Results for “Approximations and Expansions” — Page 14

DOE OSTI2022

Impact of nuclear data covariance libraries on uncertainty quantification of sodium cooled fast reactor simulation

Uncertainty quantification in core modelling to assess reactor performance is a regular practice to identify design safety limits. Best-estimate plus uncertainty (BEPU) methods are commonly used to propagate uncertainties to core responses from input parameters, characterized by variance-covariance libraries. This study evaluates the impact of different covariance libraries on the uncertainty associated with core safety parameters and their propagation through reactor transient modelling for a metallic core (ABR-1000). The COMAC-1.0, COMMARA-2.0, and COMMARA-2.1 covariance libraries are used to propagate nuclear data uncertainties to neutron feedback coefficients using the Generalized Perturbation Theory, then through transient safety analyses to establish the confidence interval for safety performance of the reactor using stochastic sampling. The considered transients include Unprotected Transient Over Power and Unprotected Loss Of Flow. Most influential nuclide and reaction pairs in different variance-covariance libraries are identified and their impact on the uncertainty of safety parameters are evaluated. Significant differences were observed between uncertainties from COMAC compared to COMMARA libraries. Uncertainties from COMMARA libraries were consistently larger than COMAC for all cases. For structure, coolant density feedback coefficients and control rod worth, total nuclear data uncertainties were approximately 50% larger for COMMARA than COMAC. Differences were also observed in identification of top contributors of uncertainty in terms of reaction-cross sections. For instance, largest contribution to total uncertainty of radial expansion coefficient from COMMARA-2.0 and 2.1 originates from Na{sup 23} P1 Elastic cross section (0.81%) but from Pu{sup 239} Fission (0.53%) with COM C-1.0. Such differences are evaluated in this research for all quantities of interest. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

MARVEL Reactor Fuel Performance Report (Rev.2)

The Microreactor Applications Research Validation and EvaLuation (MARVEL) project is producing a high temperature liquid metal-cooled nuclear test bed at Idaho National Laboratory (INL) to ultimately improve the integration of microreactors to end-user applications. This ambitious effort seeks to design, authorize, construct, test, and operate the reactor within five years. In order to construct and operate the MARVEL reactor in a timely manner, the system will utilize materials and component designs which have already been used, qualified, or licensed from previous reactors. The MARVEL reactor will be located at the INL Transient Reactor Test (TREAT) facility in the north high-bay equipment pit and will use the existing 304 stainless steel-clad U-ZrH1.6 pin-type fuel system developed by General Atomics and purchased from TRIGA International. This fuel has been previously qualified under the United States Department of Energy’s (US DOE) Reduced Enrichment for Research and Test Reactors (RERTR) Program. Even though the regulator of the MARVEL reactor is the US DOE, the standards and overall approach recommended by the Nuclear Regulatory Commission is well-defined and utilized here. Following NUREG-1537 regulatory guidance, this report documents the authorization case for the MARVEL fuel system’s application to MARVEL and establishes stable and predictable fuel performance during the most thermophysically unfavorable conditions achievable in the MARVEL reactor. To that end, this report provides a comprehensive survey of the known thermophysical properties, performance, and quantitative relationships associated with the MARVEL reactor fuel element and uses this information to determine its mechanical integrity and risk of reaching unacceptable conditions during the most extreme accident scenarios predicted for the reactor using the most conservative assumptions available. The information contained herein is compiled from a combination of historical reports and peer reviewed scientific publication manuscripts. Known mechanisms under which the fuel is susceptible to failure are highlighted and compared to conditions that could exist in the MARVEL reactor during an unanticipated transient or accident scenario. The two scenarios considered for analysis in this report are (1) an unprotected loss of flow accident and (2) a hypothetical unprotected loss of coolant accident during the loss of flow accident. Preliminary 2D steady-state analyses herein indicate that both fuel-cladding chemical interactions and fuel-cladding mechanical interactions are negligible throughout the fuel’s operational cycle under both normal and high temperature accident scenario conditions. Although higher fidelity 3D time-dependent modeling and simulations are planned, the following may be concluded presently. The MARVEL fuel element maintains its geometric stability and structural integrity during the most extreme accident scenarios predicted for the MARVEL reactor. The hoop stress during the unprotected loss of flow accident reaches about -1.27 MPa; this negative stress indicates that it is compressive rather than tensile. The compressive stress is a result of the NaK pressure on the outside of the fuel element, caused by the restricted thermal expansion of the NaK coolant, exceeding the internal pressures generated inside of the fuel element. The hoop stress generated in the cladding during the unprotected loss of coolant accident reaches a maximum of about approximately 10 MPa, which is nearly an order of magnitude less than the predicted yield strength of the cladding under high-temperature accident scenario conditions. Calculations were compared with results from high performance computational simulations using BISON and are in very close agreement. A conservative MARVEL fuel meat peak temperature limit of 900 °C is recommended presently, which is about 180 °C higher than the peak fuel temperature predicted to occur during the most extreme accident. Based on the known properties and behavior of the MARVEL fuel element, the fuel successfully meets its design and safety requirements under normal and most extreme accident conditions with a large safety margin.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

MARVEL Reactor Fuel Performance Report

The Microreactor Applications Research Validation and EvaLuation (MARVEL) project is producing a high temperature liquid metal-cooled nuclear test bed at Idaho National Laboratory (INL) to ultimately improve the integration of microreactors to end-user applications. This ambitious effort seeks to design, authorize, construct, test, and operate the reactor within five years. In order to construct and operate the MARVEL reactor in a timely manner, the system will utilize materials and component designs which have already been used, qualified, or licensed from previous reactors. The MARVEL reactor will be located at the INL Transient Reactor Test (TREAT) facility in the north high-bay equipment pit and will use the existing 304 stainless steel-clad U-ZrH1.6 pin-type fuel system developed by General Atomics and purchased from TRIGA International. This fuel has been previously qualified under the United States Department of Energy’s (US DOE) Reduced Enrichment for Research and Test Reactors (RERTR) Program. Even though the regulator of the MARVEL reactor is the US DOE, the standards and overall approach recommended by the Nuclear Regulatory Commission is well-defined and utilized here. Following NUREG-1537 regulatory guidance, this report documents the authorization case for the MARVEL fuel system’s application to MARVEL and establishes stable and predictable fuel performance during the most thermophysically unfavorable conditions achievable in the MARVEL reactor. To that end, this report provides a comprehensive survey of the known thermophysical properties, performance, and quantitative relationships associated with the MARVEL reactor fuel element and uses this information to determine its mechanical integrity and risk of reaching unacceptable conditions during the most extreme accident scenarios predicted for the reactor using the most conservative assumptions available. The information contained herein is compiled from a combination of historical reports and peer reviewed scientific publication manuscripts. Known mechanisms under which the fuel is susceptible to failure are highlighted and compared to conditions that could exist in the MARVEL reactor during an unanticipated transient or accident scenario. The two scenarios considered for analysis in this report are (1) an unprotected loss of flow accident and (2) a hypothetical unprotected loss of coolant accident during the loss of flow accident. Preliminary 2D steady-state analyses herein indicate that both fuel-cladding chemical interactions and fuel-cladding mechanical interactions are negligible throughout the fuel’s operational cycle under both normal and high temperature accident scenario conditions. Although higher fidelity 3D time-dependent modeling and simulations are planned, the following may be concluded presently. The MARVEL fuel element maintains its geometric stability and structural integrity during the most extreme accident scenarios predicted for the MARVEL reactor. The hoop stress during the unprotected loss of flow accident reaches about -1.27 MPa; this negative stress indicates that it is compressive rather than tensile. The compressive stress is a result of the NaK pressure on the outside of the fuel element, caused by the restricted thermal expansion of the NaK coolant, exceeding the internal pressures generated inside of the fuel element. The hoop stress generated in the cladding during the unprotected loss of coolant accident reaches a maximum of about approximately 10 MPa, which is nearly an order of magnitude less than the predicted yield strength of the cladding under high-temperature accident scenario conditions. Calculations were compared with results from high performance computational simulations using BISON and are in very close agreement. A conservative MARVEL fuel meat peak temperature limit of 900 °C is recommended presently, which is about 180 °C higher than the peak fuel temperature predicted to occur during the most extreme accident. Based on the known properties and behavior of the MARVEL fuel element, the fuel successfully meets its design and safety requirements under normal and most extreme accident conditions with a large safety margin.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Impacts of Solar Land Availability on the Evolution of the U.S. Power System

Long-term planning scenarios of the United States electricity system have not identified solar resource availability to be a limiting factor in how much solar capacity might be deployed. However, there are some smaller regions where siting challenges indicate solar deployment could be limited by solar resource availability. In this work, we use geospatial modeling tools to develop a restrictive siting scenario that significantly reduces the amount and location of utility-scale solar resources. We use that restrictive siting regime, along with other previously defined siting scenarios, to examine how solar resource availability impacts the buildout of the electricity system using business-as-usual and decarbonization futures in a national-scale capacity expansion model. The restrictive siting scenario uses observed siting pressures to exclude many types of land on which development is allowed today and results in a greater than 90% reduction in solar resource potential-to approximately 3000 GW. Even with this drastic reduction, utility-scale solar capacity grows by more than 3 times through 2050 in the business-as-usual scenarios and by more than 6 times in the decarbonization scenarios, though less solar is deployed in scenarios with lower available solar resource. We quantify how system costs and generation mixes change as solar resource availability changes.

14 SOLAR ENERGY↗

DOE OSTI2024

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Machine learned potential for high-throughput phonon calculations of metal—organic frameworks

Metal–organic frameworks (MOFs) are highly porous and versatile materials studied extensively for applications such as carbon capture and water harvesting. However, computing phonon-mediated properties in MOFs, like thermal expansion and mechanical stability, remains challenging due to the large number of atoms per unit cell, making traditional Density Functional Theory (DFT) methods impractical for high-throughput screening. Recent advances in machine learning potentials have led to foundation atomistic models, such as MACE-MP-0, that accurately predict equilibrium structures but struggle with phonon properties of MOFs. In this work, we developed a workflow for computing phonons in MOFs within the quasi-harmonic approximation with a fine-tuned MACE model, MACE-MP-MOF0. The model was trained on a curated dataset of 127 representative and diverse MOFs. The fine-tuned MACE-MP-MOF0 improves the accuracy of phonon density of states and corrects the imaginary phonon modes of MACE-MP-0, enabling high-throughput phonon calculations with state-of-the-art precision. The model successfully predicts thermal expansion and bulk moduli in agreement with DFT and experimental data for several well-known MOFs. These results highlight the potential of MACE-MP-MOF0 in guiding MOF design for applications in energy storage and thermoelectrics.

Elena, Alin Marin↗

DOE OSTI2023

Validation of a detonation product equation of state for an insensitive high explosive via slab geometry expansion tests

Slab expansion (SLABEX) tests are conducted to validate a process for calibrating the detonation products equation of state (EOS) of a high explosive (HE). The SLABEX tests use rectangular slabs of PBX 9502, a polymer-bonded HE formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene bound with Kel F-800, a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Three PBX 9502 slab thicknesses are examined, each confined symmetrically by two rectangular copper (Cu) plates approximately one-tenth the thickness of the HE slab. For the duration of each experiment, the detonation flow along the central axis of the PBX 9502 slab remains two-dimensional. The lateral flow velocity component of the outer surfaces of the expanding Cu plates is measured, along with the steady axial detonation speed along the central axis of the SLABEX. Hydrodynamic simulations of the Cu plate expansion in the SLABEX geometry, driven by the energy stored in the detonation products by the detonation combustion event, are conducted using a Jones–Wilkins–Lee EOS for the detonation products. This EOS form was recently parameterized for PBX 9502 in the cylinder expansion test geometry using a newly developed calibration technique [Voelkel et al., Combust. Flame 246, 112373 (2022)]. Good agreement between the experiment and prediction is found in each SLABEX test, demonstrating that the detonation product EOS calibration technique produces EOSs that are predictive when applied to other geometries.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2024

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗

DOE OSTI2020

Dynamic Amplification of Subtropical Extreme Precipitation in a Warming Climate

Projected precipitation changes in a warming climate vary considerably, spatially, and between intensities. The changes can be greater or less than the ~7% K -1 Clausius-Clapeyron (CC) prediction, owing to dynamic effects. Using two global-climate-model large ensembles, we quantify the dynamically induced changes to precipitation extremes from the present (1996–2005) to late-21st-century (2071–2080) climates, as a function of recurrence interval, focusing on the subtropics. We separate non-CC changes into a term proportional to the present-day vertical-velocity spatial pattern (i.e., an amplification or damping thereof by a constant factor) and a residual. The amplitude term varies with recurrence interval, approximately canceling (doubling) CC for moderate (large) extremes, increasing precipitation variability. Contrastingly, the residual is quasi-uniform across recurrence intervals but spatially heterogeneous, weakening extremes over dry zones. This residual may be related to Hadley cell expansion, although this explanation is insufficient to explain many features, and other possible mechanisms are discussed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Performance Assessment for the Environmental Restoration Disposal Facility (Annual Status Report FY 2022)

DOE O 435.1 and DOE M 435.1-1 require that a determination of continued adequacy of the performance assessment (PA) (CP-60089), composite analysis (CA), and disposal authorization statement (DAS) be made on an annual basis, and that the determination must consider the results of data collection and analysis from research, field studies, and monitoring as well as the need to update any Radioactive Waste Management Basis (RWMB) documents. Beginning in 1996, the Environmental Restoration Disposal Facility (ERDF) started accepting low-level radioactive, hazardous, and mixed wastes that were generated during cleanup activities at the Hanford Site. ERDF is composed of a series of cells or disposal areas and can accommodate future design expansions as needed. Currently, there are eight cells and two supercells in ERDF. Each supercell is the equivalent of two cells. During this reporting period (fiscal year 2022, extending from October 1, 2021, through September 30, 2022), approximately 8.52E+04 metric tons (9.39E+04 U.S. tons) of waste was disposed at ERDF. From ERDF inception through September 30, 2022, approximately 17.0 million metric tons (18.7 million U.S. tons) of waste has been disposed at ERDF, which equates to consumption of approximately 89.1% of the currently constructed disposal volume. According to the design of ERDF, the facility has the ability to be expanded as needed. As a condition of the DAS, disposal operations within ERDF must be in accordance with the waste acceptance criteria (ERDF-00011) that provide specific radionuclide disposal limits, waste form restrictions, and descriptions of acceptable waste packages in compliance with the requirements of DOE M 435-1.1. The ERDF waste acceptance criteria stipulate that waste destined for disposal at ERDF be controlled based on source, physical form, and contaminant concentration and activity levels. There have been no changes to the physical configuration of ERDF or to the waste forms (source, physical form, etc.). No new unreviewed disposal question screenings or evaluations have been generated in this reporting period. Therefore, there are no noted impacts to the PA, CA, DAS, or RWMB resulting from the evaluations and screenings. Sum-of-fractions analysis shows that the disposed inventory meets both the concentration and inventory threshold requirements. A sum-of-fractions value is computed for ERDF sensitive radionuclides contributing to the groundwater pathways and the air pathway inventory limits. Computed values were 5.50E-04 and 3.30E-03, respectively. The disposed waste inventory remained well under the PA imposed limits, as shown in Table 4 and Table 5 in the main text of this report. Required monitoring was satisfactorily completed during the fiscal year reporting period. Compliance with performance objectives were met as each of the reported values were well below the established limit. Overall, there are no substantive changes to primary PA assumptions or changes to the PA analysis conclusion; therefore, compliance with DOE O 435.1 and the DAS is maintained.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Performance Assessment for the Environmental Restoration Disposal Facility (Annual Status Report FY 2021)

DOE O 435.1 and DOE M 435.1-1 require that a determination of continued adequacy of the performance assessment (PA) (CP-60089), composite analysis (CA), and disposal authorization statement (DAS) be made on an annual basis, and that the determination must consider the results of data collection and analysis from research, field studies, and monitoring as well as the need to update any Radioactive Waste Management Basis (RWMB) documents. Beginning in 1996, the Environmental Disposal Facility (ERDF) started accepting low-level radioactive, hazardous, and mixed wastes that were generated during cleanup activities at the Hanford Site. ERDF is composed of a series of cells or disposal areas and can accommodate future design expansions as needed. Currently, there are eight cells and two supercells in ERDF. Each supercell is the equivalent of two cells. During this reporting period (fiscal year 2021, extending from October 1, 2020, through September 30, 2021), approximately 9.14E+04 metric tons (1.01E+05 U.S. tons) of waste was disposed at ERDF. From ERDF inception through September 30, 2021, approximately 16.9 million metric tons (18.9 U.S. tons) of waste has been disposed of at ERDF, which equates to consumption of approximately 88.7% of the currently constructed disposal volume. According to the design of ERDF, the facility has the ability to be expanded as needed. As a condition of the DAS, disposal operation within ERDF must be in accordance with the waste acceptance criteria (ERDF-00011) that provide specific radionuclide disposal limits, waste form restrictions, and descriptions of acceptable waste packages in compliance with the requirements of DOE M 435-1.1. The ERDF waste acceptance criteria stipulate that waste destined for disposal at ERDF be controlled based on source, physical form, and contaminant concentration and activity levels. There have been no changes to the physical configuration of ERDF or to the waste forms (source, physical form, etc.). No new unreviewed disposal question screenings or evaluations have been generated in this reporting period. Therefore, there are no noted impacts to the PA, CA, DAS, or RWMB resulting from the evaluations and screenings. Sum-of-fractions analysis shows that the disposed inventory meets both the concentration and inventory threshold requirements. A sum-of-fractions value is computed for ERDF sensitive radionuclides contributing to the all pathways and the air pathway inventory limits. Computed values were 7.63E-03 and 1.49E-03, respectively. The disposed waste inventory remained well under the PA imposed limits, as shown in Table 4 and Table 5 in the main text of this report. Required monitoring was satisfactorily completed during the fiscal year reporting period. Compliance with performance objectives were met as each of the reported values were well below the established limit. Overall, there are no substantive changes to primary PA assumptions or changes to the PA analysis conclusion; therefore, compliance with DOE O 435.1 and the DAS is maintained.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Performance Assessment for the Environmental Restoration Disposal Facility (Annual Summary Report - FY 23)

Beginning in 1996, the Environmental Restoration Disposal Facility (ERDF) started accepting low-level radioactive, hazardous, and mixed wastes that were generated during cleanup activities at the Hanford Site. ERDF is composed of a series of cells or disposal areas and can accommodate future design expansions as needed. Currently, there are eight cells and two supercells in ERDF. Each supercell is the equivalent of two cells. During this reporting period (fiscal year 2023, extending from October 1, 2022, through September 30, 2023), approximately 9.37E+04 metric tons (1.03E+05 U.S. tons) of waste was disposed at ERDF. From ERDF inception through September 30, 2023, approximately 17.1 million metric tons (18.8 million U.S. tons) of waste has been disposed at ERDF, which equates to consumption of approximately 89.1% of the currently constructed disposal volume. According to the design of ERDF, the facility has the ability to be expanded as needed.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗

DOE OSTI2023

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈σσϵσσ〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆ cutoff . We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Target mass corrections in lepton–nucleus DIS: Theory and applications to nuclear PDFs

Motivated by the wide range of kinematics covered by current and planned deep-inelastic scattering (DIS) facilities, we revisit the formalism, practical implementation, and numerical impact of target mass corrections (TMCs) for DIS on unpolarized nuclear targets. An important aspect is that we only use nuclear and later partonic degrees of freedom, carefully avoiding a picture of the nucleus in terms of nucleons. After establishing that formulae used for individual nucleon targets (p,n), derived in the Operator Product Expansion (OPE) formalism, are indeed applicable to nuclear targets, here we rewrite expressions for nuclear TMCs in terms of re-scaled (or averaged) kinematic variables. As a consequence, we find a representation for nuclear TMCs that is approximately independent of the nuclear target. We go on to construct a single-parameter fit for all nuclear targets that is in good numerical agreement with full computations of TMCs. We discuss in detail qualitative and quantitative differences between nuclear TMCs built in the OPE and the parton model formalisms, as well as give numerical predictions for current and future facilities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗