Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “surrogates”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Analysis of semivolatile organics in liquid radioactive residue using sorptive stir bar and solvent back-extraction

Current methods for semivolatiles analysis in radioactive samples can produce large volumes of radioactive solvent residue. A method utilizing stir-bar sorptive extraction has been explored in this work for its applicability to radioactive waste samples. This low solvent analytical method may accelerate remediation, minimize hazardous solvent waste, and reduce exposure risk to workers. Organic compounds (polyaromatic hydrocarbons, chlorinated aromatics, and phenolic compounds) were chosen as surrogates for common Liquid Waste System (LWS) contaminants at Savannah River Site (Aiken, SC). Stir-bar extraction parameters (extraction time, matrix modification, and effective pH range) and solvent back extraction parameters (solvent type, volume, and extraction time) were optimized experimentally for the chosen compounds. Affinity of the stir-bar extraction polymer to radionuclides Cs-137 and Am-241 was observed to determine radionuclide concentration effects. The stir-bar method achieved mean recovery of 100 ± 0.7% (1σ), relative to 114 ± 7% using solvent extraction, while reducing weekly method hands-on time by 93.4% and solvent volume consumption by 99.3%. Sensitivity was improved by 378% in simulated tank waste and 278% in real-world LWS matrix, relative to solvent extraction. This work has produced a safe and optimized method for the low solvent analysis of organics in legacy radioactive tank waste by stir-bar sorptive extraction.

GC-MS↗
DOE OSTI2022

Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models

We report lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This computational expense may be particularly burdensome in many-query applications, such as optimization. We develop a stress-constrained topology optimization method for lattice-like structures that uses component-wise reduced order models as a cheap surrogate, providing accurate computation of stress fields while greatly reducing run time relative to a full order model. We demonstrate the ability of our method to produce large reductions in mass while respecting a constraint on the maximum stress in a pair of test problems. The ROM methodology provides a speedup of about 150x in forward solves compared to full order static condensation and provides a relative error of less than 5% in the relaxed stress.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity, via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias–variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Furthermore, our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.

42 ENGINEERING↗
DOE OSTI2023

Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

Here we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

42 ENGINEERING↗
DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2025

Real-time inference and extrapolation with Time-Conditioned UNet: Applications in hypersonic flows, incompressible flows, and global temperature forecasting

Neural Operators are fast and accurate surrogates for nonlinear mappings between functional spaces within training domains. Extrapolation beyond the training domain remains a grand challenge across all application areas. We present Time-Conditioned UNet (TC-UNet) as an operator learning method to solve time-dependent PDEs continuously in time without any temporal discretization, including in extrapolation scenarios. TC-UNet incorporates the temporal evolution of the PDE into its architecture by combining a parameter conditioning approach with the attention mechanism from the Transformer architecture. After training, TC-UNet makes real-time inferences on an arbitrary temporal grid. We demonstrate its extrapolation capability on a climate problem by estimating the global temperature for several years and also for inviscid hypersonic flow around a double cone. We propose different training strategies involving temporal bundling and sub-sampling. We demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals and zero-shot super-resolution time.

Deep learning↗
DOE OSTI2025

Micropolar deep material network

This study extends the Deep Material Network (DMN), a physics-informed machine learning framework, to predict the homogenized mechanical response of composite materials with micropolar (Cosserat-type) constitutive behavior. This extension incorporates microstructure-dependent size effects, enabling accurate, efficient, and size-aware predictions for composites with complex internal architectures. While traditional, direct numerical simulation micropolar models effectively capture size effects by introducing extra local degrees of freedom, they bring significant computational challenges, particularly for multiscale analyses relevant to engineering applications. The micropolar DMN developed in this paper achieves high accuracy while significantly reducing computation time compared to micropolar direct numerical simulations. This advancement enables multiscale analyses and parameter studies that were previously impractical, such as high-cycle fatigue simulations and comprehensive investigations of internal length scale effects notably in size-dependent plastic response and the optimization of lattice structures. By uniting microstructure-sensitive modeling, physics-driven learning, and scalable surrogate modeling, the micropolar DMN paves the way for accelerated material design, large-scale parametric studies, and the reliable incorporation of size-dependent effects across a wide range of engineering applications, including optimization and next-generation composite design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2025

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗
DOE OSTI2023

High-gradient magnetic separation of colloidal uranium oxide particles from soil components in aqueous suspensions

The separation of uranium oxide (UO 2 ) particles from soil-surrogate particles in aqueous suspensions was achieved using filtration enhanced by a magnetic field. Enhanced attraction of paramagnetic UO 2 colloids to a ferromagnetic stainless-steel filter placed in a strong magnetic field arises because of the positive magnetic susceptibility of the particles and the high-gradient field generated near ferromagnetic fibers. Enhanced uptake of smaller particles over larger ones occurs through Brownian motion that promotes the collision of particles with the ferromagnetic fibers of the filter. Hence, this work focused on UO 2 particles in the colloidal size range. Experiments used a water-cooled electromagnet and an array of permanent magnets. Chemical analysis showed that the magnetic field increased the capture efficiency of uranium particles from a range of 27–53% with the magnet off up to 98% with the magnet on after a single pass of the suspension through the filter. Further, the recovery of the UO 2 particles from the filter, however, was more difficult to achieve. Small amounts of UO 2 , together with significant amounts of background SiO 2 particles, were removed from the filter during a first flush with the magnetic field on. A much larger recovery of UO 2 was not observed until a second out-of-field flush was performed, which also released some SiO 2 . The degree to which particle separation was enhanced through the use of multi-stage filtration compared to single pass-through filtration was also examined. A design was suggested that could be used to optimize the separation efficiency for a continuous process.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

A direct numerical simulation of Jet A flame kernel quenching

The safe operation of aeronautical engines requires an understanding of flame ignition, propagation and extinction. In this study, direct numerical simulations are performed using a 29 species reduced chemical mechanism for jet fuel surrogate Jet A to understand the flame quenching process. Here, initially laminar spherical flames of varying sizes and equivalence ratios are subject to an identical periodic domain of decaying and isotropic high intensity turbulence with a turbulent Reynolds number of 2400. All cases become quenched, except for the larger kernel with lower Karlovitz number. An analysis of the flame structure shows broadened preheat zone, flame shortening on the product side, differential species diffusion and partial fuel pyrolysis in the fresh mixture. Two extinction mechanisms are identified arising from flame shortening and high flame stretch. Flame shortening occurs due to turbulence-chemistry interactions that resemble the flame–flame interaction in a laminar counterflow reactant-to-reactant configuration, which contorts and breaks up the ignition kernel. Flame stretch is a local effect that attenuates the heat release rate and causes the flame to retreat towards the product mixtures, similar to what has been observed for reactant-to-product laminar counterflow flames. Chemical explosive mode analysis was also performed to quantify the flame structure and local combustion mode. The diffusion–reaction balance in pinched-off flame islands favors extinction of these smaller structures, while auto-ignition modes are observed within the flame kernel after fresh mixture is engulfed and preheated in the product kernel. Statistics of the density-weighted displacement speed conditional on local combustion mode indicates strong correlation between the local extinction mode and negative displacement speed. The local balance between diffusion and reaction ultimately determines the propensity for local extinction in both laminar and turbulent flames, the extent of which has an impact on global flame propagation.

42 ENGINEERING↗
DOE OSTI2021

Probing intermediate temperature heat release in autoignition of C3-C4 iso-alcohol/gasoline blends

In this work, we report an experimental and modeling study on the blending effects of C3–C4 iso-alcohols, namely iso-propanol and iso-butanol, on the characteristics of intermediate temperature heat release (ITHR) for a research-grade gasoline (FACE-F) in a rapid compression machine operating at diluted/stoichiometric fuel loading, compressed pressure of 43 bar, and compressed temperatures from 700 to 970 K. Changes in ITHR behavior are characterized through ITHR extent and evolution at 0 to 30 vol% iso-alcohol blending levels. Experimental observations reveal the strong promoting and decelerating effects on ITHR extent and evolution, respectively, within the low-temperature regime for both iso-alcohols, with stronger effects seen for iso-propanol; within the intermediate-temperature regime, the influence of both iso-alcohols diminishes greatly. Comprehensive chemical kinetic modeling is undertaken using a recently developed gasoline surrogate/alcohol model in conjunction with a five-component gasoline surrogate (FGF-LLNL), with good agreement obtained with the experiments for all the blends. Sensitivity, rate of production and flux analyses highlight the importance of chemical kinetic interactions via both fuel-specific and non-fuel-specific reactions. Disabling all the chemical kinetic interactions between iso-alcohol and FGF-LLNL in carbonated/non-fuel-specific species leads to somewhat extended ITHR duration and reduced ignition reactivity. Direct comparison between FGF-LLNL/iso-propanol and FGF-LLNL/iso-butanol blends is also made, where iso-propanol and iso-butanol are found to influence ITHR characteristics via significantly different chemical kinetic interactions.

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

Unraveling the role of EGR olefins at advanced combustion conditions in the presence of nitric oxide: Ethylene, propene and isobutene

We report the role of EGR (exhaust gas recirculation) olefinic constituents at advanced combustion conditions in the presence of nitric oxide is unraveled in this study through experimental and modeling efforts using a twin-piston rapid compression machine operating at a stochiometric fuel loading with 20% EGR by mass, pressures of 20 and 40 bar, and temperatures from 680 to 950 K. Five different levels of olefin addition, focusing on ethylene, propene and isobutene, with a fixed amount of NO at 70 ppm are doped into test mixtures of PACE-20, a multi-component gasoline surrogate, where olefin addition effects are characterized through changes in ignition times and heat release rates. Experiments indicate that all three EGR olefins inhibit autoignition reactivity and low-temperature heat release at Tc < 850 K, with isobutene exhibiting the greatest impact, while at Tc > 850 K, low ethylene and propene additions promote reactivity. A recently updated chemical kinetic model, with detailed gasoline/NO x interacting and olefin/NO x interacting chemistry incorporated, is adopted to simulate the experiments. Simulation results are somewhat inconsistent with the experiments, where the model captures the inhibiting effects of all olefins on first-stage ignition reactivity, while consistently predicting a promoting effect on main ignition reactivity. Sensitivity and rate of production analyses reveal that adding olefins greatly alters the role of the consuming pathways for the olefins and their primary derivatives at the initial stage of the oxidation process, particularly with the presence of NO, where the olefins and their derivatives interact with both NO x species such as NO 2 and other species such as OH and HO 2 . The olefin/NO x interactions are particularly pronounced with propene and isobutene addition, where these lead to increased ignition reactivity by facilitating NO production and are mostly responsible for the disagreement between the model and experiments. Further investigations of olefin interacting chemistry, particularly those with NOx species, are needed for chemistry models to accurately predict the complicated effects of EGR.

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

Molecular weight growth by the phenyl + cyclopentadienyl reaction: Well-skipping, ring-opening, and dissociation

Radical-radical reactions contribute to molecular weight growth of polycyclic aromatic hydrocarbons (PAHs), but their role is not well understood. The phenyl (Ph, C 6 H 5 ) + cyclopentadienyl (C 5 H 5 ) reaction has not been studied but can serve as a surrogate reaction for many reactions of larger aryl-σ radicals with resonance-stabilized π-radicals. The adducts of these reactions easily lose an H atom to produce a new π-radical. Here, through a combination of dilute flash pyrolysis experiments, theory, and simulation, we find that for the title reaction, substantial Ph—C 5 H 4 + H is formed, dominantly by a well-skipping pathway, at conditions around 30 Torr and 1400 K. This radical is thermally stable at moderate temperatures but decomposes at higher temperatures following ring opening of the 5-member ring. Products corresponding to the loss of H, C 2 H 2 , and C 3 H 3 are observed experimentally. Calculation of the C 11 H 9 potential energy surface affirms that these are expected decomposition products and reveals multiple possible pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Autoignition of cyclohexane at low-to-intermediate temperatures: Rapid compression machine experiments and improved comprehensive chemical kinetic model

Cycloalkanes are an important class of hydrocarbons found in conventional and alternative transportation fuels. Being one of the simplest practical cycloalkanes, cyclohexane is often used as a surrogate in studies to understand the oxidation, ignition, and sooting characteristics of cycloalkanes more broadly. Although cyclohexane has been extensively studied, very limited datasets for cyclohexane oxidation at low-to-intermediate temperatures are available in the literature. Moreover, the literature autoignition data from rapid compression machines (RCMs) did not provide information on volume histories or experimental heat transfer characteristics which can significantly impact model predictions, thereby hindering the detailed validation of chemical kinetic models. It has also been observed that the cyclohexane kinetic models developed so far are not able to predict the literature data across a wide range of operating and mixture conditions. Hence, further studies are recommended to understand and improve model predictions for cyclohexane oxidation. In this study, RCM experiments were conducted using cyclohexane/air mixtures at varying compressed pressures (P C =15, 20, and 30 bar), equivalence ratios (ϕ=0.5, 1.0, and 2.0), and compressed temperatures (T C =670–960 K). The current RCM results of cyclohexane were found to complement well with the literature data, with the first-stage IDTs at high pressures and volume histories at all test conditions being first reported for better development and validation of chemical kinetic models. Additionally, a detailed chemical kinetic model for the cyclohexane oxidation has been developed and validated using both newly acquired experimental IDTs in this study and literature experimental studies (IDTs in RCMs and STs, species profiles in jet-stirred reactors, and laminar burning velocities). Unlike literature models, the proposed model was observed to provide an overall better prediction for experimental results over a wide range of conditions. Chemical kinetic analysis of the developed model was further conducted to identify the reaction pathways controlling the autoignition of cyclohexane.

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

Simulations of flaming combustion and flaming-to-smoldering transition in wildland fire spread at flame scale

Our objective in the present study is to provide basic insights into the coupling between external-gas and solid biomass vegetation processes that control the dynamics of flame spread in wildland fire problems. Here we focus on a modeling approach that resolves processes occurring at vegetation and flame scales, i.e., the formation of flammable vapors due to the thermal degradation of the solid biomass, the subsequent combustion in ambient air, the thermal feedback to the biomass through radiative and convective heat transfer, and the possible transition from flaming combustion (taking place outside of the solid biomass) to smoldering combustion (taking place inside the solid biomass). The capability uses a multiphase combustion framework and treats external-gas processes through a Large Eddy Simulation solver and solid biomass processes through a discrete particle model. The discrete particle model adopts a one-dimensional porous medium formulation, includes descriptions of drying, thermal pyrolysis, oxidative pyrolysis, and char oxidation, as well as a description of the external-gas-to-solid-biomass diffusion of oxygen mass; the discrete particle model thereby provides a treatment of in-depth oxidative processes and allows the simulation of smoldering combustion. The modeling capability is applied to the simulation of fire spread across a surrogate biomass vegetation bed corresponding to a discrete array of cylindrical-shaped, vertically-oriented, pine wood sticks, characterized by a monomodal size distribution, in horizontal flat terrain and under wind-aided conditions. The numerical results demonstrate that the model can simulate successful flaming-to-smoldering transition followed by complete biomass consumption.

01 COAL, LIGNITE, AND PEAT↗