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DOE OSTI2022

Physically rigorous reduced-order flow models of fractured subsurface environments without explosive computational cost

Fractured media models comprise discontinuities of multiple lengths (e.g. fracture lengths and apertures, wellbore area) that fall into the relatively insignificant length scales spanning millimeter-scale fractures to centimeter-scale wellbores in comparison to the extensions of the field of interest, and challenge the conventional discretization methods imposing highly-fine meshing and formidably large numerical cost. By utilizing the recent developments in the finite element analysis of electromagnetics that allow to represent material properties on a hierarchical geometry, this project develops computational capabilities to model fluid flow, heat conduction, transport and induced polarization in large-scale geologic environments that possess geometrically-complex fractures and man-made infrastructures without explosive computational cost. The computational efficiency and robustness of this multi-physics modeling tool are demonstrated by considering various highly-realistic complex geologic environments that are common in many energy and national security related engineering problems.

42 ENGINEERING↗

DOE OSTI2017

Continuous and Smooth Envelopes of Topological Algebras. Part 1

Since the first optical instruments were invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env{sub Φ}{sup Ω}A in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a “projection of functional analysis into geometry,” and the standard “geometric disciplines,” like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of “categorical construction of geometries” with many interesting applications, in particular, “geometric generalizations of the Pontryagin duality” (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Continuous and Smooth Envelopes of Topological Algebras. Part 2

Since the first optical instruments were invented, the idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env{sub Φ}{sup Ω} A in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a “projection of functional analysis into geometry,” and the standard “geometric disciplines,” like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of “categorical construction of geometries” with many interesting applications, in particular, “geometric generalizations of the Pontryagin duality” (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations

The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH{sub 4}-H{sub 2}O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

NASA-IGES Translator and Viewer

NASA-IGES Translator (NIGEStranslator) is a batch program that translates a general IGES (Initial Graphics Exchange Specification) file to a NASA-IGES-Nurbs-Only (NINO) file. IGES is the most popular geometry exchange standard among Computer Aided Geometric Design (CAD) systems. NINO format is a subset of IGES, implementing the simple and yet the most popular NURBS (Non-Uniform Rational B-Splines) representation. NIGEStranslator converts a complex IGES file to the simpler NINO file to simplify the tasks of CFD grid generation for models in CAD format. The NASA-IGES Viewer (NIGESview) is an Open-Inventor-based, highly interactive viewer/ editor for NINO files. Geometry in the IGES files can be viewed, copied, transformed, deleted, and inquired. Users can use NIGEStranslator to translate IGES files from CAD systems to NINO files. The geometry then can be examined with NIGESview. Extraneous geometries can be interactively removed, and the cleaned model can be written to an IGES file, ready to be used in grid generation.

Chou, Jin J.↗

DOE OSTI2015

Geometry effects on magnetization dynamics in circular cross-section wires

Three-dimensional magnetic memory design based on circular-cross section nanowires with modulated diameter is the emerging field of spintronics. The consequences of the mutual interaction between electron spins and local magnetic moments in such non-trivial geometries are still open to debate. This paper describes the theoretical study of domain wall dynamics within such wires subjected to spin polarized current. We used our home-made finite element software to characterize the variety of domain wall dynamical regimes observed for different constriction to wire diameter ratios d/D. Also, we studied how sizeable geometry irregularities modify the internal micromagnetic configuration and the electron spin spatial distribution in the system, the geometrical reasons underlying the additional contribution to the system's nonadiabaticity, and the specific domain wall width oscillations inherent to fully three-dimensional systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Coefficient rings of formal group laws

We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients. Bibliography: 37 titles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Extension of TOUGH-FLAC to the finite strain framework

Here, the TOUGH-FLAC simulator for coupled thermal-hydraulic-mechanical processes modeling has been extended to the finite strain framework. In the approach selected, this extension has required modifications to the flow simulator (TOUGH2) and to the coupling scheme between the geomechanics and the flow sub-problems. In TOUGH2, the mass and energy balance equations have been extended to account for volume changes. Additionally, as large deformations are computed by FLAC 3D , the geometry is updated in the flow sub-problem. The Voronoi partition needed in TOUGH2 is computed using an external open source library (Voro++) that uses the centroids of the deformed geomechanics mesh as generators of the Voronoi diagram. TOUGH-FLAC in infinitesimal and finite strain frameworks is verified against analytical solutions and other approaches to couple flow and geomechanics. Within the finite strain framework, TOUGH-FLAC is also successfully applied to a large-scale case. The extension of TOUGH-FLAC to the finite strain framework has little impact to the user as only one additional executable is needed (for Voro++), and the input files and the workflow of a simulation are the same as in standard TOUGH-FLAC. With this new provision for finite strains, TOUGH-FLAC can be used in the analysis of a wider range of engineering problems, and the areas of application of this simulator are therefore broadened.

58 GEOSCIENCES↗

NASA NTRS2013

Raster-Based Approach to Solar Pressure Modeling

An algorithm has been developed to take advantage of the graphics processing hardware in modern computers to efficiently compute high-fidelity solar pressure forces and torques on spacecraft, taking into account the possibility of self-shading due to the articulation of spacecraft components such as solar arrays. The process is easily extended to compute other results that depend on three-dimensional attitude analysis, such as solar array power generation or free molecular flow drag. The impact of photons upon a spacecraft introduces small forces and moments. The magnitude and direction of the forces depend on the material properties of the spacecraft components being illuminated. The parts of the components being lit depends on the orientation of the craft with respect to the Sun, as well as the gimbal angles for any significant moving external parts (solar arrays, typically). Some components may shield others from the Sun. The purpose of this innovation is to enable high-fidelity computation of solar pressure and power generation effects of illuminated portions of spacecraft, taking self-shading from spacecraft attitude and movable components into account. The key idea in this innovation is to compute results dependent upon complicated geometry by using an image to break the problem into thousands or millions of sub-problems with simple geometry, and then the results from the simpler problems are combined to give high-fidelity results for the full geometry. This process is performed by constructing a 3D model of a spacecraft using an appropriate computer language (OpenGL), and running that model on a modern computer's 3D accelerated video processor. This quickly and accurately generates a view of the model (as shown on a computer screen) that takes rotation and articulation of spacecraft components into account. When this view is interpreted as the spacecraft as seen by the Sun, then only the portions of the craft visible in the view are illuminated. The view as shown on the computer screen is composed of up to millions of pixels. Each of those pixels is associated with a small illuminated area of the spacecraft. For each pixel, it is possible to compute its position, angle (surface normal) from the view direction, and the spacecraft material (and therefore, optical coefficients) associated with that area. With this information, the area associated with each pixel can be modeled as a simple flat plate for calculating solar pressure. The vector sum of these individual flat plate models is a high-fidelity approximation of the solar pressure forces and torques on the whole vehicle. In addition to using optical coefficients associated with each spacecraft material to calculate solar pressure, a power generation coefficient is added for computing solar array power generation from the sum of the illuminated areas. Similarly, other area-based calculations, such as free molecular flow drag, are also enabled. Because the model rendering is separated from other calculations, it is relatively easy to add a new model to explore a new vehicle or mission configuration. Adding a new model is performed by adding OpenGL code, but a future version might read a mesh file exported from a computer-aided design (CAD) system to enable very rapid turnaround for new designs

Wright, Theodore W. II↗

NASA NTRS2012

Axisymmetric Plume Simulations with NASA's DSMC Analysis Code

A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.

Stewart, B. D.↗

DOE OSTI2019

CFD-Guided Combustion System Optimization of a Gasoline Range Fuel in a Heavy-Duty Compression Ignition Engine Using Automatic Piston Geometry Generation and a Supercomputer

A computational fluid dynamics (CFD) guided combustion system optimization was conducted for a heavy-duty diesel engine running with a gasoline fuel that has a research octane number (RON) of 80. The goal was to optimize the gasoline compression ignition (GCI) combustion recipe (piston bowl geometry, injector spray pattern, in-cylinder swirl motion, and thermal boundary conditions) for improved fuel efficiency while maintaining engine-out NO x within a 1-1.5 g/kW-hr window. The numerical model was developed using the multi-dimensional CFD software CONVERGE. A two-stage design of experiments (DoE) approach was employed with the first stage focusing on the piston bowl shape optimization and the second addressing refinement of the combustion recipe. For optimizing the piston bowl geometry, a software tool, CAESES, was utilized to automatically perturb key bowl design parameters. This led to the generation of 256 combustion chamber designs evaluated at several engine operating conditions. The second DoE campaign was conducted to optimize injector spray patterns, fuel injection strategies and in-cylinder swirl motion for the best performing piston bowl designs from the first DoE campaign. This comprehensive optimization study was performed on a supercomputer, Mira, to accelerate the development of an optimized fuel-efficiency focused design. Compared to the production combustion system in the baseline engine, the new combustion recipe from this study showed significantly improved closed-cycle fuel efficiency across key engine operating points while meeting the engine-out NO x targets. Optimized piston bowl designs and injector spray patterns were predicted to provide enhanced in-cylinder air utilization and more rapid mixing-controlled combustion, thereby leading to a fuel efficiency improvement. In addition, shifting the engine thermal boundary conditions toward leaner operation was also key to the improved fuel efficiency.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1964

Orbiter heat flux computer program

A two-phased contract is currently underway to develop 1) a set of parametric curves of absorbed heat flux for specific geometries, and 2) a generalized computer program whose output is absorbed heat flux on the surfaces of a planet orbiting spacecraft. The absorbed heat fluxes include the effects of blockage by and reflections from adjacent spacecraft surfaces, assuming all surfaces to be diffuse. The final computer program will calculate fluxes on any of ten arbitrarily positioned plane surfaces, with any surface properties, planetary radiation characteristics, solar intensity, and orbital parameters. Outputs will be heat fluxes versus time, geometrical configuration factors, and radiant flux interchange factors.

COMPUTER PROGRAM↗

DOE OSTI2013

Proteus-MOC: A 3D deterministic solver incorporating 2D method of characteristics

A new transport solution methodology was developed by combining the two-dimensional method of characteristics with the discontinuous Galerkin method for the treatment of the axial variable. The method, which can be applied to arbitrary extruded geometries, was implemented in PROTEUS-MOC and includes parallelization in group, angle, plane, and space using a top level GMRES linear algebra solver. Verification tests were performed to show accuracy and stability of the method with the increased number of angular directions and mesh elements. Good scalability with parallelism in angle and axial planes is displayed. (authors)

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

A new spherical model for computing the radiation field available for photolysis and heating at twilight

Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. These results are compared with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90 deg adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90 deg this pseudospherical plane parallel approximation overstimates the mean intensity.

Dahlback, Arne↗

NASA NTRS1976

Calculation of the three-dimension, supersonic, inviscid, steady flow past an arrow-winged airframe, part 1

A detailed description of the procedure used to compute three dimensional, supersonic, inviscid, steady flows past airframes is given. No limitations are imposed on the geometry of the airplane. Suitable computational grids are generated by automatic conformal mappings. The equations of motion, with pressure, entropy, and velocity direction as basic unknowns, are written and discretized in the computational space. Special rules to approximate derivatives are given. Boundary points are treated by a modified method of characteristics.

Moretti, G.↗

NASA NTRS2004

Statistical Analysis of CFD Solutions from 2nd Drag Prediction Workshop

In June 2001, the first AIAA Drag Prediction Workshop was held to evaluate results obtained from extensive N-Version testing of a series of RANS CFD codes. The geometry used for the computations was the DLR-F4 wing-body combination which resembles a medium-range subsonic transport. The cases reported include the design cruise point, drag polars at eight Mach numbers, and drag rise at three values of lift. Although comparisons of the code-to-code medians with available experimental data were similar to those obtained in previous studies, the code-to-code scatter was more than an order-of-magnitude larger than expected and far larger than desired for design and for experimental validation. The second Drag Prediction Workshop was held in June 2003 with emphasis on the determination of installed pylon-nacelle drag increments and on grid refinement studies. The geometry used was the DLR-F6 wing-body-pylon-nacelle combination for which the design cruise point and the cases run were similar to the first workshop except for additional runs on coarse and fine grids to complement the runs on medium grids. The code-to-code scatter was significantly reduced for the wing-body configuration compared to the first workshop, although still much larger than desired. However, the grid refinement studies showed no sign$cant improvement in code-to-code scatter with increasing grid refinement.

Hemsch, M. J.↗

DOE OSTI2019

Message-passing neural networks for high-throughput polymer screening

Machine learning methods have shown promise in predicting molecular properties, and given sufficient training data, machine learning approaches can enable rapid high-throughput virtual screening of large libraries of compounds. Graph-based neural network architectures have emerged in recent years as the most successful approach for predictions based on molecular structure and have consistently achieved the best performance on benchmark quantum chemical datasets. However, these models have typically required optimized 3D structural information for the molecule to achieve the highest accuracy. These 3D geometries are costly to compute for high levels of theory, limiting the applicability and practicality of machine learning methods in high-throughput screening applications. In this study, we present a new database of candidate molecules for organic photovoltaic applications, comprising approximately 91,000 unique chemical structures. Compared to existing datasets, this dataset contains substantially larger molecules (up to 200 atoms) as well as extrapolated properties for long polymer chains. We show that message-passing neural networks trained with and without 3D structural information for these molecules achieve similar accuracy, comparable to state-of-the-art methods on existing benchmark datasets. Furthermore, these results therefore emphasize that for larger molecules with practical applications, near-optimal prediction results can be obtained without using optimized 3D geometry as an input. We further show that learned molecular representations can be leveraged to reduce the training data required to transfer predictions to a new density functional theory functional.

14 SOLAR ENERGY↗

DOE OSTI2025

Computational Modeling of Molten Salt Infiltration and Oxidation in Nuclear Graphite

Graphite is utilized as a moderator and reflector in advanced nuclear reactor designs due to its high thermal conductivity, neutron moderation properties, and resistance to radiation damage. However, its longterm performance and reliability are challenged by degradation mechanisms such as molten salt infiltration in molten salt reactors (MSRs) and oxidation in gas-cooled reactors (GCRs). These mechanisms can compromise the structural integrity and operational lifetime of graphite components, necessitating a more detailed assessment of their physical behavior. This report focuses on the development of computational models for molten salt infiltration and oxidation of graphite to aid the design and performance analysis of graphite components. For molten salt infiltration, a computational framework is developed that couples incompressible Navier-Stokes and phase-field model to simulate the penetration of molten salt into graphite?s interconnected pore structure. Initial model verification is performed using two-phase flows in two dimensions, demonstrating the models ability to capture fundamental physical behavior and agree with analytical solution. This framework is then applied to a realistic IG110 nuclear graphite , where a computed tomography extracted pore geometry is used to analyse the infiltration behavior of FLiNaK molten salt. This model provides insights into how the microstructure and other relevant parameters influence the transport pathways of molten salt into graphite, potentially offering a means to rapidly evaluate a graphite grade?s resistance to infiltration. For oxidation, the report details pore-scale mass and heat transport models, describing the diffusion of gases, reaction kinetics, and thermal effects. Additionally, this report highlights inconsistencies in the existing volume-averaged macroscopic model, particularly in upscaling of reaction kinetics and flux terms, and surface to volume transformations. These inconsistencies suggest that current formulations may not accurately capture the experimentally observed graphite oxidation process, highlighting the need for improved model development. This work advances the development of physics-based computational models for graphite degradation, contributing to improved predictive models for next-generation nuclear reactor designs. Future efforts will focus on refining the infiltration model to address non-physical behaviors and enhance its robustness. Additionally, for oxidation, further studies will employ the principles of volume averaging to rigorously derive the upscaled equations, potentially in collaboration with subject matter experts.

Computational Modeling of Molten Salt Infiltration↗