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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations

We present here the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov–Galerkin (VEM-SUPG) stabilization for the numerical resolution of convection–diffusion–reaction problems in the convective-dominated regime. According to the virtual discretization approach, the bilinear form is split as the sum of a consistency and a stability term. The consistency term is given by substituting the functions of the virtual space and their gradients with their polynomial projection in each term of the bilinear form (including the SUPG stabilization term). Polynomial projections can be computed exactly from the degrees of freedom. The stability term is also built from the degrees of freedom by ensuring the correct scalability properties with respect to the mesh size and the equation coefficients. The nonconforming formulation relaxes the continuity conditions at cell interfaces and a weaker regularity condition is considered involving polynomial moments of the solution jumps at cell interface. Optimal convergence properties of the method are proved in a suitable norm, which includes contribution from the advective stabilization terms. Experimental results confirm the theoretical convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

MOOSE Optimization Module Overview: Application to Residual Stress Inversion in Nuclear Fuel Plates

Manufacturing methods, material selections and unique plate geometries used in low enriched uranium plate fuels for the High Performance Research Reactor (HPRR) have led to concerns about the residual stresses effect on bond strength of the fuel/cladding interfaces and overall fuel performance under irradiation. The current HPRR plate fuel test program performed residual stress calculations using the contour method with experimental displacement data obtained by incrementally cutting the plate fuel. In this work, we use a gradient based inverse optimization module developed within the MOOSE framework to estimate normal and shear residual stresses within the plate fuels using displacement data taken from a cut placed in the HPRR fuel plate. These results are verified against residual stress calculations obtained from the contour method. The inversion protocol used in this work utilizes two meshes to separately discretize the physics and parameter space. This allows a fine mesh to be used to fully resolve the physics and geometry of the forward problem. A coarser mesh is used to resolve the parameter space with spatially varying mesh density determined from a sensitivity analysis. The adaptive resolution of the parameter space essentially has the effect of regularization as it is designed to achieve the bias-variance tradeoff.

42 ENGINEERING↗
DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

CFD Evaluation of Pressure Change Along Coolant Passages in Sodium-Cooled Fast Reactor with Nek5000

To support the design efforts of advanced sodium-cooled fast reactors (SFRs), a series of computational fluid dynamics (CFD) simulations are performed to investigate the pressure change along various flow passages in the proposed SFR system. The simulations are carried out with the state-of-the-art spectral element flow solver, Nek5000. Two specific case studies are presented in this paper: the flow exiting the axial neutron reflector channels and the flow entering the fuel pin bundle. Due to the high Reynolds numbers expected, a Reynolds-averaged Navier-Stokes (RANS) approach is necessary to model the turbulence. A newly developed regularized k-omega RANS model is adopted in the related CFD calculations. The first case study explores the effect of Reynolds number on the pressure change when flow exits the reflector channels. The pressure change in this case has two major contributors: the change due to wall friction and the Bernoulli effect. It is noted that the nondimensional pressure loss follows a log-linear trend up to Re = 10 5 , and then the trend is flattened. In the second case study, the advanced NekNek coupling capability is tested where an integral domain can be divided into multiple subdomains with coupling interfaces, which would greatly ease the meshing process of complex engineering geometries and potentially save computational resources. The preliminary results obtained so far confirm the consistency between the NekNek results and those produced by regular Nek5000 simulation. The presented work demonstrates the readiness and flexibility of the related CFD techniques, which is part of the broader effort to leverage cutting-edge CFD to inform the advanced nuclear reactor designs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

Design, analysis and numerical experiments for the virtual element p and hp approximations of elliptic eigenvalue problems

We discuss the p- and the hp-versions of the virtual element method for the approximation of the eigenvalues of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr¨odinger equation with a pseudo-potential term. We present in details the analysis of the p-version of the method, proving the exponential convergence in the case of analytic eigenfunctions. The theoretical results are supplied with a wide set of experiments. We also show numerically that, in the case of eigenfunctions with finite Sobolev regularity, an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing hp-refinements. Importantly, the geometric flexibility of polygonal meshes is exploited in the construction of the hp-spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Efficient high-order singular quadrature schemes in magnetic fusion

Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated in terms of integral equation expressions. Based on Biot–Savart-like formulae, these integrals contain singular integrands. The regularization method commonly used to address the computation of various singular surface integrals along general toroidal surfaces is low-order accurate, and therefore requires a dense computational mesh in order to obtain sufficient accuracy. In this work, we present a fast, high-order quadrature scheme for the efficient computation of these integrals. Several numerical examples are provided demonstrating the computational efficiency and the high-order accurate convergence. A corresponding code for use in the community has been publicly released.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Not so HOT Triangulations

Here, we propose primal–dual mesh optimization algorithms that overcome shortcomings of the standard algorithm while retaining some of its desirable features. “Hodge-Optimized Triangulations” defines the “HOT energy” as a bound on the discretization error of the diagonalized Delaunay Hodge star operator. HOT energy is a natural choice for an objective function, but unstable for both mathematical and algorithmic reasons: it has minima for collapsed edges, and its extrapolation to non-regular triangulations is inaccurate and has unbounded minima. We propose a different extrapolation with a stronger theoretical foundation, and avoid extrapolation by recalculating the objective just beyond the flip threshold. We propose new objectives, based on normalizations of the HOT energy, with barriers to edge collapses and other undesirable configurations. We propose mesh improvement algorithms coupling these. When HOT optimization nearly collapses an edge, we actually collapse the edge. Otherwise, we use the barrier objective to update positions and weights and remove vertices. By combining discrete connectivity changes with continuous optimization, we more fully explore the space of possible meshes and obtain higher quality solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Neural network–based pore flow field prediction in porous media using super resolution

Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the velocity fields therein based on neural networks. However, such trained neural networks do not perform well for unseen porous media with a large degree of heterogeneity. In this study we propose that incorporating a coarse velocity field in the input of neural networks is an effective way to improve the prediction performance. The coarse velocity field can be simulated with a low computational cost and provides global information to regularize the ill-posedness of the learning problem, which is usually caused by the use of local geometries due to the computational resource constraints. We show that incorporating the coarse-mesh velocity field significantly improves the prediction accuracy of the fine-mesh velocity field by comparison to the prediction that relies on geometric information alone, especially for the porous medium with a large interior vuggy pore space. We also show the flexibility of training the network in using coarse velocity fields with various resolutions. The results suggest that even using coarse velocity field with a very low resolution, the predictions are still enhanced and close to the ground truths. The feasibility of the method is further demonstrated by testing the trained network on real rocks. This study highlights the merits of incorporating a coarse-mesh velocity field into the input for neural networks, which provides global, physics-based information for the model, thereby improving the model's generalization capability.

42 ENGINEERING↗
DOE OSTI2022

CFD Simulation of Floating Body Motion with Mooring Dynamics: Coupling MoorDyn with OpenFOAM

It is increasingly popular to use Computational Fluid Dynamics (CFD) models to study floating structures subjected to ocean waves, especially when it comes to applications of floating offshore wind turbines and Wave Energy Converters (WECs). Mooring dynamics are currently lacking in most of these applications. This paper presents a coupled simulation study of moored floating body motion by coupling two open-source libraries: a finite volume CFD toolbox, OpenFOAM, and a lumped-mass mooring model, MoorDyn. The instantaneous floating body position and velocity are passed from the body motion solver in the CFD model to the mooring model to calculate the fairlead kinematics. The mooring reaction forces, which are calculated by MoorDyn after updating the mooring system states, are then returned to the body motion solver to update the floating body motion. Both mesh deformation and overset mesh methods are used as the mesh motion solver in the CFD model to account for the floating body motion. The coupled model was validated against experimental measurements for a floating box moored with four catenary lines under the action of regular waves, which came from a preliminary test campaign for WECs. Apart from the lumped-mass mooring model, the present work also coupled a quasi-static mooring model and a finite element model with the floating body motion solver in OpenFOAM. The mooring line tensions predicted by these models were compared. The coupled model equipped with three mooring line codes may be further used to carry out survivability studies of FOWTs and WECs subject to severe sea states.

floating body↗
DOE OSTI2026

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING↗
DOE OSTI2021

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗
DOE OSTI2019

Finite Element Modeling of Orthogonal Machining of Brittle Materials Using an Embedded Cohesive Element Mesh

Machining of brittle materials is common in the manufacturing industry, but few modeling techniques are available to predict materials’ behavior in response to the cutting tool. The paper presents a fracture-based finite element model, named embedded cohesive zone–finite element method (ECZ–FEM). In ECZ–FEM, a network of cohesive zone (CZ) elements are embedded in the material body with regular elements to capture multiple randomized cracks during a cutting process. The CZ element is defined by the fracture energy and a scaling factor to control material ductility and chip behavior. The model is validated by an experimental study in terms of chip formation and cutting force with two different brittle materials and depths of cut. The results show that ECZ–FEM can capture various chip forms, such as dusty debris, irregular chips, and unstable crack propagation seen in the experimental cases. For the cutting force, the model can predict the relative difference among the experimental cases, but the force value is higher by 30–50%. The ECZ–FEM has demonstrated the feasibility of brittle cutting simulation with some limitations applied.

Takabi, Behrouz↗
DOE OSTI2021

An Investigation of the Effects of Volume Fraction on Drag Coefficient of Non-Spherical Particles Using PR-DNS

Prediction of the drag coefficient is required in gas-particle multiphase flow modeling and simulation. Experimental data and correlations on the fixed-bed system of spherical particles with high volume fractions for various possible arrangements are available in the literature. However, the effect of volume fraction on the drag coefficient of non-spherical particles is not well studied. In solving the momentum equation, the volume fraction plays a vital role in determining the flow resistances. In this paper, we study the impact of volume fraction in the range of 0.069 to 0.65 on the drag coefficient using the computational fluid dynamics (CFD) simulation of air for Reynold number in the range of 10 to 10000 using particle resolved direct numerical solution (PR-DNS). Regular non-spherical particles such as a cube, tetrahedron, and spheroids are used in this study since their single particle’s drag coefficient data are available in the literature for comparison. For this work, the simulations are carried out in the Ansys Fluent using polyhedral mesh, which consumes significantly less computational time and power. The study showed the sphericity and volume fraction have significant impact on the bed pressure drop and average drag coefficient of the particles in the bed especially in high Reynolds number regime. The bed of the spheroid experiences the lowest drag being the most streamlined particle, and the particles with the edges result in a large drag coefficient due to flow separation at the discontinuity. The vector plots verify this behavior where large wake regions are observed behind the tetrahedron particle.

Mahyawansi, Pratik↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Regularized Finite Element Formulations for Shear Band Instabilities in Metals

In my research I have addressed several fundamental issues of dynamic fracture: 1. established the role of heat conduction as a natural regularizing mechanism in shearband problems (i.e. using the correct physics for this problem), 2. developed a unified model to incorporate fracture through a modified phase field formulation, 3. developed stability analysis tools to determine the onset of localization, 4. developed discretization methods and solvers to solve this problem (on parallel computers) that lead to mesh insensitive results and fast convergence. For such difficult problems, the physics and numerics are strongly coupled. To accurately model the physics, one must develop reliable numerics but reliable numerics depends on correct description of the physics. To this end, we have already made significant progress in the field showing that a fully-coupled implicit solution with heat conduction is the key to obtain reliable results for shear bands (see the next sections for more details). This research fits well within the mission of DOE ASCR program on all aspects: from governing equations to discretization to solvers to parallel computers to applications problems. It also relies on the computational tools developed through the SciDAC institutes FASTMath and SDAV, such as PETSc (and SLEPc), ParaView, Trilinos and Masquite.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗
DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗