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NASA NTRS2001

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗
NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗
NASA NTRS2013

Comparative Study on High-Order Positivity-preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

WENO↗
NASA NTRS2014

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density ρ and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ρ may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Schemes↗
NASA NTRS2018

High-Order Stabilized Finite Elements on Dynamic Meshes

The development of dynamic mesh capability for turbulent flow simulations using the Streamlined Upwind Petrov-Galerkin (SUPG) discretization is described. The current work extends previous research to include high-order spatial accuracy, including the satisfaction of the discrete geometric conservation law (GCL) on curved elements. Two closely-related schemes are described and the ability of these schemes to satisfy the GCL, while also maintaining temporal accuracy and conservation is assessed. Studies indicate that although one scheme discretizes the time derivative in conservative form, both schemes exhibit temporal conservation errors that decrease according to the expected design order of accuracy. The source of the temporal conservation errors is examined, and it is demonstrated that many finite-volume and finite-element schemes can also be expected to have difficulty strictly satisfying conservation in time. The effects on conservation are examined and, while present in the simulations, are seen to be negligible for the problems considered.

Anderson, W. Kyle↗
DOE OSTI2021

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1], [2], [3], [4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Helicity, spin, and infra-zilch of light: A Lorentz covariant formulation

Highlights: • Spin and orbital parts of angular momentum. • The helicity tensor contains the helicity, spin and infra-zilch currents. • The helicity tensor is a Noether current for a duality-symmetric action. • Symmetry generator for the helicity tensor. • The helicity tensor is conserved in Lorenz gauge. In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by Cameron et al. (2012), including helicity, spin, as well as the spin-flux or infra-zilch. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory. This symmetry transformation generalizes the duality symmetry and includes the symmetry underlying the conservation of the spin part of the angular momentum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Degrees of rate control and AutoDiff-driven direct sensitivity analysis in heterogeneous catalysis

Despite the wide application and benefits of the degree of rate control (DRC) analysis, several details remain argued, particularly about the conservation of DRCs at transient (TR) and steady-state (SS) conditions, especially for complex reaction networks. This work argues that previous proofs about the conservation properties of DRCs have been incomplete, and we provide new mathematical proofs at TR and SS conditions. In addition, we use both analytical (automatic differentiation) and numerical (finite difference) approaches to compute DRCs for the case study of ethane hydrogenolysis (EH) over Pt(111). This work confirms that at both TR and SS conditions, the sum of all DRCs, i.e., sum of the degrees of kinetic (DKRC) and thermodynamic rate control (DTRC), is conserved at zero. At SS conditions, the sum of DKRC is conserved at 1 while the sum of DTRC is conserved at −1. In corroboration of previous works, we show that the DTRC for any adsorbate at SS is equal to the product of the species coverage and a constant. In contrast, at TR conditions, the individual sums of both DTRC and DKRC are not conserved and can be any real number, with potential implications for the novel field of dynamic catalysis. Finally, we show that the conventional finite difference (FD) approach, only useful at SS, is prone to inaccuracy and very sensitive to the value of the differential change applied. The optimal differential value also varies significantly with system and rate definition. Consequently, we describe and illustrate in this work the application of the automatic differentiation (AD) approach for the more accurate determination of DRCs at both TR and SS conditions.

Automatic differentiation↗
DOE OSTI2022

A Moving Embedded Boundary Approach for the Compressible Navier-Stokes Equations in a Block-Structured Adaptive Refinement Framework

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement (SAMR) framework of AMReX [1], [91], [92]. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second-order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds - acoustic (harmonically pulsating sphere), smooth flows (expansion fan created by a receding piston) and flows with shocks (shock-cylinder interaction, shock-wedge interaction, pitching NACA 0012 airfoil and shock-cone interaction). A closed system with moving boundaries - an oscillating piston in a cylinder, showed that the percentage error in mass within the system decreases with refinement, demonstrating that the numerical scheme is conservative with grid refinement, but is not discretely conservative. Viscous test cases involve that of a horizontally moving cylinder at Re = 40, an inline oscillating cylinder at Re = 100, and a transversely oscillating cylinder at Re = 185. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

adaptive refinement↗
DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Evaluating How Climate Adaptation Measures Affect the Interconnected Water‐Energy Resource Systems of the Western United States

Abstract The Western US faces increasing water stress from the impacts of climate change, making it difficult to meet water demands for the region's cities, agriculture, and hydropower generators. Existing literature suggests that climate adaptation measures such as water conservation, cropland retirement, wastewater recycling, and managed aquifer recharge can alleviate some of these challenges. Few analyses, however, compare the relative efficacy and system‐wide effects of these adaptations under different climate projections across the entire Western United States. Here we use a Western US‐wide water systems model to evaluate, by sector and sub‐region, how the widespread implementation of these adaptive measures impacts water demands, water deliveries, and electricity use related to the water system for three different climate projections. We find that wastewater recycling has greater potential to lower unmet indoor water demands than urban indoor water conservation measures. However, when implemented at scale, indoor water conservation reduces electricity use by an average of 683 Terawatt hours while wastewater recycling increases energy use by an average of 721 Terawatt hours, cumulatively from 2020 to 2070. Cropland retirement and aquifer recharge adaptations increase the ability to meet agricultural water demand, increase groundwater storage, and reduce summertime electricity use. While most of these findings are consistent across different climate projections, the benefits of aquifer recharge are sensitive to spatial variation of precipitation. Given the limitations and tradeoffs of each individually, the results suggest that a portfolio of adaptation measures will be needed for a climate‐resilient water and energy future in the Western US. Plain Language Summary The Western US faces increased water stress from the impacts of climate change, making it difficult to meet demands for cities, agriculture, and hydropower facilities. Adaptation measures like water conservation, retiring agricultural lands, recycling wastewater, and storing water underground can address these challenges. However, there is little modeling to understand the impact of these adaptations if they were implemented across the entire Western US while also considering climate change. We use a Western US‐wide water systems model to evaluate how implementing adaptation measures impacts groundwater levels, the ability to meet water demands, and electricity use related to water in three different possible climate futures. We find that recycling wastewater to drinking water standards does a better job of meeting urban water demands than water conservation measures. However, indoor water conservation reduces energy use for water while recycling wastewater increases energy use for water. Retiring agricultural lands and storing water underground both increase the ability to meet agricultural water demands, increase underground water storage, and reduce summertime energy use. No adaptation measures provides benefits across every metric we track. Therefore, multiple adaptation measures will likely be needed to achieve a climate‐resilient future for energy and water in the Western US. Key Points Water‐related climate change adaptations have different benefits and tradeoffs for interconnected water‐energy systems in the Western U.S. Wastewater recycling most increases urban water coverage, but has a significant tradeoff in the form of greater electricity use Cropland retirement and aquifer recharge benefit water and electricity systems most in the summer when those systems are most stressed

Singhal, A↗
DOE OSTI2023

Multiple highly expressed phospho enol pyruvate carboxylase genes have divergent enzyme kinetic properties in two C4 grasses

Abstract Background and Aims Phosphoenolpyruvate (PEP) carboxylase (PEPC) catalyses the irreversible carboxylation of PEP with bicarbonate to produce oxaloacetate. This reaction powers the carbon-concentrating mechanism (CCM) in plants that perform C4 photosynthesis. This CCM is generally driven by a single PEPC gene product that is highly expressed in the cytosol of mesophyll cells. We found two C4 grasses, Panicum miliaceum and Echinochloa colona, that each have two highly expressed PEPC genes. We characterized the kinetic properties of the two most abundant PEPCs in E. colona and P. miliaceum to better understand how the enzyme’s amino acid structure influences its function. Methods Coding sequences of the two most abundant PEPC proteins in E. colona and P. miliaceum were synthesized by GenScript and were inserted into bacteria expression plasmids. Point mutations resulting in substitutions at conserved amino acid residues (e.g. N-terminal serine and residue 890) were created via site-directed PCR mutagenesis. The kinetic properties of semi-purified plant PEPCs from Escherichia coli were analysed using membrane-inlet mass spectrometry and a spectrophotometric enzyme-coupled reaction. Key Results The two most abundant P. miliaceum PEPCs (PmPPC1 and PmPPC2) have similar sequence identities (>95 %), and as a result had similar kinetic properties. The two most abundant E. colona PEPCs (EcPPC1 and EcPPC2) had identities of ~78 % and had significantly different kinetic properties. The PmPPCs and EcPPCs had different responses to allosteric inhibitors and activators, and substitutions at the conserved N-terminal serine and residue 890 resulted in significantly altered responses to allosteric regulators. Conclusions The two, significantly expressed C4Ppc genes in P. miliaceum were probably the result of genomes combining from two closely related C4Panicum species. We found natural variation in PEPC’s sensitivity to allosteric inhibition that seems to bypass the conserved 890 residue, suggesting alternative evolutionary pathways for increased malate tolerance and other kinetic properties.

DiMario, Robert J. (ORCID:0000000250566868)↗
DOE OSTI2023

Assessment of Potential Dose and Environmental Impacts from Proposed Testing at the INL Radiological Response Training Range

This assessment uses screening-level models to calculate potential environmental impacts from proposed tests at the Idaho National Laboratory (INL) Radiological Response Training Range (RRTR) site. Proposed tests could be conducted using 11 different radioactive material types that include K2O, LaBr3, KBr, Cu, Zr, F, Ga, Ga2O3, NaNO2, Ga-68, and Tc-99m. The tests could potentially release radioactive material to the atmosphere and radionuclides and other contaminants to the soil, which could leach into the unsaturated zone and migrate to the aquifer. Atmospheric transport of radionuclides to potential human receptors and time-integrated air concentrations were calculated with a Gaussian plume model and three years of hourly meteorological data. Potential surface-soil impacts were calculated with the computer program mixing-cell model (MCM). Groundwater impacts were calculated with the computer programs MCM and GWSCREEN. Radiological doses from potential atmospheric releases were calculated for public receptors off the INL Site and for workers at nearby INL facilities. Results were compared to regulatory dose limits. Maximum potential groundwater concentrations were estimated in the aquifer below the NSTR site and compared to drinking water standards or risk-based screening levels for resident tap water. Soil concentrations were calculated and compared to risk-based screening levels for workers and potential future residents. All impacts were estimated assuming 12 tests are conducted annually using all 11 material types for a period of 15 years. This document provides the resources to enable a subject matter expert in the field of environmental assessments to replicate the modeling and calculations. The methodology and parameters are presented in the text. All electronic files, including computer-code input, output, executable files, batch files, scripts, and spreadsheet files are contained in a zip file that can be accessed by selecting “Additional Information” (select Native File) in the INL Electronic Document Management System (EDMS). It is highly unlikely the test scenarios evaluated in this ECAR will adversely impact human health based on comparisons of calculated dose and concentration against regulatory standards and risk-based screening levels. Conservative estimates of dose to workers and the public from atmospheric transport of possible radionuclide releases are far below federal radiation protection standards. Conservative estimates of potential contaminant concentrations in groundwater are less than federal drinking water standards or screening levels. Predicted radionuclide concentrations in surface soils are below risk-based screening levels, except for Ge-68 (material Ga-68) for the worker. The Ge-68 soil concentration can be made less than the worker PRG, if the number of annual tests using Ga-68 is reduced from 12 to 6. However, the sum of ratios still exceeds one because of the high K-40 ratio. If the EF of the worker (number of days the worker is in the contaminated testing area) is reduced from 225 days/yr (default value for full time worker) to 112 days/yr, the Ge-68 ratio is less than one and the sum of ratios is less than one. Actual radiation doses and groundwater and surface-soil concentrations are likely to be much less than those calculated because of the conservative assumptions and parameters employed in the modeling. For example, atmospheric-transport calculations assume the entire inventory of each material type is readily released to the atmosphere and no plume deposition, depletion, or radioactive decay occurs during transport. The calculations also assume the same meteorological conditions (e.g., wind velocity, wind direction, stability class) that produce the maximum 95th percentile concentration (i.e., concentration representing the 95th percentile of a distribution of concentrations derived from 3 years of hourly meteorological data) at each receptor location are the same for all 12 tests during the year, and each receptor is assumed to be present during all 12 tests. The surface-soil assessment assumes the entire inventory of each test is deposited in the top 5 cm of soil. No atmospheric dispersal is assumed, and the radionuclides are subject only to leaching and radioactive decay. The groundwater-pathway modeling is conservative in that it is one-dimensional in the unsaturated zone (no lateral spreading/dilution) and assumes the entire inventory of contaminants infiltrates into the ground at the same location for every test. This is especially conservative for particulate radionuclides because they would have to dissolve or corrode first and some would be dispersed into the atmosphere. The groundwater receptor is also assumed to consume water directly from a hypothetical well positioned in the location of maximum concentration. In addition, conservative degradation rates were used, and volatilization was not considered for the nonradioactive chemical

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

An expanded role for the transcription factor WRINKLED1 in the biosynthesis of triacylglycerols during seed development

The transcription factor WRINKLED1 ( WRI1 ) is known as a master regulator of fatty acid synthesis in developing oilseeds of Arabidopsis thaliana and other species. WRI1 is known to directly stimulate the expression of many fatty acid biosynthetic enzymes and a few targets in the lower part of the glycolytic pathway. However, it remains unclear to what extent and how the conversion of sugars into fatty acid biosynthetic precursors is controlled by WRI 1. To shortlist possible gene targets for future in-planta experimental validation, here we present a strategy that combines phylogenetic foot printing of cis-regulatory elements with additional layers of evidence. Upstream regions of protein-encoding genes in A. thaliana were searched for the previously described DNA-binding consensus for WRI1, the ASML1/WRI1 (AW)-box. For about 900 genes, AW-box sites were found to be conserved across orthologous upstream regions in 11 related species of the crucifer family. For 145 select potential target genes identified this way, affinity of upstream AW-box sequences to WRI1 was assayed by Microscale Thermophoresis. This allowed definition of a refined WRI1 DNA-binding consensus. We find that known WRI1 gene targets are predictable with good confidence when upstream AW-sites are phylogenetically conserved, specifically binding WRI1 in the in vitro assay, positioned in proximity to the transcriptional start site, and if the gene is co-expressed with WRI1 during seed development. When targets predicted in this way are mapped to central metabolism, a conserved regulatory blueprint emerges that infers concerted control of contiguous pathway sections in glycolysis and fatty acid biosynthesis by WRI1. Several of the newly predicted targets are in the upper glycolysis pathway and the pentose phosphate pathway. Of these, plastidic isoforms of fructokinase ( FRK 3) and of phosphoglucose isomerase ( PGI 1) are particularly corroborated by previously reported seed phenotypes of respective null mutations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

State Insights On The Water-Energy Nexus And Policy Ideas To Achieve Greater Savings

Governors, state policymakers, utilities and other stakeholders across the country are increasingly aware of the connection between energy and water production and use, and the need to conserve both resources to meet economic and environmental goals. It requires substantial amounts of water to produce energy and considerable amounts of energy to treat and deliver water. The critical interdependence between energy and water was clearly illustrated during the recent winter storm in Texas and other parts of the South in February 2021. Initial power outages contributed to a longer-term water crisis. Power outages led to water pump failures while water demand increased from frozen water pipes that burst. This caused low water pressure that can lead to harmful bacteria growth in the water. The power outages also prevented water treatment plants from properly treating the water for several days, thereby leaving many residents without clean drinking water and worsening the storm’s impacts. The National Governors Association has been working with states on this connection between water and energy and strategies for conserving those resources for several years. NGA held a Water-Energy Nexus Learning Lab in September 2020. This event invited two leading states in the water-energy nexus space, Arizona and Wisconsin, to showcase some of their model policies and programs to other states, Maryland, Nevada, North Carolina, North Dakota, and Washington, looking for greater savings opportunities. This paper provides an overview of challenges that states are facing in developing integrated water and energy conservation policies; provides background on Arizona and Wisconsin’s innovative water-energy policies and programs; and summarizes action items the participating state teams identified for their respective states. The main categories of policy solutions identified by states at NGA’s Water-Energy Nexus Learning Lab were: Funding & Financing – providing financial incentives for water efficiency modeled after established energy efficiency programs, and an emphasis on financial support for small water and energy utilities. Education & Technical Assistance – providing more education and training opportunities about ways to achieve cost-effective energy and water savings, and the needs of resource-constrained small and medium utilities for training and other assistance. Structural Changes to Encourage Conservation – developing ways to incentivize agricultural conservation such as through water allocation strategies; adopting water reuse or water loss standards; and requiring electric utilities to consider water impacts as part of their integrated resource planning process. Communications & Data – conducting energy audits, reviewing water data provided to state agencies, and developing data benchmarking tools to measure and better manage energy and water use. Climate Strategy – establishing a multi-agency working group or other collaborative approach to determine ways to integrate energy and water savings in state policies and help meet the state climate objectives.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Anti-symmetric representation of the extended magnetohydrodynamic equations

We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator (∇·ν+ν·∇) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass (√ρ), momentum (√ρν), and pressure (√ p ). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗