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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Building and Executing Aggressive Research Plans in a Large National Laboratory Consortium: Insights from the Co-Optimization of Fuels and Engines Initiative

This report describes lessons learned in the establishment, execution and termination of a large, multi-institutional consortium, derived from the Co-Optimization of Fuels and Engines experience. The decision to form a consortium comes with benefits (in advancing challenging multidisciplinary research) and costs (in time and additional management funds). Once the decision is made, key elements to a strong start include establishing a shared vision and goals; engaging an experienced project manager early; instituting feedback and oversight mechanisms to ensure relevance, strong performance, and situational awareness. Once a consortium is up and running, DOE and leadership should strike the right balance between competition and collaboration; foster an environment that builds trust; and adjust the organizational structure as needed to maintain collaboration. Finally, DOE and the labs can plan effectively for a smooth transition as a consortium winds down. This report provides some additional lessons and details on these lessons that we hope future DOE and lab leaders will find useful as they contemplate standing up new consortia.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

Hydrated Metal and Metal-Nitrate Complexes in Water: Full Lanthanide(III) Series plus Miscellaneous Metal Ions

This is a dataset of hydrated metal complexes and metal–nitrate hydrated complexes intended for public use, reproducibility, and downstream structural analysis. A key feature is coverage across the full lanthanide(III) series (La–Lu), enabling systematic comparisons of coordination motifs and bonding trends across the entire lanthanide sequence. In addition to the lanthanides, the dataset also includes other metal ions such as UO2(VI), Fe(II), and Fe(III). The dataset provides optimized geometries for hydrated and nitrate-containing hydrated complexes, together with representative ab initio molecular dynamics (AIMD) trajectories saved in standard XYZ formats. The accompanying NWChem input decks enable reproduction of the reported calculations and provide a starting point for extending the simulations to related coordination environments. Computationally, DFT calculations employ the B3LYP functional with DFT-D3BJ dispersion corrections and a COSMO continuum solvent model (dielectric constant 78.4) to represent solvation beyond the explicitly treated first hydration shell. AIMD simulations are performed with the NWChem qmd module at 298 K, integrating nuclear motion with the velocity-Verlet algorithm and controlling temperature using a Nosé–Hoover thermostat. Trajectories are approximately 4.8 ps in length and are used primarily to assess short-time stability of candidate coordination motifs, including (for lanthanides) differences between 8- versus 9-water coordination and comparisons between nitrate-bound and nitrate-free hydrated complexes.

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗
NASA NTRS1991

Flow analysis and design optimization methods for nozzle afterbody of a hypersonic vehicle

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the three dimensional Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Argon. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. In the second phase of this project, the Aerodynamic Design Optimization with Sensitivity analysis (ADOS) was developed. Pre and post optimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Baysal, Oktay↗
NASA NTRSDate not supplied

Baseline Medical System Translation for the Impact Medical Database

NASA has developed a new evidence-based data-driven probabilistic risk assessment and tradespace analysis tool as a successor to the Integrated Medical Model (IMM). This updated decision support tool is known as IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces). Whereas IMM focuses on the resources and risks associated with International Space Station (ISS) and Low Earth Orbit (LEO) missions, IMPACT estimates the frequency and consequences of medical conditions that might arise during exploration missions. One of the services offered by IMM is a series of generic or baseline medical systems associated with typical mission types or DRMs (Design Reference Missions), such that requestors may prioritize questions pertaining to the mission itself over the medical supplies indicated by the model outputs for that DRM. In a mission focused request, the appropriate baseline medical system is used in place of a prepared or optimized medical kit. In preparation, an effort was undertaken to create baseline systems of medical resources within IMPACT suitable for typical DRMs. Using an existing baseline medical system within IMM’s Integrated Medical Evidence Database (iMED) as a starting point, the resources found within the medical kit were compared to and substituted for equivalent resources available within the IMPACT MD (Medical Database). In consultation with clinicians with knowledge of IMPACT’s MD, each resource was matched as closely as possible to a similarly purposed resource in IMPACT, seeking to preserve the treatment capabilities and procedures offered by the IMM medical system while reconciling the differences in modeled resources and medical conditions between the models. To demonstrate the efficacy of this work, a prototype ISS medical system in IMPACT was translated from the baseline used in the IMM. The appropriate medical system was then run through its associated medical model to compare and validate the resultant risks and risk mitigation provided by each baseline ISS medical kit.

S Schwartz↗
DOE OSTI2020

Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulation

In this work we address the problem of accelerating complex power-grid simulation through machine learning ( ML). Specifically, we develop a framework, Smart-PGSim,which generates multitask-learning (MTL) neural network (NN)models to predict the initial values of variables critical to the problem convergence. MTL models allow information sharing when predicting multiple dependent variables while including customized layers to predict individual variables. We show that,to achieve the required accuracy, it is paramount to embed domain-specific constraints derived from the specific power-grid components in the MTL model. Smart-PGSim then employs the predicted initial values as a high-quality initial condition for the power-grid numerical solver (warm start), resulting in both higher performance compared to state-of-the-art solutions while maintaining the required accuracy. Smart-PGSim brings 2.60×speedup on average (up to 3.28×) computed over 10,000 problems, without losing solution optimality.

machine learning, neural networks↗
NASA NTRS1989

An algorithm for the solution of dynamic linear programs

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

Psiaki, Mark L.↗
DOE OSTI2021

Monte Carlo Analysis of the Performance of the ITER Diagnostic Residual Gas Analyzer

The composition of exhausted gas is a key parameter in long-pulse plasma fusion experiments, and its evolution shall be monitored at timescales relevant to plasma dynamics and plasma-wall interactions. A diagnostic residual gas analyzer (DRGA) is a multisensor instrument particularly suited to these studies, and ITER will adopt DRGAs in the equatorial and in the divertor tokamak regions. In this work, we have revisited the design of the ITER divertor DRGA through simple vacuum analytical considerations supported by simulations conducted with Molflow+, a test particle Monte Carlo (TPMC) simulation code commonly used in the particle accelerator community. Here, starting with recommendations on the manufacturing of the vacuum piping of the DRGA, this work is followed by a complete vacuum characterization of the diagnostic vacuum setup (pressure profiles at base pressure and during sampling, orifice diameter, and length optimization), and finally, the in-vessel residence time of the most important gas species is simulated. These studies have allowed us to give insights into some experimental results recently found on the prototype DRGA installed in the Wendelstein W7-X stellarator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Software Defined Architectures for Portability and Performance

The Software Defined Architectures for Portability and Performance (SODAPOP) project developed a co-design framework to partition and map converged applications on specialized heterogeneous architectures. We started from key domain applications that combine scientific simulation with data analytics and machine learning as drivers to integrate our framework. The framework includes high-level compilers that interfaces with high-level programming frameworks, domain-specific optimization passes, and hardware-oriented optimizations. The framework leverages hardware generators to enable specialization and facilitate exploration of custom system designs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Post-Fragmentation Whole Genome Amplification-Based Method

This innovation is derived from a proprietary amplification scheme that is based upon random fragmentation of the genome into a series of short, overlapping templates. The resulting shorter DNA strands (<400 bp) constitute a library of DNA fragments with defined 3 and 5 termini. Specific primers to these termini are then used to isothermally amplify this library into potentially unlimited quantities that can be used immediately for multiple downstream applications including gel eletrophoresis, quantitative polymerase chain reaction (QPCR), comparative genomic hybridization microarray, SNP analysis, and sequencing. The standard reaction can be performed with minimal hands-on time, and can produce amplified DNA in as little as three hours. Post-fragmentation whole genome amplification-based technology provides a robust and accurate method of amplifying femtogram levels of starting material into microgram yields with no detectable allele bias. The amplified DNA also facilitates the preservation of samples (spacecraft samples) by amplifying scarce amounts of template DNA into microgram concentrations in just a few hours. Based on further optimization of this technology, this could be a feasible technology to use in sample preservation for potential future sample return missions. The research and technology development described here can be pivotal in dealing with backward/forward biological contamination from planetary missions. Such efforts rely heavily on an increasing understanding of the burden and diversity of microorganisms present on spacecraft surfaces throughout assembly and testing. The development and implementation of these technologies could significantly improve the comprehensiveness and resolving power of spacecraft-associated microbial population censuses, and are important to the continued evolution and advancement of planetary protection capabilities. Current molecular procedures for assaying spacecraft-associated microbial burden and diversity have inherent sample loss issues at practically every step, particularly nucleic acid extraction. In engineering a molecular means of amplifying nucleic acids directly from single cells in their native state within the sample matrix, this innovation has circumvented entirely the need for DNA extraction regimes in the sample processing scheme.

Benardini, James↗
DOE OSTI2023

Coolant Pump Predictive Data Analytics from Signatures Generated by the Recursive Short Time Fast Fourier Transform

Although a nuclear reactor is a hostile environment for sensors and signal transmissions, the reactor core is amenable to acoustic communication. An acoustic measurement infrastructure installed at the Advanced Test Reactor (ATR) nozzle trench area records acoustic signals that can capture reactor operating states. The distinct states produce unique signatures that can be identified and tracked using data processing and data analytics. The infrastructure relies on acoustic transmission through ATR in-pile structural components, piping, and coolant that transmit acoustically modified signals generated by the coolant pumps. This paper will discuss results from using the Recursive Short Time Fast Fourier Transform (RSTFFT) technique used to process acoustic signals and provide signatures that are identified and monitored by analytics. The RSTFFT is applied to ATR data to understand the vibration levels and signatures for different operating regimes as displayed by the spectrogram. The combination of coolant pumps for normal and high-power operation generate unique signatures. These acoustic signatures are used to develop machine learning approaches to automatically classify operating regimes. Two machine-learning models, Support Vector Machines and Linear Discriminant Analysis, were developed to classify two event classes. Class 1 is a normal steady-state operation, and Class 2 is any event that is due to start up, shut down, or other actions. Both types of machine learning models had over a 96% prediction accuracy for the two classes. These results lay the foundation for predictive analytic frameworks that can be leveraged by ATR to optimize operations and maintenance.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2014

Quantification of In-flight Physical Changes: Anthropometry and Neutral Body Posture

Currently, NASA does not have sufficient in-flight anthropometric data gathered to assess the impact of physical body shape and size changes on suit sizing. For developing future planetary and reduced gravity suits, NASA needs to quantify the impacts of microgravity on anthropometry, body posture, and neutral body postures (NBP) to ensure optimal crew performance, fit, and comfort. To obtain these impacts, anthropometric data, circumference, length, height, breadth, and depth for body segments (i.e. chest, waist, bicep, thigh, calf) from astronauts for pre, in-, and postflight conditions needs to be collected. Once this data has been collected, a comparison between pre, in-, and postflight anthropometric values will be analyzed, yielding microgravity factors. The NBP will be used to determined body posture (joint angle) changes between subjects throughout the duration of a mission. Data collection, starting with Increments 37/38, is still in progress with the completion of 3 out of 12 subjects. NASA suit engineers and NASA's Extravehicular Activity (EVA) Project Office have identified that suit fit in microgravity could become an issue. It has been noted that crewmembers often need to adjust their suit sizing once they are in orbit. This adjustment could be due to microgravity effects on anthropometry and postural changes, and is necessary to ensure optimal crew performance, fit, and comfort in space. To date, the only data collected to determine the effects of microgravity on physical human changes have been during Skylab, STS-57, and a recent HRP study on seated height changes due to spinal elongation (Spinal Elongation, Master Task List [MTL] #221). The Skylab and the STS-57 studies found that there is a distinct neutral body posture (NBP) based on photographs. The still photographs showed that there is a distinguishable posture with the arms raised and the shoulder abducted; and, in addition, the knees were flexed with noticeable hip flexion and the foot plantar flexed [1,2]. This is the one standard set of body joint angles for a NBP in microgravity. A recent simulated microgravity NBP study [3] has shown an individual variability and inconsistencies in defining NBP. This variation may be influenced by spinal growth, the type of suit fit, and other potential anthropometry factors such as spinal curvature, age, and gender. The variation aspect of this essential data is required for all kinds of space device designs (e.g. suits, habitat, mobility aids, etc.). The method proposed considers the dynamic nature of body movement and will use a measurement technique to continually monitor posture and develop a probability likelihood of the natural posture and how the NBP postures are affected by anthropometry. Additionally, Skylab studies found that crewmembers experienced a stature growth of up to 3%. The data included 3 crewmembers that showed that there is a bi-phasic stature growth once the crew enters into weightlessness. However, the Spinal Elongation study identified that the crewmembers could experience about a 6% growth in seated height and a 3% stature growth, when exposed to microgravity. The results prove that not all anthropometric measurements have the same microgravity percent growth factor. For EVA and suit engineers to properly update the sizing protocol for microgravity, they need additional anthropometric data from space missions. Hence, this study is aimed to gather additional in-flight anthropometric measurements, such as length, depth, breadth, and circumference, to determine the changes to body shape and size due to microgravity effects. It is anticipated that by recording the potential changes to body shape and size, a better suit sizing protocol will be developed for ISS and other space missions. In essence, this study will help NASA quantify the impacts of microgravity on anthropometry to ensure optimal crew performance, fit, and comfort. This study will use simplistic data collection techniques, 3D laser scanning, digital still, and video data, and perform photogrammetric analyses to determine the changes that occur to the body shape, size, and NBP when exposed to a microgravity environment.

Young, K. S.↗
NASA NTRS2005

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

Venter, Gerhard↗
DOE OSTI2021

Heavy Oil Polymer EOR in the Challenging Alaskan Arctic - It Works!

Under co-sponsorship of the US Department of Energy and Hilcorp Alaska LLC the first ever polymer field pilot commenced on 8/28/2018 in the Schrader Bluff heavy oil reservoir at the Milne Point Field on Alaska North Slope (ANS). The primary objective of the pilot is to prove the efficacy of polymer Enhanced Oil Recovery (EOR) to unlock the vast heavy oil resources on ANS. More than two and half years after startup, the polymer injection, supporting laboratory experiments and simulation studies steadily continue. The pilot started injecting hydrolyzed polyacrylamide (HPAM), at a concentration of 1,750 ppm to achieve a target viscosity of 45 cP, into the two horizontal injectors in the flood pattern. Production is monitored in the two horizontal producers. Based on laboratory measurements of polymer viscosity at reservoir conditions, the team decided to reduce polymer concentration to 1,200 ppm since July 2020 in an effort to control injection pressure and optimize polymer utilization. Quality control (QC) on the field ensures uniform polymer solution properties. Representative rock and fluid systems and test conditions are utilized in the corefloods on polymer retention, effect of injection water salinity, polymer loading, and their combinations on oil recovery. A history matched reservoir simulation model for forecasting oil recovery was developed on the basis of all the available field data. Field concerns related to the post-polymer breakthrough impact on flow assurance is addressed via specialized laboratory tests. Notwithstanding early operational disruptions and hydration issues, continuous polymer injection in both injectors has been achieved. To date, 950,000 lbs of polymer or 2 million barrels of polymer solution, equating to 13% of total pore volume (PV), has been placed in the flood pattern, serving as an effective indicator of adequate polymer injectivity. So far, the success of polymer EOR is evident from drastically reduced water cut in the producers, an estimated incremental 1,000 bopd over waterflood, and a favorable polymer utilization of 1.7 lbs/barrel of incremental oil. Polymer breakthrough was observed 26 months after the start of polymer injection. Main observations from corefloods are unusually high polymer retention values in some cases and a positive response to low salinity water. Although the heterogeneity in the flood pattern and exceptionally low water cut pose some challenges, persistent novel and justifiable simulation approaches have resulted in a robust history matched model. Experimental results on produced fluids treatment provide operational guidance for improved oil-water separation and mitigation of heater tube fouling. The ongoing success of the pilot is a key indicator of bringing the team ever closer to meeting the project’s primary objective. The encouraging results of the pilot is one of the drivers that has provided the impetus to apply polymer EOR throughout the Milne Point Field, which would increase oil recovery and extend the economic life of the Trans Alaska Pipeline System. The scientific knowledge, including the many lessons learned from this pilot also has referential value for other potential heavy oil EOR projects throughout the world. The collected data, operational lessons learned, and the overall success of the pilot are summarized in the paper.

None, None↗
DOE OSTI2022

Strong Upper-Plate Heterogeneity at the Hikurangi Subduction Margin (North Island, New Zealand) Imaged by Adjoint Tomography

We use earthquake-based adjoint tomography to invert for three-dimensional structure of the North Island, New Zealand, and the adjacent Hikurangi subduction zone. The study area, having a shallow depth to the plate interface below the North Island, offers a rare opportunity for imaging material properties at an active subduction zone using land-based measurements. Starting from an initial model derived using ray tomography, we perform iterative model updates using spectral element and adjoint simulations to fit waveforms with periods ranging from 4–30 s. We perform 28 model updates using an L-BFGS optimization algorithm, improving data fit and introducing P- and S-wave velocity changes of up to ±30%. Resolution analysis using point spread functions show that our measurements are most sensitive to heterogeneities in the upper 30 km. The most striking velocity changes coincide with areas related to the active Hikurangi subduction zone. Lateral velocity structures in the upper 5 km correlate well with New Zealand geology. Here, the inversion reveals increased along-strike heterogeneity on the margin. In Cook Strait we observe a low-velocity zone interpreted as deep sedimentary basins. In the central North Island, low-velocity anomalies are linked to surface geology, and we relate velocity structures at depth to crustal magmatic activity below the Taupō Volcanic Zone.

58 GEOSCIENCES↗
DOE OSTI2024

Additive Manufacturing for Large Displacement Unmanned Underwater Vehicles (LDUUVs)

Oak Ridge National Laboratory partnered with Anduril Industries to develop the process for adapting large format additive manufacturing for the production of underwater vehicles. This research started by defining and selecting a polymer for the vehicle panels. Coatings were tested at 9000PSI to ensure proper bonding to the 3D printed panels, then tensile tested to understand the mechanical properties. A vehicle panel fairing set was design optimized for the 3D printing process and then 3D printed. Additional work optimized coatings and tested additional reinforcements methods such as fiber weave and z-casting with fiber rods and resin. Finally, a full vehicle was constructed and successfully tested in open water by Anduril.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Electrospinner Upgrades for Nanofiber Production

Electrospinning is an inexpensive method for producing nanofibers, with applications in accelerator targets, air filtration, and biomedicine. This project aims to upgrade and test an existing roll-to-roll electrospinner that is economical for industrial production. Our unit cannot adjust spinneret to collector separation and thus nanofiber diameter (application dependent). The electro-spinneret channel also does not have lateral adjustment capabilities. Lastly, the viscosities of our polymers have not been quantified, which can inform future injector nozzle designs. Modeling was done with Siemens NX CAD, and viscosity was measured using a Brookfield DVE-LV viscometer. A dual scissor lift design was approved, and construction was started, along with channel modifications. Viscosity measurements of polyvinyldimethylformamide were recorded with inconsistent results. Going forward, the scissor lift and channel modifications will be evaluated with our electrospinner. Future viscosity trials must be completed in accordance with testing requirements. The optimization of electrospinner units can make nanofiber production more feasible for many industries.

Black, Niko↗
NASA NTRS1978

Stirling engine design manual

This manual is intended to serve both as an introduction to Stirling engine analysis methods and as a key to the open literature on Stirling engines. Over 800 references are listed and these are cross referenced by date of publication, author and subject. Engine analysis is treated starting from elementary principles and working through cycles analysis. Analysis methodologies are classified as first, second or third order depending upon degree of complexity and probable application; first order for preliminary engine studies, second order for performance prediction and engine optimization, and third order for detailed hardware evaluation and engine research. A few comparisons between theory and experiment are made. A second order design procedure is documented step by step with calculation sheets and a worked out example to follow. Current high power engines are briefly described and a directory of companies and individuals who are active in Stirling engine development is included. Much remains to be done. Some of the more complicated and potentially very useful design procedures are now only referred to. Future support will enable a more thorough job of comparing all available design procedures against experimental data which should soon be available.

Martini, W. R.↗
NASA NTRS1997

Thermal History and Mantle Dynamics of Venus

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished.

Hsui, Albert T.↗