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All sources NASA NTRS DOE OSTI

DOE OSTI2020

A Hierarchical Volt-var Optimization with Discrete Variables in Unbalanced Distribution Systems

This paper proposes a framework to determine the optimal active and reactive power dispatch of distributed photovoltaic (PV) generation, switched capacitors, and voltage regulators in multi-phase unbalanced distribution systems. The objectives of the optimal dispatch are minimization of the energy loss, PV real power curtailment, and switching operations of capacitors and voltage regulators, in addition to elimination of voltage violation and reverse power flow. The optimization problem is formulated in rectangular coordinates as a nonlinear, nonconvex problem with discrete variables. A hierarchical twostage framework is proposed to effectively handle those discrete variables and reduce the computational time compared to the unified approach in which all variables are solved simultaneously. The efficacy of the proposed approach and the accuracy of the obtained numerical solution is validated using the unbalanced multi-phase IEEE 34-bus with 15-minute load and PV data.

Nguyen, Quan H.↗

DOE OSTI2024

Thermal Management of Discretized Heaters Using CuW Microchannel Heat Sinks and FC3283

Single-phase cooling using microchannel heat sinks (MCHS) has become a popular approach for overcoming the thermal challenges associated with high-powered microelectronic devices. Thermal management is one of the largest barriers to higher power densities in electronics and frequently limits overall device performance. The implementation of forced convective cooling via single-phase liquid cooling in MCHS reduces the thermal resistance resulting in lower device temperatures at high-power conditions, which can decrease the package size and extend the lifespan of devices. The goal of the work described in this article was to investigate practical cooling solutions for laser diode bars. This study examined the effectiveness of a copper tungsten (CuW) microchannel heat sink paired with a dielectric coolant (FC3283) for dissipating both discrete and uniform heat fluxes up to 600 W/cm2 across a 0.25-cm2 surface area through a numerical and experimental study. CuW was chosen as the MCHS material because it is thermal expansion matched to GaAs, which is a common laser diode substrate. FC3283 serves as a dielectric coolant that is compatible with power electronics cooling. The microchannels utilized in this work were approximately $365$ $μ$ m deep and $100$ $μ$ m wide resulting in a hydraulic diameter of $160$ $μ$ m. The study investigated the cooling performance across a variety of applied power loads and flow rates to determine optimal effectiveness. The resulting thermal resistance ranged from 0.15 cm2 K/W at the highest flow rate to 0.26 cm2 K/W at the lowest flow rate. Further, the resulting thermal performance from this study demonstrates the importance of considering discrete heat sources separately from uniform heat sources and proved that the unique combination of CuW microchannels with FC3283 can be a promising cooling option toward future advancements of laser diode bars and other high-power microelectronics.

42 ENGINEERING↗

DOE OSTI2020

A Method to Represent a Well in a Three‐Dimensional Discrete Fracture Network Model

Abstract In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three‐dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high‐resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real‐world case study.

Pham, Hai (ORCID:0000000310164394)↗

DOE OSTI2020

A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems

This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The well-known mortar finite element discretization method is modified to admit a local structure, providing an element-by-element or subdomain-by-subdomain assembly property. This is achieved via the introduction of additional trace finite element spaces and degrees of freedom (unknowns) associated with the interfaces between adjacent elements or subdomains. The resulting nonconforming formulation and a reduced-via-static-condensation Schur complement form on the interfaces are used in the construction of auxiliary space preconditioners for a given conforming finite element discretization problem. Overall, the properties of these preconditioners are studied and their performance is illustrated on model second order scalar elliptic problems utilizing high order elements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)

This article investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a “steady” advection-diffusion problem in $(d+1)$-dimensions and AIR has been shown to be a robust solver for steady advection-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable, space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Generic Discretization Library

The GenDiL library is a collection of C++ software abstractions designed to discretize and solve partial differential equations (PDEs) for high-performance computing (HPC) applications. Its primary focus is on modern C++ generic programming, which helps ensure portability across various hardware architectures. The central idea behind the library is to provide building blocks for numerical algorithms-such as discretization methods and iteration patterns-so that domain experts can focus on the math, rather than the low-level details of hardware or implementation. By defining abstractions for data types, iteration over computational grids, and scheduling of operations, the library isolates the high-level PDE algorithms from the platform-specific optimizations needed to achieve efficient performance.

Dudouit, Yohann [Lawrence Livermore National Labor↗

DOE OSTI2023

Diagonally implicit Runge–Kutta schemes: Discrete energy-balance laws and compactness properties

Abstract We study diagonally implicit Runge–Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Mathematics↗

DOE OSTI2021

PyGDH: Python Grid Discretization Helper

Mathematical models expressed in the form of discretized equations play an important role inmany scientific disciplines. In our experience, few domain scientists have sufficient backgroundin numerical computing (or the time required to acquire such a background) to use manyflexible and powerful but complex open source packages, such as FEniCS (Alnæs et al., 2015)and OpenFOAM (The OpenFOAM Foundation Ltd, n.d.). Many user-friendly open sourcepackages, such as FiPy (J. E. Guyer & Warren, 2009), and many commercial packages, suchas COMSOL Multiphysics (COMSOL AB, n.d.) and Simcenter STAR-CCM+ (Siemens DigitalIndustries Software, n.d.), provide limited flexibility in the equations that users can express.Additionally, the use of commercial packages, which by nature do not perform calculationstransparently, can hinder reproducibility, which is vital to the scientific process. PyGDH(“pigged”) is a Python 2 / Python 3 (Python Software Foundation, 1991–2020) package thatis meant to be accessible to scientists who might not be specialists in scientific computing,while approaching the level of flexibility associated with writing dedicated programs tailoredto solving specific problems. The PyGDH User’s Guide provides detailed instructions forcreating numerical models, including a brief introduction to necessary command line andPython (Python Software Foundation, 1991–2020) skills, and discussions of discretization andvalidation. Note that PyGDH emphasizes flexibility and simplicity over performance, and wasnot designed for high-performance applications or models describing complex spatial domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

High Order Implicit Residual-Based Spatial Discretization Error Estimation for S N Neutron Transport

This work demonstrates our novel residual source spatial discretization error estimator (LeR/TEAD) for a DGFEM-1 discretization and assesses it along with two contemporary estimators, Ragusa and Wang's h -refinement estimator (RW) and Duo, Azmy, and Zikatanov's explicit residual-based estimator (DAZ), on a suite of Method of Manufactured Solutions (MMS) 2D problems and three realistic problem geometries. LeR/TE-AD is attractive because it directly estimates the local error in the angular flux, as opposed to a mere indicator of the error's behavior, on the same mesh and method order as the original numerical solution, thus typically being less computationally intensive than a refinement-based method. On the MMS suite, LeR/TE-AD consistently displayed a reduced performance versus its DGFEM-0 results in terms of accuracy and precision metrics, though it was not typically grossly inaccurate. This is attributed to the irregularities in the true solution across singular characteristics limiting the local accuracy of the numerical flux solution, leading to poor derivative approximations used in the residual approximations. The error transport problem then spreads the error in the residual to nearby cells, causing a greater degree of imprecision that did not afflict DAZ or RW. In testing the estimators on realistic problem geometries, however, LeR/TE-AD fared better. In practice, the true error is much larger in non-idealized geometries like in MMS, and a superlinear true solution means that RW and DAZ are not beneficially biased for DGFEM-1 error estimation. LeR/TE-AD was typically first or second in accuracy, primarily competing with RW, but the latter usually consumed 2-4 times the computational time as LeR/TE-AD, and requires a solution with four times as many unknowns. Furthermore, RW and LeR/TE-AD can be used to compute direct estimates of the error in any quantity of interest that is based on the angular ux solution, such as the fission rate density in a fuel pin, whereas DAZ requires a heuristic extension due to its norm-based nature.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Statistical Hauser-Feshbach model calculation for (α, n) reaction cross section and discrete level population

We calculate the α-particle induced reactions on 17,18 O, 19 F, and 23 Na, in the energy range 0 ≤ E α ≤ 10 MeV, with a particular attention to the branching ratios of populated discrete levels in the (α,n) channels. Since there are too many open channels to employ the R-matrix theory, we apply the statistical Hauser-Feshbach model to calculate these reaction cross sections and branching ratios. The branching ratio is defined as b n = $\frac{σ_n}{Σ_iσ_i + σ_c}$ , where σ n is the n-th level production cross section after the neutron emission, and σ c is the production of the continuum state. In the cases of our target nuclei and the energy range of interest, the residual nuclei of the neutron emission channel are always in their discrete states, so that σ c can be negligible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Effects of finite element discretization and model simplification on calculations of ductile failure initiation

The finite element method is a scheme to discretize the infinite number of degrees of freedom in continuum-level problems down to a finite number of degrees of freedom. This discretization is done in conjunction with methods that also reduce the field differential equations to sets of algebraic ones that can be solved by arithmetical operations. Therefore, solutions attained by finite element models are approximations to the exact solutions of the field equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Hybrid Quantum Networks with Discrete Polarizations and Continuous Quadrature Variables

Final Scientific/Technical Report for DOE Project DE-SC0022069. Quantum communication and computation systems have evolved along two largely independent paradigms: discrete-variable (DV) systems that encode information in qubits such as photon polarizations or photon-number states, and continuous-variable (CV) systems that encode information in optical field quadratures. Each approach offers distinct advantages—DVs provide low error rates and compatibility with single-photon platforms, while CVs support deterministic operations and efficient quantum state manipulation. A fundamental challenge for building a scalable Quantum Internet lies in interfacing these two regimes into a unified hybrid architecture that can coherently distribute and process quantum information across heterogeneous quantum nodes. This project aims to develop and demonstrate a hybrid optical quantum network that seamlessly integrates DV and CV systems. Specifically, we investigate a new class of hybrid entanglement between the discrete polarizations of single photons and the continuous quadrature variables of optical cat states, overcoming incompatibilities in existing DV–CV demonstrations. Using this new entanglement resource, the team investigates a multi-node hybrid quantum local area network (Q-LAN) testbed capable of DV–CV entanglement generation, swapping, and distribution across fiber links.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗

DOE OSTI2025

Emergent discrete space-time crystal of Majorana-like quasiparticles in chiral liquid crystals

Time crystals spontaneously break the time translation symmetry, as recently has been frequently reported in quantum systems. Here we describe the observation of classical analogues of both 1+1-dimensional and 2+1-dimensional discrete space-time crystals in a liquid crystal system driven by a Floquet electrical signal. These classical time crystals comprise particle-like structural features and exists over a wide range of temperatures and electrical driving conditions. The phenomenon-enabling period-doubling effect comes from their topological Majorana-like quasiparticle features, where periodic inter-transformations of co-existing topological solitons and disclinations emerge in response to external stimuli and play pivotal roles. Our discrete space-time crystals exhibit robustness against temporal perturbations and spatial defects, behaving like a time-crystalline analogues of a smectic phase. Our findings show that the simultaneous symmetry breaking in time and space can be a widespread occurrence in numerous open systems, not only in quantum but also in a classical soft matter context.

FOS: Physical sciences↗

DOE OSTI2022

Diversification of multipotential postmitotic mouse retinal ganglion cell precursors into discrete types

The genesis of broad neuronal classes from multipotential neural progenitor cells has been extensively studied, but less is known about the diversification of a single neuronal class into multiple types. We used single-cell RNA-seq to study how newly born (postmitotic) mouse retinal ganglion cell (RGC) precursors diversify into ~45 discrete types. Computational analysis provides evidence that RGC transcriptomic type identity is not specified at mitotic exit, but acquired by gradual, asynchronous restriction of postmitotic multipotential precursors. Some types are not identifiable until a week after they are generated. Immature RGCs may be specified to project ipsilaterally or contralaterally to the rest of the brain before their type identity emerges. Optimal transport inference identifies groups of RGC precursors with largely nonoverlapping fates, distinguished by selectively expressed transcription factors that could act as fate determinants. Our study provides a framework for investigating the molecular diversification of discrete types within a neuronal class.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1970

Discrete control of linear distributed systems with application to the deformable primary mirror of a large orbiting telescope

One of the more significant technological problems associated with the orbital operation of large astronomical telescope's is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror by means of discrete actuators located on its rear surface: The realization of diffraction-limited performance from a telescope in space by this method rests on the ability of the designer to achieve extremely accurate control of a highly complex, interacting, multivariable system. This paper presents the results of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number (equal.to the number of actuators) of the most significant modes. Through the application of the modal expansion technique the mirror equation of motion is transformed tb a set of uncoupled, linear, time-invariant, ordinary differential equations. The desired dynamic response and static accuracy may then be achieved by the application of classical single-variable design techniques. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the-number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.

Jeremiah F Creedon↗

NASA NTRS1971

An Evaluation of Current NASTRAN Discrete Element Models for Monocoque and Semimonocoque Structures

The current discrete element analysis models in NASTRAN, Levels 8. 1.0 and 11. 1. 0, are evaluated for semi-rnonocoque and monocoque structures. Comparative results are presented with the FORMAT-I11 general-purpose code for a swept wing statics analysis and a Skylab substructure vibration analysis. Good agreement between Level i I. 1.0 and FORMAT-111 is demonstrated; however, a major error in Level 8. 1.0 was discovered on the Skylab vibration problem. The computational performance of NASTRAN was superior to FORMAT, but the vibration rigid format was found to have several inefficiencies. Comparative results are also presented between Level 11. 1. 0 and STACUSS, SLADE, BOND, UNIVALVE, and another special-purpose code. Results for two of the structures analyzed, a cylindrical shell and an elliptic plate, indicate curved discrete elements are significantly more accurate than the plate elements in NASTRAN for the same number of degrees of freedom.

Edward L. Stanton↗

NASA NTRS1972

Discrete ordinates-Monte Carlo coupling: A comparison of techniques in NERVA radiation analysis

In the radiation analysis of the NERVA nuclear rocket system, two-dimensional discrete ordinates calculations are sufficient to provide detail in the pressure vessel and reactor assembly. Other parts of the system, however, require three-dimensional Monte Carlo analyses. To use these two methods in a single analysis, a means of coupling was developed whereby the results of a discrete ordinates calculation can be used to produce source data for a Monte Carlo calculation. Several techniques for producing source detail were investigated. Results of calculations on the NERVA system are compared and limitations and advantages of the coupling techniques discussed.

Lindstrom, D. G.↗