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DOE OSTI2021

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.2)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.4)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.6)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( $Re$ < 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.6)

Aria is a Galerkin nite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

42 ENGINEERING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual - Version 5.8

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual - Version 5.8

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process ows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.10)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ($Re$ < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.10)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ($Re$ < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

42 ENGINEERING↗

DOE OSTI2020

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.4.56)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Advancements in NEAMS Tool Capabilities for Multiphysics Simulation of Fast Reactor Core Bowing and Identification of Validation Test Data

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves Multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Last year, thermal fluids and mechanics were coupled on a multi-assembly benchmark problem based on ABR-1000 design. This year, the reactor physics code Griffin was assessed for readiness of core bowing calculations. Preliminary integration of Griffin’s ring-heterogeneous model with thermal fluids and thermal mechanics solvers was performed. Specifically, thermal-mechanics and reactor physics were coupled for single- and multi-assembly problems, and reactor physics and subchannel methods were coupled for a single assembly model. Finally, the workflow of all three physics was preliminarily demonstrated on a single assembly model. Caveats and future development needed have been identified. To supplement the multiphysics demonstration, verification and assessment efforts of thermos-mechanical capabilities for modeling thermo-mechanical core bowing behavior were continued by analyzing IAEA Verification Problem 5 which includes radiation swelling and creep. Additionally, a small core reactor physics benchmark defined by Japan Atomic Energy Agency (JAEA) was performed to assess neutronics models for estimating reactivity feedback. Finally, Fast Flux Test Facility (FFTF) validation test data for core bowing phenomena has been identified and summarized, with a recommended path forward for validation once this capability is mature.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Feasibility of a Novel Density Functional Method Outside the Kohn-Sham Framework for Modeling Global Potential Energy Surfaces of Molecular Chemical Reactions (Final Technical Report)

The project aimed towards the construction of computational methods capable of modeling the global potential energy surface (PES) of small molecules, molecular ions, and radicals — including the parts of the PES which correspond to chemical reactions, and the reaction paths connecting reactants, intermediates, and reaction products. This goal may seem humble at first glance, but for chemical systems with more than about six atoms in total, at the time the project was proposed, there were no established theoretical methods capable of simulating such systems reliably, not even for small molecules in the gas phase which are electronically benign. This restriction severely hampers our ability to model and control chemical processes under harsh conditions. With the goal of constructing a method capable of modeling such chemical systems, we proposed to pursue a novel approach towards a Multi-Configuration (MC) DFT outside the traditional frameworks of Kohn-Sham theory and other methods of coupling wave function theory with DFT. Rather than being a complete active space (CAS) method, the proposed DOCI-DFT would employ a special restricted form of the active space wave function, called Doubly-Occupied CI (DOCI)—this wave function form is sufficient to describe not only heterolytic, but also homolytic bond dissociation processes at the zeroth order (i.e., as active space wave function). There are no other standard mean field methods which can do so. In the original proposal, we also outlined strong formal and practical arguments speaking for this method. The project proposal was accepted by the Department of Energy and provided two years of seed funding for one graduate student, as well as two years of two weeks PI summer-salary for the PI. However, ultimately the project could not be effectively pursued due to severe interferences outside the context scientific problems and was cancelled. Apart from two weeks of PI salary (and associated fringe & overhead costs issues by the performing institution), no costs were charged against the award, with the entire rest of funding returned to the Department of Energy. This report reiterates the primary background information regarding the project, its original goals, and outlines the preliminary work performed during the two weeks of DOE funding charged.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Ab initio study and assignment of electronic states in molecular RaCl

Radium compounds have attracted recently considerable attention due to both development of experimental techniques for high-precision laser spectroscopy of molecules with short-lived nuclei and amenability of certain radium compounds for direct cooling with lasers. Currently, radium monofluoride (RaF) is one of the most studied molecules among the radium compounds, both theoretically and recently also experimentally. Complementary studies of further diatomic radium derivatives are highly desired to assess the influence of chemical substitution on diverse molecular parameters, especially on those connected with laser cooling, such as vibronic transition probabilities, and those related to violations of fundamental symmetries. Here in this article high-precision ab initio studies of electronic and vibronic levels of diatomic radium monochloride (RaCl) are presented. Recently developed approaches for treating electronic correlation with Fock-space coupled cluster methods are applied for this purpose. Theoretical results are compared to an early experimental investigation by Lagerqvist and used to partially reassign the experimentally observed transitions and molecular electronic levels of RaCl. Effective constants of $\mathscr{P}$-odd hyperfine interaction W a and $\mathscr{P, T}$-odd scalar-pseudoscalar nucleus-electron interaction Ws in the ground electronic state of RaCl are estimated within the framework of a quasirelativistic Zeroth-Order Regular Approximation approach and compared to parameters in RaF and RaOH.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Atomic isotropic hyperfine properties for second row elements (Al–Cl)

Isotropic hyperfine properties have been obtained for the second row elements Al–Cl using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV7Z, along with configuration interaction and coupled cluster methods. The best nonrelativistic final values for the atomic ground states (in MHz) are -1.80 27 Al ( 2 P o 1/2 ), -24.31 29 Si ( 3 P 0 ), 63.70 31 P ( 4 So 3/2 ), 20.77 33 S ( 3 P 2 ), and 35.42 35 Cl ( 2 P o 3/2 ). We find a large K shell contribution to the spin density at the nucleus that is almost canceled by the L and M shell contributions. The spin density in atomic units is approximately linear with respect to the atomic number.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗

DOE OSTI2022

Diffusion Monte Carlo evaluation of disiloxane linearisation barrier

The disiloxane molecule is a prime example of silicate compounds containing the Si-O-Si bridge. The molecule is of significant interest within the field of quantum chemistry, owing to the difficulty in theoretically predicting its properties. Herein, the linearisation barrier of disiloxane is investigated using a fixed-node diffusion Monte Carlo (FNDMC) approach, which is one of the most reliable ab initio methods in accounting for the electronic correlation. Calculations utilizing the density functional theory (DFT) and the coupled cluster method with single and double substitutions, including noniterative triples (CCSD(T)) are carried out alongside FNDMC for comparison. It is concluded that FNDMC successfully predicts the disiloxane linearisation barrier and does not depend on the completeness of the basis-set as much as DFT or CCSD(T), thus establishing its suitability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

New procedure for evaluation of U(3) coupling and recoupling coefficients

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group–subgroup chains is presented. While the canonical U(3) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and in so doing provides a faster and more accurate determination of any and all required results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(3).

Cross-Coupling Reaction↗

DOE OSTI2022

Precise 3D reactor core calculation using spherical harmonics and discontinuous Galerkin finite element methods

We study the use of P{sub N} method in angle and discontinuous Galerkin is space to solve 3D neutron transport problem. P{sub N} method consists in developing the angular flux on truncated spherical harmonics basic. In this paper, we couple this method with the discontinuous finite elements in space to obtain a complete discretization of the multigroup neutron transport equation. To investigate its precision, the method was applied to Takeda and C5G7 benchmark problems. These calculations point out that the proposed P{sub N}-DG method is capable of producing accurate solutions in small computational time, and that it is able to handle complex 3D geometries. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Instability and treatments of the coupled discrete element and lattice Boltzmann method by the immersed moving boundary scheme

The immersed moving boundary (IMB) scheme has been extensively used to couple the discrete element method (DEM) with the lattice Boltzmann method (LBM). In the literature, only the formulation of IMB for lattice nodal cells covered by a single-solid particle was given. The treatment of situations where a nodal cell is covered by two or more solid particles is seldom discussed. It is found that some numerical instability can occur for such situations due to an inappropriate computation of the weighting function in the IMB formulation. This work presents an enhanced treatment that can resolve the issue and validates it using some benchmark tests. Furthermore, to avoid the extra costs associated with the treatment and simplify the complicated procedure introduced, a simplified IMB scheme is proposed. The accuracy of both enhanced and simplified IMB schemes are validated by test cases including single-particle sedimentation, two-particle drafting-kissing-tumbling phenomenon, and multiple-particle sedimentation. Then, the robustness of both schemes is examined and discussed using a specially designed flow past cylinders test. Overall, the simplified IMB scheme is proved to be robust and sufficiently accurate and simpler and more effective than the enhanced scheme.

42 ENGINEERING↗