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Results for “Mathematics and Computing, Physics - Nuclear physics and radiation physics”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical Modeling of Laser Heating and Evaporation of a Single Droplet

Laser technology is being widely studied for controlled energy deposition for a range of applications, including flow control, ignition, combustion, and diagnostics. The absorption and scattering of laser radiation by liquid droplets in aerosols affects propagation of the laser beam in the atmosphere, while the ignition and combustion characteristics in combustion chambers are influenced by the evaporation rate of the sprayed fuel. In this work, we present a mathematical model built on OpenFOAM for laser heating and evaporation of a single droplet in the diffusion-dominated regime taking into account absorption of the laser radiation, evaporation process, and vapor flow dynamics. The developed solver is validated against available experimental and numerical data for heating and evaporation of ethanol and water droplets. The two main regimes—continuous and pulsed laser heating—are explored. For continuous laser heating, the peak temperature is higher for larger droplets. For pulsed laser heating, when the peak irradiance is close to transition to the boiling regime, the temporal dynamics of the droplet temperature does not depend on the droplet size. With the empirical normalization of time, the dynamics of the droplet shrinkage and cooling are found to be independent of droplet sizes and peak laser intensities.

42 ENGINEERING↗
DOE OSTI2024

AI-Enhanced Co-Design for Next-Generation Microelectronics: Innovating Innovation (Workshop Report)

The Artificial Intelligence Enhanced Co-Design for Next Generation Microelectronics virtual workshop was held April 4-5, 2023, and attended by subject matter experts from universities, industry, and national laboratories. This was the third in a series of workshops to motivate the research community to identify and address major challenges facing microelectronics research and production. The 2023 workshop focused on a set of topics from materials to computing algorithms, and included discussions on relevant federal legislation and such as the Creating Helpful Incentives to Produce Semiconductors and Science Act (CHIPS Act) which was signed into law in the summer of 2022. Talks at the workshop included edge computing in radiation environments, new materials for neuromorphic computing, advanced packaging for microelectronics, and new AI techniques. We also received project updates from several of the Department of Energy (DOE) microelectronics co-design projects funded in the fall of 2021, and from three of the Energy Frontier Research Centers (EFRCs) that had been funded in the fall of 2022. The workshop also conducted a set of breakout discussions around the five principal research directions (PRDs) from the 2018 Department of Energy workshop report: 1) define innovative material, device, and architecture requirements driven by applications, algorithms, and software; 2) revolutionize memory and data storage; 3) re-imagine information flow unconstrained by interconnects; 4) redefine computing by leveraging unexploited physical phenomena; 5) reinvent the electricity grid through new materials, devices, and architectures. We tasked each breakout group to consider one primary PRD (and other PRDs as relevant topics arose during discussions) and to address questions such as whether the research community has embraced co-design as a methodology and whether new developments at any level of innovation from materials to programming models requires the research community to reevaluate the PRDs developed back in 2018.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

CHUWD-H v1.0: a comprehensive historical hourly weather database for U.S. urban energy system modeling

Reliable and continuous meteorological data are crucial for modeling the responses of energy systems and their components to weather and climate conditions, particularly in densely populated urban areas. However, existing long-term datasets often suffer from spatial and temporal gaps and inconsistencies, posing great challenges for detailed urban energy system modeling and cross-city comparison under realistic weather conditions. Here we introduce the Historical Comprehensive Hourly Urban Weather Database (CHUWD-H) v1.0, a 23-year (1998-2020) gap-free and quality-controlled hourly weather dataset covering 550 weather station locations across all urban areas in the contiguous United States. CHUWD-H v1.0 synthesizes hourly weather observations from stations with outputs from a physics-based solar radiation model and a reanalysis dataset through a multi-step gap filling approach. A 10-fold Monte Carlo cross-validation suggests that the accuracy of this gap filling approach surpasses that of conventional gap filling methods. Designed primarily for urban energy system modeling, CHUWD-H v1.0 should also support historical urban meteorological and climate studies, including the validation and evaluation of urban climate modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗
DOE OSTI2019

The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

Physics↗
DOE OSTI2026

Dynamical Downscaling of Earth System Model Data for Energy System Analysis

Assessing energy resources (e.g., solar, wind, and hydro) under future scenarios requires datasets with sufficient spatial and temporal detail to capture variability and extreme events. While global-scale Earth System Model (ESM) projections are widely used, their coarse resolution limits direct application to regional energy system analyses. Dynamical downscaling offers a robust approach to generate physically consistent, fine-scale datasets that better represent local atmospheric processes impacting energy resources. In this work, we present a two-stage approach for producing high-resolution historical and future projections over the contiguous United States (CONUS). First, we optimize the Weather Research and Forecasting (WRF) model configuration for energy-relevant variables - solar irradiance, wind speed, and precipitation - by conducting ERA5-driven simulations at 8-km and 28-km resolution. Multiple physics schemes and model configurations within the WRF are evaluated against observational datasets including the National Solar Radiation Database (NSRDB), the Parameter-elevation Regressions on Independent Slopes Model (PRISM), and the Stage IV multi-radar/multi-sensor precipitation product for the CONUS domain. Using the best-performing configuration, we dynamically downscale MPI-ESM1-2-HR simulations for 2000-2060 under SSP2-4.5 and SSP5-8.5 scenarios at 4-km spatial and hourly temporal resolution. This presentation will provide a comprehensive analysis of the results from multiple numerical experiments and high-resolution ESM projections. In addition, we will discuss potential applications of our high-resolution datasets within the energy sector and outline future research avenues dedicated to evaluating how extreme weather events influence system performance and resilience.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

From Interstellar Cloud to Star to Laboratory: Frontier HEDP Studies of Magnetized Colliding Plasma Flows with Strong Radiative Cooling (Final Report)

High-speed flows of gas are the norm in astrophysics where exploding stars, winds from the regions around black holes and streams of galactic material create “supersonic flows”. As the flows collide, strong shock waves are formed where gas is compressed and heated. The regions behind these shock waves are of great interest to scientists. New stars can form in these shock regions in the context of galaxies. In the context of planets like our Earth, the shocks waves come from the interaction of the solar wind with our planets’ magnetic field causing Aurora and placing astronauts and satellites in jeopardy. Thus, understanding supersonic flows of magnetized plasmas is essential for progress in many fields of astronomy and space physics (relevant to planets and the Earth). Remarkably, we can also create these kinds of flows in the laboratory using Z-pinches and laser driven experiments that include magnetic fields. The exploration of these forms of “High Energy Density Physics” (HEDP) flows is also critical in order to achieve Inertial Confinement Fusion, which is a step towards developing a sustainable source of Fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Consistent solutions of the radiation diffusion equation in spherical and cylindrical geometries

We have extended the radiation diffusion model of Hammer and Rosen [Phys. Plasmas 10, 1829 (2003)] to diverging spherical and cylindrical geometries. The effect of curvilinear geometry on the supersonic, expanding wavefront increases as the internal radius of a spherical or cylindrical shell approaches zero. Small spherical geometries are important for modeling systems at the size scale of inertial confinement fusion capsules, at these scales existing quasi-analytic models for planar geometry significantly disagree with the results of simulation. With this method, the benefits of rapid iteration can be applied to common spherical systems at much smaller length scales. We present comparisons between numerical diffusion solutions and the analytic model to give ranges of applicability for the model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Fixed Source Sensitivity Calculations for Inertial Confinement Fusion Applications

A numerical code library was developed for the radiation transport code MCNP6.3 to calculate generalized response sensitivity coefficients for fixed source neutron transport problems with applications to inertial confinement fusion (ICF) experiments. The new MCNP6.3 dependency is used to generate a novel time convolution response that represents a neutron time-of-flight (nToF) signal. The traditional suite of macroscopic cross-section sensitivities and constrained fixed source probability distribution sensitivities are available for both the standard and the new response tallies in this library. However, novel sensitivity coefficients for the constrained hyperparameters of analytic fixed source probability distributions are emphasized in this work for their connection to ICF neutron transport models. Particularly, advanced Monte Carlo methods are developed for calculating the sensitivity of a nToF signal to perturbations in an ICF plasma’s ion temperature and burn history as well as perturbations in the target liner mass density and the shape parameters of the nToF detector’s impulse response function. Together, these capabilities form an advanced suite of computational tools that can be used to analyze and extract information from any ICF experimental platform.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Evaluation of the Rapid Refresh Numerical Weather Prediction Model over Arctic Alaska

Abstract Despite a need for accurate weather forecasts for societal and economic interests in the U.S. Arctic, thorough evaluations of operational numerical weather prediction in the region have been limited. In particular, the Rapid Refresh Model (RAP), which plays a key role in short-term forecasting and decision-making, has seen very limited assessment in northern Alaska, with most evaluation efforts focused on lower latitudes. In the present study, we verify forecasts from version 4 of the RAP against radiosonde, surface meteorological, and radiative flux observations from two Arctic sites on the northern Alaskan coastline, with a focus on boundary layer thermodynamic and dynamic biases, model representation of surface inversions, and cloud characteristics. We find persistent seasonal thermodynamic biases near the surface that vary with wind direction, and may be related to the RAP’s handling of sea ice and ocean interactions. These biases seem to have diminished in the latest version of the RAP (version 5), which includes refined handling of sea ice, among other improvements. In addition, we find that despite capturing boundary layer temperature profiles well overall, the RAP struggles to consistently represent strong, shallow surface inversions. Further, while the RAP seems to forecast the presence of clouds accurately in most cases, there are errors in the simulated characteristics of these clouds, which we hypothesize may be related to the RAP’s treatment of mixed-phase clouds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Physics Guided Simulation of Electrostatic Discharge: Technical Report

Triboelectrically-charged objects may create threshold sparks, electrostatic discharge (ESD) events, to equilibrate charge between themselves and other relatively charged objects. ESD events exhibit many complex physical phenomena. They are a nexus of several fields of physics with disparate characteristic scales: plasma physics, chemical kinetics, hydrodynamics, circuit models, etc. These scales can span many orders of magnitude from the varied collisions thermalizing information within a plasma on the $\mathcal{O}(fs/ps)$ to the physical size of the plasma channel on the $\mathcal{O}(100µm)$, to the speed of a nonlinear hydrodynamic wave propagating at $\mathcal{O}(µm, ns)$. These threshold ESD events may occur in situations of programmatic importance, delivering energy and power profiles to a “victim load” generating deleterious consequences. To predict and mitigate these consequences we must answer questions about the spark’s energy budget: how much energy goes into producing the spark channel; how much gets radiated away; how much energy is advected away into the hydrodynamics; and how much energy is delivered to a victim load. An ESD simulation toolset has been created and evolved in order to answer these questions. An appropriate, physics guided implementation for simulation can be done by gaining insight into its constituent physics and leveraging that intuition to choose a suitable numerical operator. We examine in detail the chemical kinetics, circuit discharge, and hydrodynamics to deter mine dominant regimes, values, timescales, and interactions to uncover the underlying physical dynamics. We also examine and propose model reduction schemes for high-dimensional chemical kinetics. We use past and current work with experimentally validated and theoretically-verified hydrodynamics to calculate applicability limits of the non-ionizing strong shock limit. We quantify the energy budget from a hydrodynamic perspective and demonstrate that a significant fraction of the stored energy is “earmarked” for hydrodynamic advection as an energy terminus. Lastly, we combine the constituent physics of an ESD event (chemical kinetics, circuit model, and hydrodynamics) into a cohesive, actionable toolset and obtain promising results from an isothermal test case. We then propose a viable, modular evolution of the ESD toolset based upon the performed examination of the physics uncovering dominant physical scales and the stiffness of the compositional differential system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Machine Learning Framework for Predicting Microphysical Properties of Ice Crystals From Cloud Particle Imagery

The microphysical properties of ice crystals are important because they significantly alter the radiative properties and spatiotemporal distributions of clouds, which in turn strongly affect Earth's climate. However, it is challenging to measure key properties of ice crystals, such as mass or morphological features. Here, we present a proof-of-concept framework for predicting three-dimensional (3D) microphysical properties of ice crystals from in situ two-dimensional (2D) imagery. First, we computationally generated synthetic ice crystals using 3D modeling software along with geometric parameters estimated from the 2021 Ice Cryo-Encapsulation Balloon (ICEBall) field campaign. Then, we used synthetic crystals to train machine learning (ML) models to predict effective density ($ρ_e$), effective surface area ($A_e$), and number of bullets ($N_b$) from synthetic rosette imagery. On unseen synthetic images, our ML models accurately predicted ice crystal properties. ResNet-18 performed best, achieving $R^2$ values of 0.99 and 0.98 for $ρ_e$ and $A_e$, respectively, and MAE of 0.10 for mathematical equation in single view tasks. Stereo view ResNet-18 further reduced RMSE by 40% for $ρ_e$ and $A_e$ and reduced MAE by 0.08 for $N_b$. This work provides a novel ML-driven framework for estimating ice microphysical properties from in situ imagery, which will allow for downstream constraints on microphysical parameterizations, such as the mass-size relationship.

Ko, J. [Columbia Univ., New York, NY (United State↗
DOE OSTI2023

SootLib: A soot model library for combustion simulation

Soot formation in combustion is an important process that affects radiative heat transfer, flame temperatures, and emissions with health and environmental impacts. Soot formation involves complex chemistry for nucleation, growth, oxidation, and coagulation processes. The soot particles vary widely in size and accurate modeling requires representation of the particle size distribution (PSD). Modeling soot is not trivial, and is only one of several physical processes active in combustion systems. This paper presents a software package called SootLib, which is an open-source library for modeling soot formation and other aerosol systems. SootLib is written in C++, is documented with Doxygen, and is available on GitHub. The library includes several models for soot chemistry and coagulation, and it represents the PSD using either a sectional model or the method of moments (MOM). Four closure approaches for the MOM are implemented allowing up to eight moments: monodispersed, an assumed-shape lognormal distribution, the quadrature method of moments, and the method of moments with interpolative closure. SootLib provides an interface for inclusion in other combustion packages including CFD or reacting flow solvers. The range of models allows comparisons and sensitivity studies, and the modularity facilitates extension to other soot models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Near-field models and simulations of pellet ablation in tokamaks

Here, detailed numerical studies of the ablation of a single neon pellet in the plasma disruption mitigation parameter space have been performed. Simulations were carried out using FronTier, a hydrodynamic/low magnetic Reynolds number MHD code with explicit tracking of material interfaces. FronTier's physics models resolve the pellet surface ablation and the formation of a dense, cold cloud of ablated material, the deposition of energy from hot plasma electrons, the expansion of the ablation cloud along magnetic field lines, and the radiation losses. A local thermodynamic equilibrium model based on Saha equations has been used to resolve atomic processes in the cloud and Redlich–Kwong corrections to the ideal gas equation of state for cold and dense gases, which have been used near the pellet surface. The FronTier pellet code is a next generation of the code described. It has been validated against the semi-analytic improved neutral gas shielding model in the 1D spherically symmetric approximation. Main results include quantification of the influence of atomic processes and Redlich–Kwong corrections on the pellet ablation in spherically symmetric approximation and verification of analytic scaling laws in a broad range of pellet and plasma parameters. Using axially symmetric MHD simulations, the properties of ablation channels and the reduction of pellet ablation rates in magnetic fields of increasing strength have been studied. While the main emphasis has been given to neon pellets for the plasma disruption mitigation, selected results on deuterium fueling pellets have also been presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A system identification approach for non-intrusive reduced order modeling of radiation-induced photocurrents

In this study, development of compact photocurrent models is currently dominated by analytical techniques that rely on physical assumptions to render the governing equations solvable in a closed form. Violation of these assumptions can reduce the accuracy of the models and/or limit their scope. In this paper we show that system identification of nonlinear state-space systems can serve as an alternative numerical basis for non-intrusive reduced order modeling of photocurrent effects. To that end we develop a compact gray box photocurrent model (GBPM) by using a state-space representation with a low-dimensional latent state equation that mimics a mathematical model for the response of an idealized class of devices to ionizing radiation. In so doing we obtain a model that learns the dynamics of a quantity of interest directly from its measurements without requiring snapshots of the internal device state or its discretized model, and can be inferred from very small data sets. To demonstrate the approach we train the GBPM using a small experimental data set for a Z5236 Zener diode and a small synthetic data set obtained by simulating a synthetic pn-junction device. We then compare the GBPMs with black box models trained on the same data and show that performance of the latter is limited by the size of the data set, while the former are able to achieve excellent performance in both the reproductive and the predictive regimes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Hybridizing Machine Learning and Physically-based Earth System Models to Improve Prediction of Multivariate Extreme Events (AI Exploration of Wildland Fire Prediction)

Focal Areas: This project responds to two focal areas identified in the DOE Call for AI4ESP White Papers: 1) Predictive modeling through the use of artificial intelligence (AI) techniques, and 2) insights gleaned from complex data using explainable AI and big data analytics. Science Challenge: Large wildland fires (hereafter wildfires) appearing as high-impact compound climate extreme events are closely related to hydroclimate and water cycle extremes that modulate surface fuel supply and combustibility. These compound events have multivariate climatic features (e.g., temperature, precipitation, relative humidity, wind, lightning) and societal drivers (e.g., forest management, land use change, human caused ignitions). Meanwhile, they induce strong feedbacks to the coupled atmosphere, biosphere, and hydrosphere by perturbing regional and global radiation budget as well as ecological, biogeochemical, and water cycles across multiple spatiotemporal scales. The nonlinear interactions between these natural and anthropogenic components of the Earth system are too complex to be completely and adequately represented in today’s Earth system models (ESMs). The inherent stochastic nature of fire activity at all scales further increases the difficulty of its prediction using ESMs that are usually developed from deterministic equations and parameterizations. Besides, concurrence of long-term (decadal to interdecadal) global climate change and fire regime shifts overlapping with short-term (intraseasonal to interannual) variations of regional fire weather and burning activity confound predictability of these compound extreme events. We propose to address the above scientific challenges by using machine learning (ML)-based data-driven modeling techniques to integrate observations and physically-based ESMs’ simulations in a computationally efficient hybrid prediction system. This prediction system is supposed to characterize the wildfire’s sensitivity to climate and exogenous drivers at high resolution (~ 0.25°) on subseasonal to seasonal (S2S) timescales providing improved predictability and explainability. We will use the system to help identify: (1) What are the computational elements of a hybrid system needed to predict compound climate extreme events such as global wildfires? (2) What are the key drivers (either natural or anthropogenic) that modulate short-term variations of multivariate fire weather and burning activity over different regions? How can one take advantage of those driver-response relationships to improve the predictability of large wildfires on S2S time scales? (3) What are the underlying physical mechanisms and sources of improved predictability? Which ML techniques are optimal in revealing and adapting these mechanisms?

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗