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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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DOE OSTI2018

ExaTN

A challenging scientific problem that will benefit from exascale computing is predictive simulation of two- and three-dimensional quantum many-body Hamiltonians in condensed matter physics, together with the related strong entanglement problems in quantum chemistry and quantum computing. Efficient numerical simulations will require new insights into wavefunction compression algorithms that scale on extremely heterogeneous HPC architectures. To address this need, we propose to develop a scalable math library of parallel multi-linear algebraic numerical primitives for hierarchical tensor compression. Our library will subsequently be used for building an efficient, performance-portable HPC framework for simulating strongly correlated quantum systems. In particular, our will will be the first to deliver a massively parallel implementation of the multiscale entanglement renormalization ansatz (MERA), a hierarchical tensor decomposition quantum scheme capable of expressing local expectation values of strongly entangled higher-dimensional quantum systems efficiently. To address the extreme complexity and high computational cost of such schemes, we will automate their parallel implementation by delivering an integrated software framework, ExaTN (Exascale Tensor Networks), that will process hierarchical tensor representations on exascale HPC systems via an asymchronous task-based programming model. As a specific application, our framework will provide scientists with a capability of simulating strongly entangled quantum systems, thus positioning ORNL as a strategic leader in modeling of strongly correlated materials.

McCaskey, AlexanderJ↗

DOE OSTI2017

Heterogeneous Diels–Alder catalysis for biomass-derived aromatic compounds

In this tutorial review, we provide an overview of heterogeneous Diels–Alder catalysis for the production of lignocellulosic biomass-derived aromatic compounds. Diels–Alder reactions afford an extremely selective and efficient route for carbon–carbon cycloadditions to produce intermediates that can readily undergo subsequent dehydration or dehydrogenation reactions for aromatization. As a result, catalysis of Diels–Alder reactions with biomass-derived dienes and dienophiles has seen a growth of interest in recent years; however, significant opportunities remain to (i) tailor heterogeneous catalyst materials for tandem Diels–Alder and aromatization reactions, and (ii) utilize biomass-derived dienes and dienophiles to access both conventional and novel aromatic monomers. As such, this review discusses the mechanistic aspects of Diels–Alder reactions from both an experimental and computational perspective, as well as the synergy of Brønsted–Lewis acid catalysts to facilitate tandem Diels–Alder and aromatization reactions. Heterogeneous catalyst design strategies for Diels–Alder reactions are reviewed for two exemplary solid acid catalysts, zeolites and polyoxometalates, and recent efforts for targeting direct replacement aromatic monomers from biomass are summarized. In conclusion, we point out important research directions for progressing Diels–Alder catalysis to target novel, aromatic monomers with chemical functionality that enables new properties compared to monomers that are readily accessible from petroleum.

09 BIOMASS FUELS↗

DOE OSTI2019

Carbon Storage and Enhanced Oil Recovery in Pennsylvanian Morrow Formation Clastic Reservoirs: Controls on Oil–Brine and Oil–CO2 Relative Permeability from Diagenetic Heterogeneity and Evolving Wettability

The efficiency of carbon utilization and storage within the Pennsylvanian Morrow B sandstone, Farnsworth Unit, Texas, is dependent on three-phase oil, brine, and CO2 flow behavior, as well as spatial distributions of reservoir properties and wettability. We show that end member two-phase flow properties, with binary pairs of oil–brine and oil–CO2, are directly dependent on heterogeneity derived from diagenetic processes, and evolve progressively with exposure to CO2 and changing wettability. Morrow B sandstone lithofacies exhibit a range of diagenetic processes, which produce variations in pore types and structures, quantified at the core plug scale using X-ray micro computed tomography imaging and optical petrography. Permeability and porosity relationships in the reservoir permit the classification of sedimentologic and diagenetic heterogeneity into five distinct hydraulic flow units, with characteristic pore types including: macroporosity with little to no clay filling intergranular pores; microporous authigenic clay-dominated regions in which intergranular porosity is filled with clay; and carbonate–cement dominated regions with little intergranular porosity. Steady-state oil–brine and oil–CO2 co-injection experiments using reservoir-extracted oil and brine show that differences in relative permeability persist between flow unit core plugs with near-constant porosity, attributable to contrasts in and the spatial arrangement of diagenetic pore types. Core plugs “aged” by exposure to reservoir oil over time exhibit wettability closer to suspected in situ reservoir conditions, compared to “cleaned” core plugs. Together with contact angle measurements, these results suggest that reservoir wettability is transient and modified quickly by oil recovery and carbon storage operations. Reservoir simulation results for enhanced oil recovery, using a five-spot pattern and water-alternating-with-gas injection history at Farnsworth, compare models for cumulative oil and water production using both a single relative permeability determined from history matching, and flow unit-dependent relative permeability determined from experiments herein. Both match cumulative oil production of the field to a satisfactory degree but underestimate historical cumulative water production. Differences in modeled versus observed water production are interpreted in terms of evolving wettability, which we argue is due to the increasing presence of fast paths (flow pathways with connected higher permeability) as the reservoir becomes increasingly water-wet. The control of such fast-paths is thus critical for efficient carbon storage and sweep efficiency for CO2-enhanced oil recovery in heterogeneous reservoirs.

Rasmussen, Lindsey↗

DOE OSTI2018

Numerical analysis of experimental studies of methane hydrate dissociation induced by depressurization in a sandy porous medium

Methane Hydrates (MHs) are a promising energy source abundantly available in nature. Understanding the complex processes of MH formation and dissociation is critical for the development of safe and efficient technologies for energy recovery. Many laboratory and numerical studies have investigated these processes using synthesized MH-bearing sediments. A near-universal issue encountered in these studies is the spatial heterogeneous hydrate distribution in the testing apparatus. In the absence of direct observations (e.g. using X-ray computed tomography) coupled with real time production data, the common assumption made in almost all numerical studies is a homogeneous distribution of the various phases. In an earlier study (Yin et al., 2018) that involved the numerical description of a set of experiments on MH-formation in sandy medium using the excess water method, we showed that spatially heterogeneous phase distribution is inevitable and significant. In the present study, we use as a starting point the results and observations at the end of the MH formation and seek to numerically reproduce the laboratory experiments of depressurization-induced dissociation of the spatially-heterogeneous MH distribution. This numerical study faithfully reproduces the geometry of the laboratory apparatus, the initial and boundary conditions of the system, and the parameters of the dissociation stimulus, capturing accurately all stages of the experimental process. Using inverse modelling (history-matching) that minimized deviations between the experimental observations and numerical predictions, we determined the values of all the important flow, thermal, and kinetic parameters that control the system behaviour, which yielded simulation results that were in excellent agreement with the measurements of key monitored variables, i.e. pressure, temperature, cumulative production of gas and water over time. We determined that at the onset of depressurization (when the pressure drop – the driving force of dissociation – is at its maximum), the rate of MH dissociation approaches that of an equilibrium reaction and is limited by the heat transfer from the system surroundings. Furthermore, as the effect of depressurization declines over time, the dissociation reaction becomes kinetically limited despite significant heat inflows from the boundaries, which lead to localized temperature increases in the reactor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Athena: High-Performance Sparse Tensor Contraction Sequence on Heterogeneous Memory

Sparse tensor contraction sequence has been widely employed in many fields, such as chemistry and physics. However, how to efficiently implement the sequence faces multiple challenges, such as redundant computations and memory operations, massive memory consumption, and inefficient utilization of hardware. To address the above challenges, we introduce Athena, a high-performance framework for SpTC sequences. Athena introduces new data structures, leverages emerging Optane-based heterogeneous memory (HM) architecture, and stage parallelism. In particular, Athena introduces shared hash table-represented sparse accumulator to eliminate unnecessary input processing and data migration; Athena uses a novel data-semantic guided dynamic migration solution to make the best use of the Optane-based HM for high performance; Athena also co-runs execution phases with different characteristics to enable high hardware utilization. Evaluating with 12 datasets, we show that Athena brings 327-7362× speedup over the state-of-the-art SpTC algorithm. With the dynamic data placement guided by data semantics, Athena brings performance improvement on Optane-based HM over a state-of-the-art software-based data management solution, a hardware-based data management solution, and PMM-only by 1.58×, 1.82×, and 2.34× respectively.

Liu, Jiawen↗

DOE OSTI2024

Employing artificial intelligence to steer exascale workflows with colmena

Computational workflows are a common class of application on supercomputers, yet the loosely coupled and heterogeneous nature of workflows often fails to take full advantage of their capabilities. We created Colmena to leverage the massive parallelism of a supercomputer by using Artificial Intelligence (AI) to learn from and adapt a workflow as it executes. Colmena allows scientists to define how their application should respond to events (e.g., task completion) as a series of cooperative agents. In this paper, we describe the design of Colmena, the challenges we overcame while deploying applications on exascale systems, and the science workflows we have enhanced through interweaving AI. The scaling challenges we discuss include developing steering strategies that maximize node utilization, introducing data fabrics that reduce communication overhead of data-intensive tasks, and implementing workflow tasks that cache costly operations between invocations. These innovations coupled with a variety of application patterns accessible through our agent-based steering model have enabled science advances in chemistry, biophysics, and materials science using different types of AI. In conclusion, our vision is that Colmena will spur creative solutions that harness AI across many domains of scientific computing.

Workflows↗

DOE OSTI2024

SIREN: Scaling Ion-Traps by REquiring iNnovative Heterogenous Integration

The SIREN (Scaling Ion Traps by Requiring iNnovative heterogenous integration) project explores the feasibility of heterogeneous integration (HI) as a transformative approach to scaling ion traps, a critical technology for advancing quantum computers and atomic clocks. Traditional ion trap architectures face significant challenges in scalability due to limitations in optical access, fabrication techniques, and material constraints. SIREN addresses these challenges by leveraging HI, which combines different materials and fabrication processes to create more complex and efficient ion trap structures. HI integrated structures can be manufactured without compromising the process to maintain compatibility to ion traps. This project focuses on integrating a separately fabricated waveguide with a fully functional ion trap. The respective alignment between the pieces needs to be accurate to less than 2 µm to ensure that the light from the waveguide can overlap with the trapping region. The fine alignment must also be maintained through an ultra-high vacuum bake, a critical step in preparing an ion trap experiment. The project's outcomes suggest that heterogeneous integration is a promising pathway for overcoming current scalability barriers, paving the way for the next generation of quantum technologies. SIREN's findings contribute significantly to the field, offering a scalable solution that could accelerate the development of practical quantum computers and highly accurate atomic clocks.

42 ENGINEERING↗

DOE OSTI2019

Predicting CO 2 Plume Migration in Heterogeneous Formations Using Conditional Deep Convolutional Generative Adversarial Network

Numerical simulation of flow and transport in heterogeneous formations has long been studied, especially for uncertainty quantification and risk assessment. The high computational cost associated with running large-scale numerical simulations in a Monte Carlo sense has motivated the development of surrogate models, which aim to capture the important input-output relations of physics-based models but require only a fraction of the cost of full model runs. In this work, we formulate a conditional deep convolutional generative adversarial network (cDC-GAN) surrogate model to learn the dynamic functional mappings in multiphase models. The cDC-GAN belongs to a class of semisupervised learning methods that can be used to learn the data generation processes. Like the original GAN, a main strength of the cDC-GAN is that it includes a self-training scheme for improving the quality of generative modeling in a game theoretic framework, without requiring extensive statistical knowledge and assumptions on input data distributions. In particular, our cDC-GAN model is designed to learn cross-domain mappings between high-dimensional input (e.g., permeability) and output (e.g., phase saturations) pairs, with the ability to incorporate conditioning information (e.g., prediction time). As a use case, we demonstrate the performance of cDC-GAN for predicting the migration of carbon dioxide (CO 2 ) plume in heterogeneous carbon storage reservoirs, which has both numerical and practical significance because of the safe storage requirements now mandated in many countries. Results show that cDC-GAN achieves high accuracy in predicting the spatial and temporal evolution patterns of the injected CO 2 plume, as compared to the original results obtained using a compositional reservoir simulator. The performance of cDC-GAN models, trained using the same number of training samples, stays relatively robust when the level of spatial heterogeneity is increased. Our cDC-GAN is pattern based and is not limited by the underlying physics. Thus, it provides a general framework for developing surrogate models, and for conducting uncertainty analyses for a wide range of physics-based models used in both groundwater and subsurface energy exploration applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Integrating Ultra-Coarse-Grained Protein Models into Accessible Workflows for Multiscale Molecular Dynamics

To capture protein conformational transitions using molecular dynamics (MD), several simulation resolutions covering different spatial and temporal scales are typically needed. All-atom (AA) simulations provide fine resolution, but are computationally infeasible for large systems over longer durations. Coarse-grained (CG) and ultra-coarse-grained (UCG) models have a lower resolution and computational cost while still being able to conserve essential protein features. Prior work on a Multiscale Machinelearned Modeling Infrastructure (MuMMI) combined both AA and CG simulations to study RAS-RAF protein interactions, leveraging CG models for longer time scales and using AA to investigate unusual conformations in greater detail. However, MuMMI is still resource-intensive, and this study aims to maximize exploration of the protein conformational space while reducing computational cost. In this paper, we build on prior work that integrates UCG models based on heterogeneous elastic network modeling (hENM) into the MuMMI workflow. We demonstrate that UCG models enable accurate sampling of protein conformations, focusing on simulating RAS-RAF protein interactions. Using higher-resolution CG Martini simulation data, we can automatically refine intramolecular interactions in UCG models. We present a scalable Python package that uses fluctuations observed in higher-resolution CG Martini simulations to estimate bond coefficients of the UCG model. We built novel machine learning-based backmapping methods to recover more detailed CG Martini structures from UCG structures, using diffusion models to learn the mapping between scales. Finally, we present UCG-mini-MuMMI, an accessible and less compute-intensive version of MuMMI as a resource for the scientific community. Incorporating UCG models into MD studies is applicable to a broad range of systems and proteins, and our study offers insights into the advantages and limitations of these methods.

Chemical structure↗

DOE OSTI2015

Additive manufacturing of materials: Opportunities and challenges

Additive manufacturing (also known as 3D printing) is considered a disruptive technology for producing components with topologically optimized complex geometries as well as functionalities that are not achievable by traditional methods. The realization of the full potential of 3D printing is stifled by a lack of computational design tools, generic material feedstocks, techniques for monitoring thermomechanical processes under in situ conditions, and especially methods for minimizing anisotropic static and dynamic properties brought about by microstructural heterogeneity. In this paper, we discuss the role of interdisciplinary research involving robotics and automation, process control, multiscale characterization of microstructure and properties, and high-performance computational tools to address each of these challenges. In addition, emerging pathways to scale up additive manufacturing of structural materials to large sizes (>1 m) and higher productivities (5–20 kg/h) while maintaining mechanical performance and geometrical flexibility are also discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Sub‐Nanosecond Reconfiguration of Ferroelectric Domains in Bismuth Ferrite

Abstract Domain switching is crucial for achieving desired functions in ferroic materials that are used in various applications. Fast control of domains at sub‐nanosecond timescales remains a challenge despite its potential for high‐speed operation in random‐access memories, photonic, and nanoelectronic devices. Here, ultrafast laser excitation is shown to transiently melt and reconfigure ferroelectric stripe domains in multiferroic bismuth ferrite on a timescale faster than 100 picoseconds. This dynamic behavior is visualized by picosecond‐ and nanometer‐resolved X‐ray diffraction and time‐resolved X‐ray diffuse scattering. The disordering of stripe domains is attributed to the screening of depolarization fields by photogenerated carriers resulting in the formation of charged domain walls, as supported by phase‐field simulations. Furthermore, the recovery of disordered domains exhibits subdiffusive growth on nanosecond timescales, with a non‐equilibrium domain velocity reaching up to 10 m s −1 . These findings present a new approach to image and manipulate ferroelectric domains on sub‐nanosecond timescales, which can be further extended into other complex photoferroic systems to modulate their electronic, optical, and magnetic properties beyond gigahertz frequencies. This approach could pave the way for high‐speed ferroelectric data storage and computing, and, more broadly, defines new approaches for visualizing the non‐equilibrium dynamics of heterogeneous and disordered materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Ultrasound and X-ray Cross-Characterization of a Graded Impedance Impactor used for Shock-Ramp Compression Experiments

Abstract In this work we perform ultrasound measurements on an impedance graded impactor made by tape casting magnesium, copper, and tungsten. We also destructively extract small representative samples from the part for complementary characterization with x-ray computed tomography. Combining the two data sets enables direct assignment of some of the measured ultrasound features to specific material characteristics identified by x-ray tomography. Our results demonstrate how ultrasound inspection, informed by x-ray computed tomography, can be used to identify sub-millimeter material amalgamations and spatial heterogeneities in this graded material.

36 MATERIALS SCIENCE↗

DOE OSTI2018

The geophysics, geology and mechanics of slow fault slip

We report that modern geodetic and seismologic observations describe the behavior of fault slip over a vast range of spatial and temporal scales. Slip at sub-seismogenic speeds is evident from top to bottom of lithospheric faults and plays an important role throughout the earthquake cycle. Where earthquakes and tremor accompany slow slip, they help illuminate the spatiotemporal evolution of fault slip. Geophysical subsurface imaging and geologic field studies provide information about suitable environments of slow slip. In particular, exhumed fault and shear zones from various depths reveal the importance of multiple deformation processes and fault-zone structures. Most geologic examples feature frictionally weak and velocity-strengthening materials, well-developed mineral fabrics, and abundant veining indicative of near-lithostatic fluid pressure. To produce transient slow slip events and tremor, in addition to the presence of high-pressure fluids a heterogeneous fault-zone structure, composition, and/or metamorphic assemblage may be needed. Laboratory and computational models suggest that velocity-weakening slip patches smaller than a critical dimension needed for earthquake nucleation will also fail in slow slip events. Changes in fluid pressure or slip rate can cause a fault to transition between stable and unstable fault slip behavior. Lastly, future interdisciplinary investigations of slow fault slip, directly integrating geophysical, geological and modeling investigations, will further improve our understanding of the dynamics of slow slip and aid in providing more accurate earthquake hazard characterizations.

58 GEOSCIENCES↗

DOE OSTI2022

Capacitance of Carbon Nanotube/Graphene Composite Electrodes with [BMIM + ][BF$_4^–$]/Acetonitrile: Fixed Voltage Molecular Dynamics Simulations

The capacitance of nanoporous carbon electrode materials is dictated by the physical interactions with electrolyte ions and molecules at the accessible interior electrode surface. While significant progress has been made in designing and synthesizing carbon materials with well-defined and relatively homogeneous nanoporosity, the majority of materials remain heterogeneous, and the resulting properties reflect an average over this distribution. In this regard, computer simulations can be a valuable tool to predict or validate structure/property relationships by systematically investigating well-defined, model electrode morphologies. In this work, we utilize fixed-voltage molecular dynamics simulations to predict structure/capacitance relationships for five different model morphologies of carbon nanotube/graphene (CNT/G) composite electrodes with 1-butyl-3-methylimidazolium tetrafluoroborate/acetonitrile electrolyte. The CNT/G electrode models are inspired by experimental “layer-by-layer” syntheses and strike a balance between realism and computational tractability. Comparison between different model electrode architectures elucidates important structure/property relationships. We find that CNT/graphene contact points serve as “hot spots” with significantly enhanced charge separation relative to the rest of the electrode. Furthermore, we demonstrate a specific nanoconfinement motif that provides substantial 3–4$\times$ enhancement of local capacitance, resulting in a ~40% increase of the total electrode differential capacitance. Because the accessible surface area of the model CNT/G electrodes is precisely determined, a comparison of per-area capacitance across systems is unambiguous. Our results thus complement a prior computational demonstration of capacitance enhancement in nanoconfinement while elucidating additional interaction motifs at CNT/G electrochemical interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Dispersion and Mixing in Three-Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity: DISPERSION AND MIXING-REGULAR VERSUS DISORDERED NETWORKS

We investigate the relative impact of topological, geometric, and hydraulic heterogeneity on transport processes in three-dimensional fracture networks. Focusing on the two largest scales of heterogeneity in these systems, individual fracture and network structure, we compare transport through analogous structured and disordered three-dimensional fracture networks with varying degrees of hydraulic heterogeneity. For the moderate levels of hydraulic heterogeneity we consider, network structure is the dominant control of transport through the networks. Less dispersion, both longitudinal and transverse, is observed in structured networks than in disordered networks, due in part to the higher connectivity in the former, independent of the level of hydraulic heterogeneity. However, increases in dispersion with higher hydraulic heterogeneity are larger in the disordered networks than in the structured networks, thereby indicating that the interplay between structural and hydraulic heterogeneity is nonlinear. Here, we propose a measure of disorder in fracture networks by computing the Shannon entropy of the spectrum of the Laplacian of a weighted graph representation of the networks, where the weights are given by a combination of topological, geometric, and hydraulic properties. Finally, this metric, as a relative indicator by comparison between two networks, is a first approach to the dispersion potential and “mixing capacity” of a fracture network.

58 GEOSCIENCES↗

DOE OSTI2021

Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis

Ab initio molecular dynamics simulations combined with enhanced sampling techniques are becoming widespread methods to investigate chemical phenomena in catalytic systems. These techniques automatically include finite temperature effects, anharmonicity, and collective dynamics in their robust description of enthalpic and entropic contributions, which can have significant impact on reaction free energy landscapes. This contrasts with standard ab initio static approaches that are based on assessing reaction free energies from various coarse-grained descriptions of the reaction potential energy surface. Enhanced sampling ab initio molecular dynamics opens the way to first principles simulations of systems of increasing complexity like solid/liquid catalytic interfaces. Here, we aim at guiding the reader through the basis of these techniques, summarizing their fundamental theoretical and practical aspects, and reviewing the relevant literature in the field. After a brief introduction to the problem, we will illustrate the advantage of using molecular simulations to include finite temperature effects, examine the most common ab initio techniques currently in use, describe their application to solid state heterogeneous catalysts, and finally critically review the most popular enhanced sampling techniques used in computational catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Introducing SpaceNet 9 - Cross-Modal Satellite Imagery Registration for Natural Disaster Responses

Computer vision algorithms are increasingly leveraged to accelerate geospatial analysis for disaster response and recovery. As the diversity of remote sensing imagery grows with optical, SAR, and other modalities, a perquisite for analytics is cross-modal image registration. There is a high potential to harness computer vision for this pre-processing requirement toward enabling downstream analytics such as heterogeneous change detection, automated feature extraction, and data fusion. Advancement in these areas has the potential to simplify data wrangling tasks and further accelerate disaster response timelines. The SpaceNet 9 challenge (launching in mid-2024) focuses on addressing the cross-modal image registration problem and demonstrating the utility of such modules on earthquake impacted scenarios. This paper describes the motivation for the SpaceNet 9 and provides a first overview of the dataset, the baseline algorithm, and implications for seeking cross-modal image registration in Earth observation. Code is available at https://github.com/SpaceNetChallenge/SpaceNet9.

Hansch, Ronny↗

DOE OSTI2021

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore (Computional Evaluation of Thermal Response of Open-Cell Foam with Circular Pore)

The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Here, two-dimensional, steady state analyses were performed on unit cells with centered, circular pores using a second order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data.

36 MATERIALS SCIENCE↗