative approach is to use data generated by a low resolution NWP model, in conjunction with statistical methods. In order to analyze the accuracy and computational efficiency of different types of NWP-based wind resource assessment methods, this paper performs a comparison of three deterministic and probabilistic NWP-based wind resource assessment methodologies: (i) a coarse resolution (0.5 degrees x 0.67 degrees) global reanalysis data set, the Modern-Era Retrospective Analysis for Research and Applications (MERRA); (ii) an analog ensemble methodology based on the MERRA, which provides both deterministic and probabilistic predictions; and (iii) a fine resolution (2-km) NWP data set, the Wind Integration National Dataset (WIND) Toolkit, based on the Weather Research and Forecasting model. Results show that: (i) as expected, the analog ensemble and WIND Toolkit perform significantly better than MERRA confirming their ability to downscale coarse estimates; (ii) the analog ensemble provides the best estimate of the multi-year wind distribution at seven of the nine sites, while the WIND Toolkit is the best at one site; (iii) the WIND Toolkit is more accurate in estimating the distribution of hourly wind speed differences, which characterizes the wind variability, at five of the available sites, with the analog ensemble being best at the remaining four locations; and (iv) the analog ensemble computational cost is negligible, whereas the WIND Toolkit requires large computational resources. Future efforts could focus on the combination of the analog ensemble with intermediate resolution (e.g., 10-15 km) NWP estimates, to considerably reduce the computational burden, while providing accurate deterministic estimates and reliable probabilistic assessments.

17 WIND ENERGY↗

DOE OSTI2020

An Overview of Gemma FY20 Verification Activities

Gemma verification activities for FY20 can be divided into three categories: the development of specialized quadrature rules, initial progress towards the development of manufactured solutions for code verification, and automated code-verification testing. In the method-of-moments implementation of the electric-field integral equation, the presence of a Green’s function in the four-dimensional integrals yields singularities in the integrand when two elements are nearby. To address these challenges, we have developed quadrature rules to integrate the functions through which the singularities can be characterized. Code verification is necessary to develop confidence in the implementation of the numerical methods in Gemma. Therefore, we have begun investigating the use of manufactured solutions to more thoroughly verify Gemma. Manufactured solutions provide greater flexibility for testing aspects of the code; however, the aforementioned singularities provide challenges, and existing work is limited in rigor and quantity. Finally, we have implemented automated code-verification testing using the VVTest framework to automate the mesh refinement and execution of a Gemma simulation to generate mesh convergence data. This infrastructure computes the observed order of accuracy from these data and compares it with the theoretical order of accuracy to either develop confidence in the implementation of the numerical methods or detect coding errors.

97 MATHEMATICS AND COMPUTING↗