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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mixing by internal gravity waves in stars: assessing numerical simulations against theory

ABSTRACT Here we present a study of radial chemical mixing in non-rotating massive main-sequence stars driven by internal gravity waves (IGWs), based on multidimensional hydrodynamical simulations with the fully compressible code MUSIC. We examine two proposed mechanisms of material mixing in stars by IGWs that are commonly quoted, relating to thermal diffusion and sub-wavelength shearing. Thermal diffusion provides a non-restorative effect to the waves, leaving material displaced from its previous equilibrium, while shearing arising within the waves drives weak localized flows, mixing the fluid there. Using IGW spectra from the simulations, we evaluate theoretical predictions of mixing rates due to these mechanisms. We show, for $20\, \mathrm{M}_\odot$ main-sequence stars, that neither of these mechanisms are likely to create mixing sufficient to correct inaccuracies in current stellar evolution models. Furthermore, we compare these predictions to results obtained from Lagrangian tracer particles, following a method recently used for global simulations of stellar interiors to measure mixing by IGWs in their radiative zones. We demonstrate that tracer particle methods face significant numerical challenges in measuring the small diffusion coefficients predicted by the aforementioned theories, for which they are prone to yielding artificially enhanced coefficients. Diffusion coefficients based on such methods are currently used with stellar evolution codes for asteroseismic studies, but should be viewed with caution. Finally, in a case where tracer particles do not suffer from numerical artefacts, we suggest that a diffusion model is not suitable for time-scales typically considered by 2D numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

Nodal Numerical Modeling of Submerged Helium Injection in a Cryogenic Propellant Tank

Subcooling of cryogenic propellant by helium injection is one of the most effective methods for suppressing bulk boiling and keeping subcooled propellant conditions for pre-launch, launch, and post-launch pressurization applications. For tank pressurization, submerged helium injection can substantially reduce helium consumption by infusing gaseous propellant into the tank ullage. This paper presents a mathematical model of the helium bubbling process in liquid oxygen to estimate the amount of oxygen vapor absorbed by the rising helium bubbles and the amount of subcooling of liquid oxygen due to evaporative heat and mass transfer. This mathematical model was incorporated in a simulation model of tank pressurization built with Generalized Fluid System Simulation Program (GFSSP), a general-purpose flow network code developed at NASA/Marshall Space Flight Center. The numerical predictions of subcooling have been compared with the experimental data of Cho et al. which investigated the propellant subcooling effect as a function of system pressure, helium injection temperature, and flowrate for a non-drained submerged injection system. The numerical predictions of helium consumption have been compared with the test data from a NASA Centaur test vehicle which included both direct and submerged injection with draining of propellants. The numerical model developed with GFSSP has been validated against two sets of experimental data and has been shown to predict both propellant subcooling and helium consumption to within 30% in most cases. The test data used for the model validation were taken in 1-g, but the mass diffusion model was developed to be applied in both 1-g and micro-g environments.

Cryogenics↗
NASA NTRSDate not supplied

Convolution-Based Numerical Solutions of Transient Temperature Fields during Powder Bed Fusion Additive Manufacturing: Theory, Accuracy, and Computational Cost

Powder bed fusion (PBF) additive manufacturing has found numerous applications in the aerospace domain. However, components fabricated via PBF have a complex time-temperature history that significantly impacts subsequent mechanical performance. This study examines convolution-based numerical solutions of transient temperature fields that support simulations involving arbitrary beam shapes and paths during PBF. The convolutional approach is verified through comparisons with analytical solutions of the temperature field. The computational speed and accuracy of the method are assessed through comparisons with other explicit and implicit numerical techniques. In addition, the straightforward translation of the approach from a CPU to a GPU implementation and the resultant performance improvement are presented. The role of the technique in predicting microstructure evolution during PBF (for a greater process-structure-property-performance framework) is also demonstrated. This work supports the development of computational materials methods for understanding and controlling the time-temperature history during PBF.

powder bed fusion↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Numerical simulation of compressible fluid-dynamics in the chamber of inertial fusion energy systems

Here, this paper aims to establish new and innovative modeling capabilities for analyzing chambers in Inertial Fusion Energy (IFE) systems. IFE is emerging as a promising method to achieve fusion power production, but several challenges must be overcome to develop an IFE pilot plant or deploy commercial IFE systems. These challenges are both theoretical and technical, encompassing a deeper understanding of the underlying physical phenomena and the development of new technologies and materials. One of the needs is to develop mathematical models to describe IFE systems and numerical tools to simulate them. This paper contributes to this endeavor by presenting a new OpenFOAM solver for IFE systems, focusing on gas dynamics in their chambers. The analysis and development of chamber designs will play a significant role in the transition from single-shot experiments to high-repetition rates, as there is a need to protect the chamber walls from the intense radiation fields produced by fusion reactions. A promising design option, normally referred to as thick wall chamber design, consists in using lithium or molten salt jet arrays within the chamber. A critical phenomenon is the venting of high-pressure gases from the center to the external part of the chamber, passing through the blanket array. This process involves the propagation and attenuation of strong pressure waves, requiring suitable modeling approaches for compressible fluid-dynamics. The solver proposed in this work implements a multi-material hydrodynamics model tailored to accurately describe the non-linear propagation of pressure waves while avoiding numerical oscillation issues typical of high-velocity compressible simulation. This solver is verified against numerical test cases, validated against experimental data, and applied to the analysis of the High-Yield Lithium-Injection Fusion-Energy (HYLIFE-I) concept. The relevance of this paper is threefold. Firstly, it contributes to developing and testing modeling approaches for compressible fluid-dynamics phenomena, with specific focus on the new and unexplored topic of IFE thick-liquid-wall blanket modeling. Secondly, it marks one of the first applications of the OpenFOAM library in the research field of IFE systems. Finally, the investigated problem is of practical interest for IFE developers, as it provides useful indications about relevant phenomena in pressure wave propagation in the chamber of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Numerically exact configuration interaction at quadrillion-determinant scale

The combinatorial growth of configuration interaction (CI) has long limited this formally exact quantum chemistry method to only the smallest molecules. Here, we report a numerically exact CI calculation exceeding one quadrillion (10 15 ) determinants, made possible by a lossless categorical compression strategy within the small-tensor-product distributed active space (STP-DAS) framework. This approach overcomes the traditional memory bottlenecks of CI by a numerically exact compression of the wavefunction representation and reformulating the most computationally demanding matrix–vector operations. Using this method, we performed a fully relativistic CI calculation of the ground state of HBrTe with over 10 15 complex-valued determinants in just 34.5 h on 1000 computing nodes—the largest CI calculation ever reported. We further achieved fast computation for systems with hundreds of billions of determinants on only a few compute nodes. Extensive benchmarks confirm that the method retains full numerical exactness while cutting memory and computational cost by orders of magnitude. Compared to previous state-of-the-art CI calculations, this work achieves a 1000 times increase in CI space, a 10 6 -fold increase in floating-point operations performed, and a 10 6 -fold improvement in computational speed.

Computational chemistry↗
DOE OSTI2024

Rethinking materials simulations: Blending direct numerical simulations with neural operators

Abstract Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Numerical challenges in modeling gravothermal collapse in Self-Interacting Dark Matter halos

When dark matter has a large cross section for self scattering, halos can undergo a process known as gravothermal core collapse, where the inner core rapidly increases in density and temperature. To date, several methods have been used to implement Self-Interacting Dark Matter (SIDM) in N-body codes, but there has been no systematic study of these different methods or their accuracy in the core-collapse phase. In this paper, we compare three different numerical implementations of SIDM, including the standard methods from the GIZMO and Arepo codes, by simulating idealized dwarf halos undergoing significant dark matter self interactions (σ/m = 50 cm 2 /g). When simulating these halos, we also vary the mass resolution, time-stepping criteria, and gravitational force-softening scheme. The various SIDM methods lead to distinct differences in a halo's evolution during the core-collapse phase, as each results in spurious scattering rate differences and energy gains/losses. The use of adaptive force softening for gravity can lead to numerical heating that artificially accelerates core collapse, while an insufficiently small simulation time step can cause core evolution to stall or completely reverse. Additionally, particle numbers must be large enough to ensure that the simulated halos are not sensitive to noise in the initial conditions. Even for the highest-resolution simulations tested in this study (10 6 particles per halo), we find that variations of order 10% in collapse time are still present. Here, the results of this work underscore the sensitivity of SIDM modeling on the choice of numerical implementation and motivate a careful study of how these results generalize to halos in a cosmological context.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Numerical Simulation of Infrasound Resonance in Underground Tunnel Structures

Remote observation of infrasound resonant signals emanating from underground tunnel structures could potentially allow the remote quantification of the geometry of the underground structures in which the signals were generated. However, the sensitivity of these observations to tunnel geometry and changes in that geometry are unknown. In this report we outline a numerical simulation study with the following three objectives: 1. Can we model infrasound resonance using numerical simulations? 2. What is the sensitivity of the modeled observations to changes in tunnel geometry or boundary conditions? And 3. Can we accurately model resonant observations of explosions occurring in Redmond Salt Mine in Central Utah. In this report we outline affirmative answers to the first two objectives, but we were unable to accurately model the Redmond Explosions due to numerical instability in the model of the complex structure of the mine. Recommendations for future work emphasize the need to acquire additional datasets and to explore a more data-based approach in which changes in data signatures are detected as a first step towards developing a method which inverts resonant infrasound signals for tunnel geometry.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Validation of Numerical Tools for Calculating Reactivity Feedback in Sodium Fast Reactors Using SEFOR Experimental Data

The Southwest Experimental Fast Oxide Reactor (SEFOR) was an experimental sodium-cooled fast breeder reactor operated from 1969 to 1972 with experiments designed to measure Doppler reactivity feedback in a wide temperature range from around 350 °F to temperatures approaching the melting point of mixed oxide fuel of around 5000 °F, providing valuable data for code validations. Co-supported by the Department of Energy (DOE) Fast Reactor Program (FRP) and the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the SEFOR benchmark project focused on using the experimental data to validate numerical tools that are used in industry and academia to design and license sodium-cooled fast reactors (SFRs). By the end of FY-25, substantial progress was achieved in the SEFOR benchmark study. A variety of numerical tools commonly used for modeling SFRs were applied to develop models for SEFOR core configurations I-D, I-E, I-I, and I-J. These included Monte Carlo codes such as MCNP, Serpent, and Shift; deterministic codes such as the legacy Argonne Reactor Computation (ARC) suite and the high-fidelity NEAMS code Griffin; and the system analysis code SAS4A/SASSYS-1 (SAS). Using these models, both SEFOR zero-power experiments and power-ascending tests were successfully simulated. Comparisons were performed against experimental measurements of core criticalities, reflector worth, kinetics parameters (Λ/βeff), isothermal reactivity feedback (from 350 °F to 760 °F at zero power), and power-ascending reactivity feedback (as power increased from 0.4 MW to 17 MW). In general, these comparisons demonstrated very good agreement between numerical results and experimental data. In Fiscal Year 26 (FY-26), the SEFOR benchmark project will continue to address the modeling issues identified in FY-25. Effort will focus on the simulation of reactivity insertion transients in SEFOR core II using the ARC/SAS model. Future work will also focus on incorporating BISON into the SEFOR core modeling process to enable the first Multiphysics simulations of the isothermal tests based on the MOOSE framework.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
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 OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
NASA NTRS1972

Numerical analysis of the transient response of an axisymmetric ablative char layer considering internal flow effects

The differential equations governing the transient response of the char layer of an ablating axisymmetric body, internal pyrolysis gas flow effects being considered, have been derived. These equations have been expanded into finite difference form and programed for numerical solution on a digital computer. Numerical results compare favorably with simplified exact solutions. The complete numerical analysis was used to obtain solutions for two representative body shapes subjected to a typical entry heating environment. Pronounced effects of the lateral flow of pyrolysis gases on the mass flow field within the char layer and the associated surface and pyrolysis interface recession rates are shown.

Pittman, C. M.↗
NASA NTRS1972

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Reese, O. W.↗
NASA NTRS1972

Numerical method for the solution of large systems of differential equations of the boundary layer type

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Green, M. J.↗
NASA NTRS1972

Numerical stability in problems of linear algebra.

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Babuska, I.↗
NASA NTRS1973

Feasibility study of the numerical integration of shell equations using the field method

The field method is developed for arbitrary open branch domains subjected to general linear boundary conditions. Although closed branches are within the scope of the method, they are not treated here. The numerical feasibility of the method has been demonstrated by implementing it in a computer program for the linear static analysis of open branch shells of revolution under asymmetric loads. For such problems the field method eliminates the well-known numerical problem of long subintervals associated with the rapid growth of extraneous solutions. Also, the method appears to execute significantly faster than other numerical integration methods.

Cohen, G. A.↗