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At least 487 records · Page 27

Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation [Slides]

We have developed a series of multiscale finite-element methods for simulating seismic wave propagation in complex media. The most important feature of multiscale finite-element methods is using medium- and mesh-dependent multiscale basis functions. For different wave equations, or for wave equation modeling in different domains, we design different local spectral/linear problems to compute multiscale basis functions. Multiscale basis functions can accurately capture the fine-scale medium information for coarse-scale modeling problems. Numerical examples have demonstrated the efficiency and accuracy of our multiscale finite-element method framework for wave equation modeling. Future works aim at further improving the efficiency using more levels of information encapsulation, and address more realistic physics problems.

58 GEOSCIENCES↗

BISON Robustness and Performance Improvements

BISON is a modern finite-element based nuclear fuel performance code that has been under development at the Idaho National Laboratory (USA) since 2009 [1]. The code is applicable to both steady and transient fuel behavior and can be used to analyze 1D (spherically symmetric), 2D (axisymmetric and generalized plane strain) or 3D geometries. BISON is the fuel performance code used within CASL for LWR fuel under both normal operating and accident conditions. BISON is built using the INL Multiphysics ObjectOriented Simulation Environment, or MOOSE [2, 3]. MOOSE is a massively parallel, finite element-based framework to solve systems of coupled non-linear partial differential equations using the Jacobian-Free Newton Krylov (JFNK) method [4]. This enables investigation of computationally large problems, for example a full stack of discrete pellets in a LWR fuel rod, or every rod in a full reactor core. MOOSE supports the use of complex two and three-dimensional meshes and uses implicit time integration, important for the widely varied time scale in nuclear fuel simulation. An object-oriented architecture is employed which greatly minimizes the programming effort required to add new material and behavioral models. The flexibility of the implicit and fully coupled multiphysics approach comes with a need for constructing suitable approximations for the Jacobian matrix of the coupled system used for either preconditioning a Krylov solve or in a direct Newton solve. Preconditioning options for Bison problems need to be revisited with new preconditioning methods becoming available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗

Incorporating geological structure into sensitivity analysis of subsurface contaminant transport

Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. Finally, the results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Numerical experiments with the extended virtual element method for the Laplace problem with strong discontinuities

The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes. In the VEM, the basis functions are implicit (virtual) — they are not known nor do they need to be computed within the problem domain. Suitable projection operators are used to decompose the bilinear form at the element-level into two parts: a consistent term that reproduces a given polynomial space and a correction term that ensures stability. In this study, we consider a low-order extended virtual element method (X-VEM) that is in the spirit of the extended finite element method for crack problems. Herein, we focus on the two-dimensional Laplace crack problem. In the X-VEM, we enrich the standard virtual element space with additional discontinuous functions through the framework of partition-of-unity. The nodal basis functions in the VEM are chosen as the partition-of-unity functions, and we study means to stabilize the standard and enriched sub-matrices that constitute the element stiffness matrix. Numerical experiments are performed on the problem of a cracked membrane under mode III loading to affirm the accuracy, and to establish the optimal convergence in energy of the method.

97 MATHEMATICS AND COMPUTING↗

Iteration-based Linearized Distribution-level Locational Marginal Price for Three-phase Unbalanced Distribution Systems

Distributed energy resources (DERs) are rocking the utilities’ business landscape. It calls for competitive market environments that incentivize DERs to form maximum operating efficiency. Among proposed pricing schemes, distribution-level locational marginal price (DLMP) is effective in signaling the marginal generation cost differences driven by energy losses and network constraints. It can be derived from a distribution-level optimal power flow (OPF) framework, as it essentially presents the sensitivity of optimized generation cost towards incremental loads. However, due to the high resistance-to-inductance ratio and unbalanced characteristics of distribution networks, computational affordable DLMPs are highly challenged. This article provides a linear-approximated DLMP that can be solved efficiently and generalized to account for reactive power flow, three-phase unbalanced loads and meshed network structure. The successive linear programming technique is introduced to enhance the model accuracy. Case studies on an IEEE 123-Bus system validate its accuracy against a nonlinear benchmark and capability in offering proper incentives.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NEAMS TH CRAB

The MOOSE framework is a library designed to make it straightforward for physicists and engineers to model partial differential equations using finite element and finite volume methods. Finite elements have been a part of the framework library since MOOSE's inception over a decade ago. Initial finite volume capability, however, was added only as recently as May of 2020. Since that time, significant work has been conducted to develop fluid modeling capability based on the finite volume method. Much of this work has taken place in MOOSE's navier_stokes module and in the NEAMS program's coarse mesh CFD code Pronghorn. We report here on development in MOOSE and Pronghorn of incompressible, porous incompressible, and weakly compressible finite volume simulation capabilities and their application to modeling of MSR and FHR advanced reactor concepts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Advancement of hybrid fluid-kinetic modeling for HEDP and ICF science

We report on the development progress of a hybrid fluid-kinetic code for simulating fluids and plasmas in a wide range of environments, such as laser–matter interactions, inertial confinement fusion, magnetic confinement fusion, and pulsed power. The suite of numerical tools under development utilizes heterogeneous computer architectures and leverages the benefits of particle–based simulation techniques. By working to combine the kinetic particle-in-cell (PIC) model with a particle-based fluid simulation technique, such as smoothed particle hydrodynamics, we are developing a flexible framework capable of accurately modeling complex flows within and between kinetic and fluid regimes. The TriForce code is under development as a C++ framework for parallel, 3D, particle-based, hybrid fluid-kinetic plasma simulations. The fluid half of TriForce will be based upon the meshless smoothed-particle-hydrodynamics (SPH) approach, well-suited for shear, mixing, and turbulence, whereas the kinetic half resembles a traditional particle-in-cell (PIC) code; other particle-based approaches to fluid modeling that do use a mesh are also possible to use and are under investigation. Maxwell’s electromagnetic field equations are solved either via explicit or implicit algorithms or approximated via resistive magnetohydrodynamics (MHD) using an Ohm’s law and resulting induction equation (extended MHD is under development). A primary goal of enabling direct comparisons, from the same code, between results from the variants of MHD and implicit electromagnetic solutions is to improve our fundamental understanding of systems with magnetic fields. The code is under development to recover results from both radiation-MHD and fully kinetic codes in those limits, and is continuing to be developed from other follow-on grants to operate in between where both descriptions may co-exist and interact. For certain applications, it is desired for a simulation to contain fluid ions and electrons as well as kinetic ions and electrons. Typically, it is too computationally intensive to model a full-scale ICF or HEDP experiment fully kinetically since many cycles are expended with very small time steps on modeling the fluid part of a material that is well treated by the fluid approximation. In this case, many traditional PIC particles can be replaced with a single fluid particle representing the thermal part of the distribution function, and there are fewer needed kinetic particles, which describe the non-thermal part and can be sub-cycled relative to the fluid particle advance. Furthermore, a pure fluid code may, depending on the problem, simply lack many physically important details that are beyond the scope of its reduced approximations and assumptions. In this report, we summarize the objectives achieved in the development of the collisional and kinetic half of the code, and the physics problems to which the code has been applied in the areas of advanced and innovative fusion concepts, pulsed power, and magneto-inertial fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗

Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method

The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.

Chang, Chau-lyan↗

Enhanced Simulation Techniques in Predicting Sonic Boom Loudness Using CFD

This paper outlines advancements in predicting sonic boom loudness within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) computational framework. Traditionally, a two step process consisting of a steady state computational fluid dynamics problem for near-field analysis and a far-field propagation solver for calculation of loudness metrics has been used. Improvements to this process made in this work include utilizing a high-order space marching method for mid-field computations, developing a novel output-based mesh adaptation method targeting error in near-field pressure sig-natures, and developing a robust scripting system using curvilinear grids to increase robustness and simplify the process of running large databases of simulation cases. These advancements are detailed and applied to the simulation of the X-59, presenting comparative cost and timing analyses between the prior two step workflow and the current three step procedure. We achieve increased accuracy and robustness for loudness predictions with at least a50%computational cost reduction.

CST↗

Performance Improvements for Coarse Mesh Finite Difference Acceleration L3:RTM.PRT.P13.02

The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solves the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, in this paper, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.

58 GEOSCIENCES↗

Interactive Visualization of Multi-Group Cross Sections on High-Fidelity Spatial Meshes

Core simulation tools utilizing Monte Carlo transport methods represent the 'Holy Grail' for nuclear reactor analysis. However, deterministic transport methods pose a number of advantages to Monte Carlo from a computational perspective, which seems likely to make these methods more viable in the near to intermediate term. Deterministic methods almost universally discretize the energy domain in a few to hundreds of energy groups. One of the key challenges for deterministic transport-based methods to be viable is accurate, reactor agnostic multi-group cross section generation. This paper describes tools for data processing and visualization of multigroup cross sections generated on high-fidelity spatial meshes from the OpenMC Monte Carlo code. Next generation deterministic transport reactor core modeling tools will require multi-group cross section (MGXS) generation on high-fidelity spatial meshes. High-fidelity MGXS are necessary for the accurate simulation of neutron physics in nuclear reactors with a high degree of spectral heterogeneity - e.g., large localized neutron flux gradients throughout a reactor core. Although many local (e.g., pin cell) approximations have been developed to model the scalar flux to compute spectral-averaged MGXS, these techniques cannot account for complex intra-pin and intra-assembly spatial self-shielding effects. Monte Carlo presents the most accurate method for reactor agnostic multi-group cross section generation since it does not require the use of local approximations to the flux. Monte Carlo has been proposed as a highly desirable framework for reactor agnostic cross section generation for many years. Monte Carlo methods can effectively embed all of the relevant spectral effects into the MGXS through the random particle tracking and interaction sampling processes. Previous work has applied MCNP and Serpent to compute few-group constants for diffusion calculations, and OpenMC to compute multi-group cross sections for transport-based methods. The primary difficulty with using Monte Carlo for MGXS generation is the tremendous computational resources required to adequately converge multi-group cross sections in each spatial region and energy group. Recent development of the OpenMC Monte Carlo code for high-performance computing platforms has made multigroup cross section generation from Monte Carlo more tractable in the foreseeable future. The recent release of OpenMC v0.7.1 includes a new Python-based module for MGXS generation. The MGXS generation module leverages many of the algorithms and features for 'big data' analysis of large tally datasets on complex spatial meshes. This paper describes the data management workflow and visualization tools which have been developed to explore the plethora of MGXS data generated with OpenMC. It is the authors' hope that the development of the visualization tool described in this paper will ultimately enable the design of machine learning algorithms to accelerate the convergence rate of high-fidelity multi-group cross section generated with Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Prelude to Simulation Diagnostics in MOOSE: Diagnosing Meshes

As finite element simulations increase in complexity, so does the need for high quality meshes. Without proper diagnostics, issues pertaining to poor mesh quality or improper mesh construction may go undetected, causing simulations to fail unexpectedly. This paper details the new mesh diagnostic system available in MOOSE, which provides users with the tools to inspect mesh quality for both externally and internally generated meshes. This system can detect issues arising from element volume size, non-conformal elements, intersecting edges, missing sidesets, as well as other common mesh issues. As meshes increase in size and complexity, such issues become more difficult to diagnose through visual inspection alone.

99 - GENERAL AND MISCELLANEOUS↗

Conforming and nonconforming virtual element methods for elliptic problems

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1 - and L 2 -error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

97 MATHEMATICS AND COMPUTING↗

Multiresolution molecular mechanics: Surface effects in nanoscale materials

Surface effects have been observed to contribute significantly to the mechanical response of nanoscale structures. The newly proposed energy-based coarse-grained atomistic method Multiresolution Molecular Mechanics (MMM) (Yang, To (2015), ) is applied to capture surface effect for nanosized structures by designing a surface summation rule SR{sup S} within the framework of MMM. Combined with previously proposed bulk summation rule SR{sup B}, the MMM summation rule SR{sup MMM} is completed. SR{sup S} and SR{sup B} are consistently formed within SR{sup MMM} for general finite element shape functions. Analogous to quadrature rules in finite element method (FEM), the key idea to the good performance of SR{sup MMM} lies in that the order or distribution of energy for coarse-grained atomistic model is mathematically derived such that the number, position and weight of quadrature-type (sampling) atoms can be determined. Mathematically, the derived energy distribution of surface area is different from that of bulk region. Physically, the difference is due to the fact that surface atoms lack neighboring bonding. As such, SR{sup S} and SR{sup B} are employed for surface and bulk domains, respectively. Two- and three-dimensional numerical examples using the respective 4-node bilinear quadrilateral, 8-node quadratic quadrilateral and 8-node hexahedral meshes are employed to verify and validate the proposed approach. It is shown that MMM with SR{sup MMM} accurately captures corner, edge and surface effects with less 0.3% degrees of freedom of the original atomistic system, compared against full atomistic simulation. The effectiveness of SR{sup MMM} with respect to high order element is also demonstrated by employing the 8-node quadratic quadrilateral to solve a beam bending problem considering surface effect. In addition, the introduced sampling error with SR{sup MMM} that is analogous to numerical integration error with quadrature rule in FEM is very small. - Highlights: • Surface effect captured by Multiresolution Molecular Mechanics (MMM) is presented. • A novel surface summation rule within the framework of MMM is proposed. • Surface, corner and edges effects are accuterly captured in two and three dimension. • MMM with less 0.3% degrees of freedom of atomistics reproduces atomistic results.

77 NANOSCIENCE AND NANOTECHNOLOGY↗