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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 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

The major goal of the project was to invent, analyze, implement, and apply new algorithms to speed up the computational simulation of complex systems in settings in which multiple simulations are needed. The main efforts we undertook are as follows: 1. Develop novel reduced order methods to reduce the costs of simulations, especially in settings (e.g., UQ, inference, optimization and control) for which numerous simulation are needed and also for nonlocal problems (e.g., fractional derivative, anomalous diffusion, nonlocal mechanics) for which lack of sparsity results in more expensive full-order simulation than encountered in partial differential equations settings; rigorous analyses as well as computational tests were carried out, 2. Develop multifidelity methods based on the usage of a variety of models having different fidelities and different costs to accelerate simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, 3. Develop ensemble methods to reduced the costs of simulations again in settings where numerous simulations are needed or are especially expensive; rigorous analyses as well as computational tests were carried out, and 4. Analyze a model for Richardson pair dispersion in turbulent flows and develop discretization methods for the efficient and accurate approximations of the solution of the model; rigorous analyses as well as computational tests were carried out.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advantages of the Samarskii-type schemes on the Shishkin mesh

The schemes of the Samarskii type are simple modifications of the upwind scheme. We use them on the Shishkin mesh and discuss their advantages over the upwind scheme when applied to the linear one-dimensional singularly perturbed convection–diffusion problem. One of the advantages is that the Samarskii-type schemes have exact first-order accuracy uniform in the perturbation parameter, as opposed to the upwind scheme which is almost first-order uniformly accurate because its accuracy is diminished by logarithmic factors. Although this is not a new result, we re-emphasize it in the paper. We also demonstrate another advantage, that the Samarskii-type schemes are almost second-order uniformly accurate on the layer component of the solution. Motivated by this fact, we present a further improvement of the numerical method.

Convection–diffusion↗
NASA NTRS1996

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗
NASA NTRS2023

Oxidation of Silicon Particles Suspended in Mullite Matrix With Dual-Mode Vacancy Diffusion of Oxygen

Mullite bond coats filled with silicon particles have recently been proposed for the next generation of environmental barrier coatings (EBCs). The sacrificial oxidation of the silicon particles eliminates some of the environmental durability issues associated with traditional EBC designs. To investigate this novel design approach, a mathematical formulation and resulting numerical method have been developed for simulating the oxidation of silicon particles embedded in a mullite matrix. The focus is on the oxidation of the silicon in a dry oxygen environment where the oxidant is presumably oxygen. Oxygen transport from the exterior environment through the mullite is assumed to occur via two lattice defect diffusion mechanisms. As a result, the rate of oxygen transport is dictated by the self-diffusivity of the lattice defects. The numerical method is implemented using the COMSOL Multiphysics® program (COMSOL, Inc.). The method is applied to simulate the oxidation of silicon particles in a mullite pellet in recent oxidation experiments. Numerical results compare favorably with the oxidation behavior observed in the oxidation experiments. The numerical method is also used to investigate the effects of various features of the mullite-silicon particle system on the oxidation behavior.

silicon oxidation↗
NASA NTRS1988

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Yung, Chain Nan↗
DOE OSTI2025

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2023

Passive Rocket Diffuser Testing: Reacting Flow Performance of Advanced Configurations

Upper stage rocket engines are optimized for operation at the edge of space. Ground testing often requires simulation of high-altitude environments to prevent damage from off-design operation. Passive supersonic diffusers are an effective means of establishing the partial vacuum needed around the nozzle exit. The low cost of diffusers relative to active vacuum sources (ejectors, pumps, etc.) provides a perpetual incentive to improve their performance and expand the envelope of passively testable engines. Second-throat diffusers have been the de facto standard for rocket testing since the 1950s, and numerous studies have focused on parametric optimization of the topology. Yet, even the best second-throat designs may require more driving pressure than an upper stage engine can provide. To overcome conventional limits, engineers at NASA’s Stennis Space Center (SSC) adapted an obscure cold-flow diffuser topology to the extremes of immersion in supersonic combustion products. Aerodynamic experimentation was conducted at SSC’s E-3 test stand to quantify the performance of prototypical hot-fire spike diffuser hardware and enable direct comparison to prior states of the art. A LO X /GH 2 thruster was contoured to approximate the regeneratively-cooled nozzle of an upper-stage engine and fired into 28 downstream diffuser configurations: 16 second-throat, 2 centerbody, and 10 spike. Temperature and pressure were recorded along the test article walls for a range of chamber pressures spanning 3.5 - 5.0 MPa. The second-throat configurations with the lowest start and unstart pressure ratios were shown to outperform equivalent systems in literature and taken as baselines for evaluation of advanced diffuser performance. Compared to these exemplars, centerbody diffusers decreased start pressure ratio by 11% but increased unstart pressure ratio by 15%. Spike diffusers reduced start and unstart pressure ratios by 24% and 9%, respectively.

Rocket↗
DOE OSTI2021

A comparative study of machine learning models for predicting the state of reactive mixing

Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass evolution. Here, to investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs to and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

GraMeR: Gra ph Me ta R einforcement learning for multi-objective influence maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, its practical uses are limited due to the computational complexity of current algorithms. Recently, deep reinforcement learning has been leveraged to solve IM in order to ease the computational burden. However, there are serious limitations in current approaches, including narrow IM formulation that only consider influence via spread and ignore self-activation, low scalability to large graphs, and lack of generalizability across graph families leading to a large running time for every test network. In this work, we address these limitations through a unique approach that involves: (1) Formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2)incorporating generalizability via meta-learning across graph families. There are previous works that combine deep reinforcement learning with graph neural network, but this work solves a more realistic IM problem and incorporates generalizability across graphs via meta reinforcement learning. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. Finally, the results indicate that GraMeR is multiple orders faster and generic than conventional approaches when applied on small to medium scale graphs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Investigation of neutron noise in a micro-scale, natural circulation molten salt fission battery system

The Molten Salt Reactor (MSR) concept is a rapidly evolving Generation IV design that has recently attracted favorable attention due to the potential for reducing waste generation, realizing passive safety features, and seizing on the opportunity for cost effective economics. A specific novel micro-MSR, natural circulation, battery design concept involves placing all primary components within a single reactor vessel containment without the need of primary forced pumping. This small modular, integral design presents potential cost savings while producing safety, reliable, and transportable carbon-free power for decades. This investigation evaluates the neutron noise induced by density and flow fluctuations in a natural circulation MSR battery concept being developed at the University of Idaho. This study finds numerical solutions to the one-dimensional, one-group, coupled diffusion equations for a bare, homogeneous core, and evaluates neutron flux and delayed neutron precursor concentration noise due to core flow and fuel salt density perturbation sources. Noise analysis shows both point kinetic and space-dependent behavior is present despite the small size, low-flow, closely-coupled nature of the natural circulation MSR concept. Analysis shows that the low flow of the convective system results in noise behavior typically representative of a larger forced-circulation MSR system. Finally, noise techniques may also be useful in MSR core diagnostics as a non-invasive, low-cost radiological option to traditional monitoring schemes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Designing High-Efficiency Thin Silicon Solar Cells Using Parabolic-Pore Photonic Crystals

We demonstrate the efficacy of wave-interference-based light trapping and carrier transport in parabolic-pore photonic-crystal, thin-crystalline silicon (c -Si) solar cells to achieve above 29% power conversion efficiencies. Using a rigorous solution of Maxwell’s equations through a standard finite-difference time domain scheme, we optimize the design of the vertical-parabolic-pore photonic crystal (PhC) on a 10 μm -thick (c -Si) solar cell to obtain a maximum achievable photocurrent density (MAPD) of 40.6 mA/cm 2 beyond the ray-optical, Lambertian light-trapping limit. For a slanted-parabolic-pore PhC that breaks x-y symmetry, improved light trapping occurs due to better coupling into parallel-to-interface refraction modes. We achieve the optimum MAPD of 41.6 mA/cm 2 for a tilt angle of 10° with respect to the vertical axis of the pores. This MAPD is further improved to 41.72 mA/cm 2 by introducing a 75-nm SiO 2 antireflective coating on top of the solar cell. We use this MAPD and the associated charge-carrier generation profile as input for a numerical solution of Poisson’s equation coupled with semiconductor drift-diffusion equations using a Shockley-Read-Hall and Auger recombination model. Using experimentally achieved surface recombination velocities of 10 cm/s, we identify semiconductor doping profiles that yield power conversion efficiencies over 29%. Practical considerations of additional upper-contact losses suggest efficiencies close to 28%. This improvement beyond the current world record is largely due to an open-circuit voltage approaching 0.8 V enabled by reduced bulk recombination in our thin silicon architecture while maintaining a high short-circuit current through wave-interference-based light trapping.

14 SOLAR ENERGY↗
DOE OSTI2022

Mesoscopic finite-size effects of unconventional electron transport in PdCoO 2

A wide range of unconventional transport phenomena has recently been observed in single-crystal delafossite metals. Here, we present a theoretical framework to elucidate electron transport using a combination of first-principles calculations and numerical modeling of the anisotropic Boltzmann transport equation. Using PdCoO 2 as a model system, we study different microscopic electron and phonon scattering mechanisms and establish the mean free path hierarchy of quasiparticles at different temperatures. We treat the anisotropic Fermi surface explicitly to numerically obtain experimentally-accessible transport observables, which bridge between the “diffusive,” “ballistic,” and “hydrodynamic” transport regime limits. Further, we illustrate that the distinction between the “quasiballistic” and “quasihydrodynamic” regimes is challenging and often needs to be quantitative in nature. From first-principles calculations, we populate the resulting transport regime plots and demonstrate how the Fermi surface orientation adds complexity to the observed transport signatures in micrometer-scale devices. Our work provides key insights into microscopic interaction mechanisms on open hexagonal Fermi surfaces and establishes their connection to the macroscopic electron transport in finite-size channels.

36 MATERIALS SCIENCE↗
DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Electrochemical Characterization of Dissolved Oxides in Molten FLiNaK

Molten fluoride salts have long been the subject of investigation given their application in a variety of industrial processes. Oxides are a common exogeneous impurity within these systems, and can lead to many operational and regulatory concerns. In recent studies, the electro-oxidation of dissolved metallic oxides has been attributed to a single step oxygen evolution reaction despite voltametric evidence suggesting otherwise. Here, we first use square wave voltammetry to confirm that the oxidation of dissolved oxides in fluorides proceeds via a two-electron transfer reaction and then demonstrate that the presence of a peroxide-mediated redox reaction better explains the electrochemical data. Numerical simulations were then used to support the determination of improved diffusion coefficients to enable electroanalytical measurements of the oxide concentration across at a variety of temperatures. A linear Arrhenius relationship was observed when the experimental data was corrected for ohmic resistance effects. Concentration measurements using the corrected square wave voltammetry data demonstrated high accuracy across a large range of concentrations, while the uncorrected data showed plateauing and high errors. In total, this work serves to rectify previously misconstrued electrochemical data of oxides in molten salts and demonstrate how accurate, in situ concentration measurements can be achieved in real-world systems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Determining Exact RANS Operators with the Macroscopic Forcing Method (Final Report)

This report contains a compilation of key results and findings from the ACT project “Determining Exact RANS Operators with the Macroscopic Forcing Method.” The Macroscopic Forcing Method (MFM), a numerical tool for determining closure operators, is used to measure eddy diffusivity moments in Rayleigh-Taylor (RT) instability. It is first applied to low-Atwood 2D RT instability; that work is then extended to 3D RT at different finite Atwood numbers. It is found that nonlocality is important for modeling the mean scalar transport closure operator in RT mixing. Additionally, work is done to improve the statistical convergence of MFM for chaotic problems like RT mixing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗