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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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All sourcesNASA NTRSDOE OSTI
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 Method Improvements in Griffin for Pebble Bed Reactors with a Focus on the Computation of Burnup

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient multiphysics modeling of advanced reactors, has been used recently to model both high-temperature gas-cooled and fluoride-salt-cooled pebble bed reactors (PBRs). Griffin uses deterministic methods for solving neutron transport and an Eulerian approach to model pebble movement. An Eulerian approach is also used to directly compute burnup instead of using a pass approach like other tools such as VSOP or PANGU. This work discusses verification efforts and numerical method improvements related specifically to the Eulerian modeling approach implemented for directly computing pebble burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Mathematical Models and Numerical Methods for High-Fidelity Simulation of Ignition of Reactive Mixtures by Nanosecond Plasma Discharges in Realistic Configurations

We present a newly developed framework for the numerical simulation of ignition of reactive mixtures using single or repeated nanosecond discharge pulses. The framework builds upon the AMReX library, using the existing compressible solver PeleC and low-Mach solver PeleLMeX and allowing for adaptive mesh refinement, complex geometries, and execution on next-generation high-performance computing (HPC) systems. High-fidelity elementary models are adopted for weakly-ionised plasma discharges with significant energy deposition, consistent with nanosecond discharge pulses, and then implemented in the solver. The treatment of non-thermal electrons and charged species, thermodynamics of non-equilbrium species, plasma kinetics, limiting time scales, and boundary conditions for charged species are discussed and addressed for computational efficiency. The framework is demonstrated for three relevant applications: single and multi-pulse discharges in air, single pulse ignition of an ethylene/air mixture, and a three-dimensional plasma discharge in air with temperature stratification. The successful application of the framework demonstrates the feasibility of high-fidelity simulation of ignition of air/hydrocarbon mixtures in three-dimensions with multiple discharge pulses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Determining the Minimum Phase‐to‐Phase Gap Distance for Unconventional Transmission Lines Using Numerical Method

With the increasing demand for power transmission, compact, high surge impedance loading (HSIL) high-voltage transmission lines have emerged as a viable solution due to their reduced land acquisition costs and higher power delivery capability. The compactness of a transmission line depends on effective insulation coordination, particularly in determining the phase-to-phase clearance, which is governed by the critical flashover voltage under switching and lightning overvoltage conditions. Traditional methods for phase-to-phase clearance rely on empirical formulas derived from experimental data, which are convenient for conventional high-voltage lines. However, unconventional HSIL lines require a faster and more adaptable evaluation method, as they involve optimized conductor positioning to reduce right-of-way requirements while enhancing natural power loadability. This study presents a simplified numerical approach to determine the minimum phase-to-phase gap, utilizing arc propagation viability curves, and offers an efficient alternative to conventional empirical methods. The proposed method was successfully applied to a 500 kV conventional line as well as 500 and 735 kV unconventional line designs, demonstrating its capability in accurately assessing insulation requirements. Results reveal that the method can support reduced gap clearances while still maintaining reliability, thereby validating its usefulness in optimizing compact transmission line configurations.

Arafat, Easir [The University of Texas at Dallas, ↗
DOE OSTI2024

Investigation of Numerical Methods for Performance Improvement of MOOSE-based System Analysis Codes

The main objective of this study is to investigate the feasibility of implementation of staggered-grid finite volume method (SG-FVM) using the MOOSE framework to support the development of the advanced system analysis code SAM. This study successfully demonstrated the integration of staggered-grid finite volume method in the application level using the MOOSE framework, although not in the framework level which should be investigated in the future. Several important properties of the implemented SG-FVM, e.g., high-order spatial accuracy and monotonicity preserving, have been demonstrated with selected numerical test cases. The superior performance in execution time was also evident based on a selected one- dimensional flow problem in a loop configuration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Flame Characterization of a Hydrogen Micromix Burner using Experimental and Numerical Methods - Extended Abstract

Micromix combustion presents a promising solution for integrating hydrogen into gas turbine combustors, offering rapid and compact air-fuel mixing that effectively shortens the combustion zone and significantly reduces nitrogen oxides (NOX) emissions. A major challenge in hydrogen combustion systems is flashback, which is mitigated through short mixing lengths and high flow velocities. This study investigates three fuel injector designs – zero swirl, low swirl, and high swirl – for a 6-mm inner diameter nozzle, where hydrogen is injected through six 0.3 mm diameter holes in a jet-in-crossflow configuration relative to the airstream. Numerical simulations indicate stable flame formation, moderate peak flame temperatures, and subsequent low NOx potential for all designs. These injectors have been fabricated using additive manufacturing, and upcoming experiments will explore flame structure and NOx behavior across varying fuel injection angles, equivalence ratios and pre-mixer velocities. These efforts aim to advance the development of low-emission hydrogen micromix combustion.

hydrogen↗
DOE OSTI2024

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

New correlated numerical methods for attosecond molecular single and double ionization

This project resulted in the development of ASTRA, a new molecular ionization code capable of describing single and double ionization processes in polyatomic molecules with correlated electrons and time-dependent fields. Key achievements include: (i) the development of the PRISM hybrid-integral library enabling core-ionization and high-angular-momentum convergence; (ii) implementation of time-dependent Schrödinger equation solvers for pump–probe spectroscopies; (iii) validation against experimental and theoretical benchmarks for atoms and molecules; and (iv) extension to two-photon double ionization using the finite-pulse virtual-sequential model. These developments establish ASTRA as a versatile platform for attosecond molecular dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Efficient general method for numerically modeling laser pulse propagation, overlap, and lifetime effects in amplifiers

An efficient numerical time-dependent general method is developed to address incoherent pulse overlap and lifetime effects in laser amplifiers. The alternating propagation-population laser energetics method (APPLE) has been validated against a semi-discrete coupled rate equation numerical method (SDRE) and analytic formalisms in bounding cases. APPLE is based on decoupled rates applied to a time-dependent framework where both space-time-dependent populations and pulse energetics are consistently updated in each time step. A significant advantage of APPLE lies in its conceptual simplicity, ease of implementation, and relatively small computational cost. SDRE tracks the populations through coupled rates and uses the method of lines to discretize the hyperbolic partial differential transport equations allowing for use of ordinary differential equation solvers. With reasonably sized mesh, we report both energetic and power pulse shape relative differences on the order of one percent between the models over a large range of initial conditions.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Opportunities and Challenges of Computational Electromagnetics Methods for Superconducting Circuit Quantum Device Modeling: A Practical Review

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational electromagnetics (CEM) methods. Although the CEM research field is mature, emerging applications can still stress the capabilities of the techniques in use today. The design of superconducting circuit quantum devices falls in this category due to the unconventional material properties and important features of the devices covering nanometer to centimeter scales. Such multiscale devices can stress the fundamental properties of CEM tools which can lead to an increase in simulation times, a loss in accuracy, or even cause no solution to be reliably found. While these challenges are being investigated by CEM researchers, knowledge about them is limited in the broader community of users of these CEM tools. This review is meant to serve as a practical introduction to the fundamental aspects of the major CEM techniques that a researcher may need to choose between to model a device, as well as provide insight into what steps they may take to alleviate some of their challenges. Our focus is on highlighting the main concepts without rigorously deriving all the details, which can be found in many textbooks and articles. After covering the fundamentals, we discuss more advanced topics related to the challenges of modeling multiscale devices with specific examples from superconducting circuit quantum devices. We conclude with a discussion on future research directions that will be valuable for improving the ability to successfully design increasingly more sophisticated superconducting circuit quantum devices. Although our focus and examples are taken from this area, researchers from other fields will still benefit from the details discussed here.

Elkin, Samuel T. [Virginia Tech., Blacksburg]↗