Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “variable selection”

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 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Identification of Metal Stresses in Arabidopsis thaliana Using Hyperspectral Reflectance Imaging

Industrial accidents, such as the Fukushima and Chernobyl disasters, release harmful chemicals into the environment, covering large geographical areas. Natural flora may serve as biological sensors for detecting metal contamination, such as cesium. Spectral detection of plant stresses typically employs a few select wavelengths and often cannot distinguish between different stress phenotypes. In this study, we apply hyperspectral reflectance imaging in the visible and near-infrared along with multivariate curve resolution (MCR) analysis to identify unique spectral signatures of three stresses in Arabidopsis thaliana : salt, copper, and cesium. While all stress conditions result in common stress physiology, hyperspectral reflectance imaging and MCR analysis produced unique spectral signatures that enabled classification of each stress. As the level of potassium was previously shown to affect cesium stress in plants, the response of A. thaliana to cesium stress under variable levels of potassium was also investigated. Increased levels of potassium reduced the spectral response of A. thaliana to cesium and prevented changes to chloroplast cellular organization. While metal stress mechanisms may vary under different environmental conditions, this study demonstrates that hyperspectral reflectance imaging with MCR analysis can distinguish metal stress phenotypes, providing the potential to detect metal contamination across large geographical areas.

multivariate curve resolution↗
DOE OSTI2024

Model and remote-sensing-guided experimental design and hypothesis generation for monitoring snow-soil–plant interactions

In this study, we develop a machine-learning (ML)-enabled strategy for selecting hillslope-scale ecohydrological monitoring sites within snow-dominated mountainous watersheds, with a particular focus on snow-soil–plant interactions. Data layers rely on spatial data layers from both remote sensing and hydrological model simulations. Specifically, a Landsat-based foresummer drought sensitivity index is used to define the dependency of the annual peak plant productivity on the Palmer drought severity index in the early growing season. Hydrological simulations provide the spatiotemporal dynamics of near-surface soil moisture and snow depth. In this framework, a regression analysis identifies the key hydrological variables relevant to the spatial heterogeneity of drought sensitivity. We then apply unsupervised clustering to these key variables, using the Gaussian mixture model, to group hillslopes into several zones that have divergent relationships regarding soil moisture, snow dynamics, and drought sensitivity. Using the datasets collected in the East River Watershed (Crested Butte, Colorado, United States), results show that drought sensitivity is significantly correlated with model-derived soil moisture and snow-free timing over space and time. The relationship is, however, non-linear, such that the correlation decreases above a threshold elevation and in a heavy snow year due to large snowpacks, lateral flow, and soil storage limitations. Clustering is then able to define the zones that have high or low sensitivity to drought, as well as the mid-elevation regions where sensitivity is associated with the topographic aspect and net potential radiation. In addition, the algorithm identifies the most representative hillslopes with road/trail access within each zone for installing monitoring sites. Our method also aims to significantly increase the use of ML and model-simulation results to guide critical zone and watershed monitoring activities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Selection of Sampling and Surrogate Modeling Methods for State-Point Evaluations of an AGN-201M Reactor

Nuclear reactor digital twins (DTs) have been proposed for use as a safeguards technology to efficiently monitor new and novel reactors as they come online. A safeguards DT needs to be capable of detecting misuse and diversion as they occur, requiring physics models to be accurate and efficient. Mathematical surrogate models are capable of achieving the necessary efficiency and can largely maintain the accuracy of higher-order models given a quality training sample. The Multiphysics Object-Oriented Simulation Environment (MOOSE) code framework is specifically equipped to generate training samples and create surrogate models using full-order reactor physics models. Utilizing an operational AGN-201M reactor’s specifications, two surrogate types were trained on samples of variable size, and using Cartesian products, Latin hypercube sampling, and quadrature sampling, each was compared and evaluated on accuracy when compared to a full-order Monte Carlo model. Both surrogate types were able to capture reactivity changes within 0.05 $ of the Monte Carlo model while reducing the computation costs by eight orders of magnitude.

MOOSE↗
DOE OSTI2023

Estimating and Calibrating DER Model Parameters Using Levenberg–Marquardt Algorithm in Renewable Rich Power Grid

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on the accurate estimation and parameter calibration of DER_A, a recently proposed aggregated IBDER model. In particular, we focus on the parameters of the reactive power–voltage regulation module. We formulate the problem of parameter tuning as a non-linear least square minimization problem and solve it using the Levenberg–Marquardt (LM) method. The LM method is primarily chosen due to its flexibility in adaptively selecting between the steepest descent and Gauss–Newton methods through a damping parameter. The LM approach is used to minimize the error between the actual measurements and the estimated response of the model. Further, the computational challenges posed by the numerical calculation of the Jacobian are tackled using a quasi-Newton root-finding approach. The proposed method is validated on a real feeder model in the northeastern part of the United States. The feeder is modeled in OpenDSS and the measurements thus obtained are fed to the DER_A model for calibration. The simulation results indicate that our approach is able to successfully calibrate the relevant model parameters quickly and with high accuracy, with a total sum of square error of 3.57 × 10 –7 .

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

On approaches to analyze the sensitivity of simulated hydrologic fluxes to model parameters in the community land model

Here, effective sensitivity analysis approaches are needed to identify important parameters or factors and their uncertainties in complex Earth system models composed of multi-phase multi-component phenomena and multiple biogeophysical-biogeochemical processes. In this study, the impacts of 10 hydrologic parameters in the Community Land Model on simulations of runoff and latent heat flux are evaluated using data from a watershed. Different metrics, including residual statistics, the Nash-Sutcliffe coefficient, and log mean square error, are used as alternative measures of the deviations between the simulated and field observed values. Four sensitivity analysis (SA) approaches, including analysis of variance based on the generalized linear model, generalized cross validation based on the multivariate adaptive regression splines model, standardized regression coefficients based on a linear regression model, and analysis of variance based on support vector machine, are investigated. Results suggest that these approaches show consistent measurement of the impacts of major hydrologic parameters on response variables, but with differences in the relative contributions, particularly for the secondary parameters. The convergence behaviors of the SA with respect to the number of sampling points are also examined with different combinations of input parameter sets and output response variables and their alternative metrics. This study helps identify the optimal SA approach, provides guidance for the calibration of the Community Land Model parameters to improve the model simulations of land surface fluxes, and approximates the magnitudes to be adjusted in the parameter values during parametric model optimization.

58 GEOSCIENCES↗
DOE OSTI2024

Low flow characteristics for regulated and unregulated streams in North Carolina and prediction using climate signals

In this work, low flow statistics of regulated and unregulated streams in the state of North Carolina were updated with streamflow data through 2019. About 22% of the streams considered show a significant downward trend, but considerable low-frequency variability confounding trends. The relationship between regional index time series of groundwater-depth low flow and the Atlantic Multidecadal Oscillation (AMO) was examined to determine whether low-frequency climate modes can account for the long-term pattern in low flows. Consequently, a significant correlation was found between AMO and groundwater-depth low flow, such that positive AMO is associated with lower groundwater-depth low flow and vice versa, particularly for the Piedmont region. Predictive equations for annual low flows at the ecoregion level shows that springtime average streamflow and AMO were selected as the primary predictors of low flow for coastal and Piedmont regions, whereas springtime average streamflow and the November–December–January average Oceanic Niño Index were used as the primary predictors for the mountain region. The relative root mean square error (RMSE) of the disaggregated predictions to US Geologic Survey gauge locations was <23% at 79% of the stations, between 24% and 43% at 10% of the stations, and greater than 44% at 1% of the stations. The remaining 10% of stations showed large RMSEs. This latter percentage is characterized by smaller drainage basins and intermittent flows, suggesting the prediction models are not applicable to drainage basins smaller than roughly 20 square km and intermittent streams.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Rainfall erosivity in Slovenia: Sensitivity estimation and trend detection

Highlights: • Rainfall erosivity for 10 rainfall stations located in Slovenia was evaluated. • Rainfall erosivity trends are mostly positive while mostly statistically insignificant. • The maximum rainfall erosivity is obtained under Alpine climate. • Monthly rainfall erosivity was computed. • Sensitivity analyses were carried out. Slovenia is one of the EU countries with the largest values and largest amounts of variability in rainfall erosivity, with maximum annual values exceeding 10,000 MJ mm ha{sup -1} h{sup -1} yr{sup -1}. Five-minute rainfall data was analysed from 10 Slovenian rainfall stations with data-length availability longer than 25 years with a maximum data length of 69 years and a total data-station length equal to 443 years. Trends in the rainfall erosivity R-factor were detected for four different sub-samples using monthly, half-year, and annual rainfall erosivity values. The results indicate that rainfall erosivity trends for the selected Slovenian stations are mostly statistically insignificant, with the selected significance level of 0.05. However, a larger share of identified trends are positive than negative. The maximum annual rainfall erosivity values were obtained for one specific mountain station. Furthermore, a sensitivity analysis regarding the rainfall erosivity factor R calculation showed that the rainfall threshold parameter (12.7 mm) that is used to remove the small-magnitude rainfall events in order to reduce the computational burden can attribute up to 10% of the average annual R-values in cases where this threshold is not used. Other parameters have, on average, a smaller impact on the calculated rainfall erosivity. Furthermore, the application of local kinetic energy equations resulted in, on average, about 20% higher annual rainfall erosivity values compared to the equation that is proposed by the Revised Universal Soil Loss Equation (RUSLE) manual and was not developed specifically for this region.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

BINARY CEPHEIDS: SEPARATIONS AND MASS RATIOS IN 5 M {sub ☉} BINARIES

Deriving the distribution of binary parameters for a particular class of stars over the full range of orbital separations usually requires the combination of results from many different observing techniques (radial velocities, interferometry, astrometry, photometry, direct imaging), each with selection biases. However, Cepheids—cool, evolved stars of ∼5 M {sub ☉}—are a special case because ultraviolet (UV) spectra will immediately reveal any companion star hotter than early type A, regardless of the orbital separation. We have used International Ultraviolet Explorer UV spectra of a complete sample of all 76 Cepheids brighter than V = 8 to create a list of all 18 Cepheids with companions more massive than 2.0 M {sub ☉}. Orbital periods of many of these binaries are available from radial-velocity studies, or can be estimated for longer-period systems from detected velocity variability. In an imaging survey with the Hubble Space Telescope Wide Field Camera 3, we resolved three of the companions (those of η Aql, S Nor, and V659 Cen), allowing us to make estimates of the periods out to the long-period end of the distribution. Combining these separations with orbital data in the literature, we derive an unbiased distribution of binary separations, orbital periods, and mass ratios. The distribution of orbital periods shows that the 5 M {sub ☉} binaries have systematically shorter periods than do 1 M {sub ☉} stars. Our data also suggest that the distribution of mass ratios depends on both binary separation and system multiplicity. The distribution of mass ratios as a function of orbital separation, however, does not depend on whether a system is a binary or a triple.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Optical and X-ray GRB Fundamental Planes as cosmological distance indicators

ABSTRACT Gamma-ray bursts (GRBs), can be employed as standardized candles, extending the distance ladder beyond Type Ia supernovae (SNe Ia, z = 2.26). We standardize GRBs using the three-dimensional (3D) Fundamental Plane relation (the Dainotti relation) among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. Combining SNe Ia and GRBs, we constrain ΩM = 0.299 ± 0.009 assuming a flat Λ cold dark matter (ΛCDM) cosmology with and without correcting GRBs for selection biases and redshift evolution. Using a 3D optical Dainotti correlation, we find this sample is as efficacious in the determination of ΩM as the X-ray sample. We trimmed our GRB samples to achieve tighter planes to simulate additional GRBs. We determined how many GRBs are needed as stand-alone probes to achieve a comparable precision on ΩM to the one obtained by SNe Ia only. We reach the same error measurements derived using SNe Ia in 2011 and 2014 with 142 and 284 simulated optical GRBs, respectively, considering the error bars on the variables halved. These error limits will be reached in 2038 and in 2047, respectively. Using a doubled sample (obtained by future machine learning approaches allowing a light-curve reconstruction and the estimates of GRB redshifts when z is unknown) compared to the current sample, with error bars halved we will reach the same precision as SNe Ia in 2011 and 2014, now and in 2026, respectively. If we consider the current SNe precision, this will be reached with 390 optical GRBs by 2054.

Dainotti, M. G.↗
DOE OSTI2023

Chaconne: A Statistical Approach to Nonlocal Compression for Supervised Learning, Semi-Supervised Learning, and Anomaly Detection

This project developed a novel statistical understanding of compression analytics (CA), which has challenged and clarified some core assumptions about CA, and enabled the development of novel techniques that address vital challenges of national security. Specifically, this project has yielded the development of novel capabilities including 1. Principled metrics for model selection in CA, 2. Techniques for deriving/applying optimal classification rules and decision theory to supervised CA, including how to properly handle class imbalance and differing costs of misclassification, 3. Two techniques for handling nonlocal information in CA, 4. A novel technique for unsupervised CA that is agnostic with regard to the underlying compression algorithm, 5. A framework for semisupervised CA when a small number of labels are known in an otherwise large unlabeled dataset. 6. The academic alliance component of this project has focused on the development of a novel exemplar-based Bayesian technique for estimating variable length Markov models (closely related to PPM [prediction by partial matching] compression techniques). We have developed examples illustrating the application of our work to text, video, genetic sequences, and unstructured cybersecurity log files.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Time Evolution and Diurnal Variability of the Parametric Sensitivity of Turbine-Height Winds in the MYNN-EDMF Parameterization

The Mellor-Yamada-Nakanishi-Niino (MYNN) parameterization applied in the Weather Research and Forecasting (WRF) model has been augmented to include the Eddy-Diffusion Mass-Flux (EDMF) approach to better represent transport by boundary-layer eddies. This change includes the addition of new parameters associated with convective updrafts and boundary-layer clouds. These additions lead to new parametric sensitivities in the hub-height wind speed compared to simulations using the standard MYNN parameterization that were explored previously. This work builds on efforts focused on WRF’s MYNN parameterization by examining the sensitivity of hub-height wind speed to parameters in the MYNN-EDMF parameterization as a function of simulation lead time. Summer and winter periods were selected from the second Wind Forecast Improvement Project (WFIP2). Five sets of simulations were completed for each season, with lead times ranging from 2 to 6 days. The results show that the sensitivity to the new parameters associated with the EDMF scheme is generally small compared to other parameters, with the largest impact in convective boundary layers. The spread in the perturbed parameter ensembles was found to grow quickly over the first 8 to 19 hours in the summer simulations and 17 to 24 hours in the winter simulations with little change after that, regardless of the simulation length. A strong diurnal cycle in the parameter sensitivity was also found associated with changes in the atmospheric stability, as well as an increase in the sensitivity to the entrainment parameter used in the EDMF parameterization that is associated with increasing fractional areas covered by plumes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Accelerating rejection-based simulation of biochemical reactions with bounded acceptance probability

Stochastic simulation of large biochemical reaction networks is often computationally expensive due to the disparate reaction rates and high variability of population of chemical species. An approach to accelerate the simulation is to allow multiple reaction firings before performing update by assuming that reaction propensities are changing of a negligible amount during a time interval. Species with small population in the firings of fast reactions significantly affect both performance and accuracy of this simulation approach. It is even worse when these small population species are involved in a large number of reactions. We present in this paper a new approximate algorithm to cope with this problem. It is based on bounding the acceptance probability of a reaction selected by the exact rejection-based simulation algorithm, which employs propensity bounds of reactions and the rejection-based mechanism to select next reaction firings. The reaction is ensured to be selected to fire with an acceptance rate greater than a predefined probability in which the selection becomes exact if the probability is set to one. Our new algorithm improves the computational cost for selecting the next reaction firing and reduces the updating the propensities of reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

On the accuracy of Hipparcos using binary stars as a calibration tool

Stellar binary systems, specifically those that present the most accurate available orbital elements, are a reliable tool to test the accuracy of astrometric observations. We selected all 35 binaries with these characteristics. Our objective is to provide standard uncertainties for the positions and parallaxes measured by Hipparcos relative to this trustworthy set, as well as to check supposed correlations between several parameters (measurement residuals, positions, magnitudes, and parallaxes). In addition, using the high-confidence subset of visual–spectroscopic binaries, we implemented a validation test of the Hipparcos trigonometric parallaxes of binary systems that allowed the evaluation of their reliability. Standard and non-standard statistical analysis techniques were applied in order to achieve well-founded conclusions. In particular, errors-in-variables models such as the total least-squares method were used to validate Hipparcos parallaxes by comparison with those obtained directly from the orbital elements. Previously, we executed Thompson's τ technique in order to detect suspected outliers in the data. Furthermore, several statistical hypothesis tests were carried out to verify if our results were statistically significant. A statistically significant trend indicating larger Hipparcos angular separations with respect to the reference values in 5.2 ± 1.4 mas was found at the 10{sup −8} significance level. Uncertainties in the polar coordinates θ and ρ of 1.°8 and 6.3 mas, respectively, were estimated for the Hipparcos observations of binary systems. We also verified that the parallaxes of binary systems measured in this mission are absolutely compatible with the set of orbital parallaxes obtained from the most accurate orbits at least at the 95% confidence level. This methodology allows us to better estimate the accuracy of Hipparcos observations of binary systems. Indeed, further application to the data collected by Gaia should yield a standard procedure to compare both data sets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

REEXAMINING THE LITHIUM DEPLETION BOUNDARY IN THE PLEIADES AND THE INFERRED AGE OF THE CLUSTER

Moderate-dispersion (R ∼ 5400), optical spectroscopy of seven brown dwarf candidate members of the Pleiades was obtained using the Echellette Spectrograph and Imager on the Keck II telescope. The proper motion and photometrically selected sample lies on the single-star main sequence of the cluster and effectively brackets the established lithium depletion boundary. The brown dwarf candidates range in spectral type from M6 to M7, implying effective temperatures between ∼2800 and 2650 K. All sources exhibit Hα emission, consistent with enhanced chromospheric activity that is expected for young, very low-mass stars and brown dwarfs. Li i λ6708 absorption is confidently detected in the photospheres of two of the seven sources. A revised lithium depletion boundary is established in the near-infrared where the effects of extinction and variability are minimized. This lithium depletion edge occurs near K{sub o} = 14.45 or M{sub K} = 8.78 mag (UKIRT Infrared Deep Sky Survey), assuming the most accurate and precise distance estimate for the cluster of 136.2 pc. From recent theoretical evolutionary models, a revised age of τ = 112 ± 5 Myr is determined for the Pleiades. Accounting for the effects of magnetic activity on the photospheres of these very low-mass stars and brown dwarfs, however, would imply an even younger age for the cluster of ∼100 Myr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

SU-E-T-225: It Is Necessary to Contouring the Brainstem On MRI Images in Radiotherapy of Head and Neck Cancer

Purpose: To analyze the error in contouring the brainstem for patients with head and neck cancer who underwent radiotherapy based on computed tomography (CT) and magnetic resonance (MR) images. Methods: 20 brain tumor and 17 nasopharyngeal cancer patients were randomly selected. Each patient underwent MR and CT scanning. For each patient, one observer contoured the brainstem on CT and MR images for 10 times, and 10 observers from five centers delineated the brainstem on CT and MR images only one time. The inter- and intra-observers volume and outline variations were compared. Results: The volumes of brainstem contoured by inter- and intra-observers on CT and MR images were similar (p>0.05). The reproducibility of contouring brainstem on MR images was better than that on CT images (p<0.05) for both inter- and intra-observer variability. The inter- and intra-observer for contouring on CT images reached mean values of 0.81±0.05 (p>0.05) and of 0.85±0.05 (p>0.05), respectively, while on MR images these respective values were 0.90±0.05 (p>0.05) and 0.92±0.04 (p>0.05). Conclusion: Contouring the brainstem on MR images was more accurate and reproducible than that on CT images. Precise information might be more helpful for protecting the brainstem radiation injury the patients whose lesion were closed to brainstem.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Improving Limit Surface Search Algorithms in RAVEN Using Acceleration Schemes: Level II Milestone

The RAVEN code is becoming a comprehensive tool to perform Probabilistic Risk Assessment (PRA); Uncertainty Quantification (UQ) and Propagation; and Verification and Validation (V&V). The RAVEN code is being developed to support the Risk-Informed Safety Margin Characterization (RISMC) pathway by developing an advanced set of methodologies and algorithms for use in advanced risk analysis. The RISMC approach uses system simulator codes applied to stochastic analysis tools. The fundamental idea behind this coupling approach to perturb (by employing sampling strategies) timing and sequencing of events, internal parameters of the system codes (i.e., uncertain parameters of the physics model) and initial conditions to estimate values ranges and associated probabilities of figures of merit of interest for engineering and safety (e.g. core damage probability, etc.). This approach applied to complex systems such as nuclear power plants requires performing a series of computationally expensive simulation runs. The large computational burden is caused by the large set of (uncertain) parameters characterizing those systems. Consequently, exploring the uncertain/parametric domain, with a good level of confidence, is generally not affordable, considering the limited computational resources that are currently available. In addition, the recent tendency to develop newer tools, characterized by higher accuracy and larger computational resources (if compared with the presently used legacy codes, that have been developed decades ago), has made this issue even more compelling. In order to overcome to these limitations, the strategy for the exploration of the uncertain/parametric space needs to use at best the computational resources focusing the computational effort in those regions of the uncertain/parametric space that are “interesting” (e.g., risk-significant regions of the input space) with respect the targeted Figures Of Merit (FOM): for example, the failure of the system, subject of the analysis. These methodologies are named, in the RAVEN environment, adaptive sampling strategies. These methodologies infer system responses from surrogate models constructed from already existing samples (produced using high fidelity simulations) and suggest the most relevant location (coordinate in the input space) of the next sampling point to be explored in the uncertain/parametric domain. When using those methodologies, it is possible to understand features of the system response with a small number of carefully selected samples. This report focuses on the development and improvement of the limit surface search. The limit surface is an important concept in system reliability analysis. Without going into the details, which will be covered later in the report, the limit surface could be briefly described as an hyper-surface in the system uncertainty/parametric space separating the regions leading to a prescribed system outcome. For example, if the uncertainty/parametric space is the one generated by the reactor power level and the duration of the batteries, the system is a nuclear power plant and the system outcome discriminating variable is the clad failure in a station blackout scenario, then the limit surface separates the combinations of reactor power level and battery duration that lead to clad failure from the ones that do not.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.

42 ENGINEERING↗