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Unstructured Euler flow solutions using hexahedral cell refinement

An attempt is made to extend grid refinement into three dimensions by using unstructured hexahedral grids. The flow solver is developed using the TIGER (topologically Independent Grid, Euler Refinement) as the starting point. The program uses an unstructured hexahedral mesh and a modified version of the Jameson four-stage, finite-volume Runge-Kutta algorithm for integration of the Euler equations. The unstructured mesh allows for local refinement appropriate for each freestream condition, thereby concentrating mesh cells in the regions of greatest interest. This increases the computational efficiency because the refinement is not required to extend throughout the entire flow field.

Melton, John E.

An adaptively-refined Cartesian mesh solver for the Euler equations

A method for adaptive refinement of a Cartesian mesh for the solution of the steady Euler equations is presented. The algorithm creates an initial uniform mesh and cuts the body out of that mesh. The mesh is then refined based on body curvature. Next, the solution is converged to a steady state using a linear reconstruction and Roe's approximate Riemann solver. Solution-adaptive refinement of the mesh is then applied to resolve high-gradient regions of the flow. The numerical results presented show the flexibility of this approach and the accuracy attainable by solution-based refinement.

De Zeeuw, Darren

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Coirier, William John

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Coirier, William J.

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

Baker, John G.

Interlaminar Stresses by Refined Beam Theories and the Sinc Method Based on Interpolation of Highest Derivative

Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory.

Slemp, Wesley C. H.

Go-Around Criteria Refinement for Transport Category Aircraft

Presently, airline pilots are trained to go around if, when lower than 500 ft above the ground, they are outside of a handful of parameters such as airspeed, position, and rate of descent. At times, pilots do not comply with these criteria, perhaps owing to their conservative nature or complexity. This paper examines potential refinements to the continue-to-land decision from the combined results of three flight simulator experiments. Potential refinements include simplifying the number of parameters and lowering the altitude at which pilots make the decision. First, refinements were developed by evaluating pilots’ touchdown performance and qualitative data in a variety of starting and environmental conditions. Second, 30 of those pilots evaluated the refinements under several induced instabilities during the approach. The results showed little difference in touchdown performance when lowering the decision altitude from 500 to 300 ft; however, significant differences arose when the decision altitude was lowered further to 100 ft. The proposed new criteria include assessments of deviations in airspeed and position, no rate-of-descent audio warning, and having an appropriate engine setting at 1000, 500, and 300 ft height above threshold. Additionally, a recommendation is made that if the proposed criteria are not met at the 1000 or 500 ft height above threshold the pilots may make corrections and continue the approach; however, if the criteria are not met at 300 ft, then a go-around should be performed.

stabilized approach criteria

Validated ligand geometries for macromolecular refinement restraints and molecular-mechanics force fields

In macromolecular structure refinement, the low observation-to-parameter ratio and the lack of high-resolution data are countered by using a priori information in the form of restraints. Having accurate geometries of the chemical entities in the sample is paramount for generating accurate chemical restraints and, therefore, accurate macromolecular structures. In particular, it is desirable to have accurate restraints for known and novel ligand entities. Quantum mechanics (QM) can minimize the energy of a ligand by adjusting its geometry, and these geometries can be used to generate restraints for macromolecular refinement. This article describes a library of approximately 37 000 small molecules extracted from the Chemical Component Dictionary in the Protein Data Bank and minimized by density-functional QM. The library includes restraint files for use in crystallography or cryo-EM refinement, along with files suitable for molecular-dynamics simulation. Because the geometries are validated using the Cambridge Structural Database, the restraints library provides users with both functional restraints and minimized geometries. This work also provides procedures for generating new and accurate restraints.

Amber

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock-Boundary Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient means to obtain a discrete approximation to a continuous boundary value problem of a specified accuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW (a computational fluid dynamics (CFD) code) is utilized to provide estimates of the exact analytical solutions to problems of interest to turbulence modeling. Predictions of surface pressure and skin friction, essentially the state of stress at the surface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on the other hand, show marked differences in flows with shocks. The AMR method, as implemented in OVERFLOW 2.2k, appears to provide the ability to produce arbitrarily accurate solutions at a predictable cost much smaller than classic uniform mesh refinement.

Turbulence Modeling

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock/Boundary-Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient meansto obtain a discrete approximation to a continuous boundary value problem of a specifiedaccuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW is utilizedto provide estimates of the exact analytical solutions to problems of interest to turbulencemodeling. Predictions of surface pressure and skin friction, essentially the state of stress at thesurface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on theother hand, show marked differences in flows with shocks. The AMR method, as implementedin OVERFLOW2.2k, appears to provide the ability to produce arbitrarily accurate solutionsat a predictable cost much smaller than classic uniform mesh refinement.

Adaptive Mesh Refinement

Hot Cracking Behavior and Beam-Induced Grain Refinement in Electron Beam Freeform Fabricated Al 7075

Electron beam freeform fabrication (EBF 3 ) is a high deposition rate, wire-based directed energy deposition (DED) additive manufacturing (AM) process used to print metallic parts in a vacuum environment. While high specific strength 7xxx-series Al alloys are of interest in the aerospace and automotive industries, these alloys suffer from hot cracking issues during fusion welding and AM. In this work, linear deposits of Al 7075 were fabricated with EBF 3 to study the effects of baseplate thickness, preheat temperature, and beam focus on hot cracking behavior. Solidification cracks were observed in the first deposition layer, and by the third layer coalesced into large “macrocracks” running vertically through the build height. Fine, intergranular liquation “microcracks” appeared between macrocracks below the root of the final deposit layer fusion zone. Increasing the substrate preheat temperature from 165°C to 320°C deepened the partially melted zone and resulted in a more than twofold increase in the liquation microcrack density. Analysis of Scheil solidification diagrams revealed that fugitive losses of Zn and Mg during deposition increased the susceptibility to solidification cracking and promoted substrate liquation cracking. Focused electron beam (EB) conditions combined with a high aspect ratio elliptical raster pattern resulted in bands of refined, equiaxed grains. The refined microstructure suppressed solidification macrocracking and caused a nearly fivefold reduction in liquation crack density, demonstrating that beam-induced grain refinement may be a promising low-cost method for reducing hot cracking during AM.

aluminum

Dara: Automated Multiple-Hypothesis Phase Identification and Refinement from Powder X-ray Diffraction

Powder X-ray diffraction (XRD) is a foundational technique for characterizing crystalline materials. However, the reliable interpretation of XRD patterns, particularly in multiphase systems, remains a manual and expertise-demanding task. As a characterization method that only provides structural information, multiple reference phases can often be fit to a single pattern, leading to potential misinterpretation when alternative solutions are overlooked. To ease humans’ efforts and address the challenge, we introduce Dara (data-driven automated Rietveld analysis), a framework designed to automate the robust identification and refinement of multiple phases from powder XRD data. Dara performs an exhaustive tree search over all plausible phase combinations within a given chemical space and validates each hypothesis using the BGMN Rietveld refinement routine. Key features include structural database filtering, automatic clustering of isostructural phases during tree expansion, and peak-matching-based scoring to identify promising phases for refinement. When ambiguity exists, Dara generates multiple hypothesis which can then be decided between by human experts or with further characterization tools. By enhancing the reliability and accuracy of phase identification, Dara enables scalable analysis of realistic complex XRD patterns and provides a foundation for integration into multimodal characterization workflows, moving toward fully self-driving materials discovery.

Biological databases

AQuaRef: machine learning accelerated quantum refinement of protein structures

Cryo-EM and X-ray crystallography provide crucial experimental data for obtaining atomic-detail models of biomacromolecules. Refining these models relies on library-based stereochemical data, which, in addition to being limited to known chemical entities, do not include meaningful noncovalent interactions. Quantum mechanical (QM) calculations could alleviate these issues but are too expensive for large molecules. Here we present a novel AI-enabled Quantum Refinement (AQuaRef) based on AIMNet2 machine learned interatomic potential (MLIP) mimicking QM at substantially lower computational costs. By refining 41 cryo-EM and 30 X-ray structures, we show that this approach yields atomic models with superior geometric quality compared to standard techniques, while maintaining an equal or better fit to experimental data. Notably, AQuaRef aids in determining proton positions, as illustrated in the challenging case of short hydrogen bonds in the parkinsonism-associated human protein DJ-1 and its bacterial homolog YajL.

Zubatyuk, Roman [Carnegie Mellon University, Pitts

Cryogenic-Refined MOSFET Modeling for Oscillator, Frequency Divider, and Amplifier Designs Below 4 K

Capturing device characteristic changes at cryogenic temperatures is crucial for cryo-CMOS circuit designs. In this work, we present an isothermal cryogenic-refined modeling approach for CMOS transistors that is simple, low overhead, and easy to implement while offering the required accuracy for predicting circuit performance at the designated temperatures. Guided by die-level measurement data and circuit design principles, the model introduces corrections to only five critical parameters: threshold voltage, carrier mobility, elevated low-frequency flicker noise, dominant high-frequency shot noise, and subthreshold swing (SS). These refinements are implemented around the foundry-provided SPICE model, which is typically validated only down to about 200 K. With these adjustments, the proposed cryogenic-refined model achieves less than 5% error in both large-signal metrics (I–V characteristics) and small-signal parameters (e.g., transconductance) when compared with device measurements at deep-cryogenic temperatures. The methodology is validated in two advanced technologies: TSMC 40-nm CMOS and GlobalFoundries (GF) 45-nm RF-SOI. We further demonstrate its applicability in three representative RF circuits: a 30-GHz LC oscillator, a high-speed current-mode-logic (CML) frequency divider (FD), and a subthreshold Gb/s amplifier, all showing close agreement between simulated predictions and measurements performed at 4 and 2.5 K. Finally, we believe that the proposed approach is implementation-friendly and can significantly accelerate the development of cryo-CMOS integrated circuits.

circuit modeling

Simulation of wind and solar energy generation over California with E3SM SCREAM regionally refined models at 3.25 km and 800 m resolutions

This study presents wind and solar power generation estimates derived from the US Department of Energy’s Simple Cloud-Resolving E3SM Atmosphere Model (SCREAM) Regionally Refined Models (RRM) over California at 3.25 km and 800 m horizontal resolutions, using the Python wrapper for the System Advisor Model (PySAM). The resulting wind and solar generation estimates are compared to monthly capacity factors reported to the Energy Information Administration (EIA), High-Resolution Rapid Refresh (HRRR, 3 km resolution) forecast model, and E3SM North American regionally refined model (NARRM, 25 km resolution). We systematically assess the impacts of generation modeling assumptions, meteorological models, and horizontal resolution. Results show that resolution plays a dominant role for wind energy: increasing from 25 to 3.25 km brings qualitative and quantitative improvements, most notably by resolving the phase error in the seasonal cycle found in coarser simulations. However, further refinement to 800 m offers minimal gains. SCREAM performs better than HRRR for solar power generation in single- and dual-axis tracking systems, likely due to more accurate surface radiation. The sensitivity of PySAM to system configuration, particularly for axis-tracking modeling in photovoltaics, is also highlighted. Overall, SCREAM-RRM shows strong potential for high-resolution energy assessments, with future progress depending on more in situ observations and clearer quantification of uncertainties in generation modeling.

Geosciences

Silicon refinement by chemical vapor transport

Silicon refinement by chemical vapor transport is discussed. The operating characteristics of the purification process, including factors affecting the rate, purification efficiency and photovoltaic quality of the refined silicon were studied. The casting of large alloy plates was accomplished. A larger research scale reactor is characterized, and it is shown that a refined silicon product yields solar cells with near state of the art conversion efficiencies.

Olson, J.

Refined numerical solution of the transonic flow past a wedge

A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.

Liang, S.-M.

Refining of metallurgical-grade silicon

A basic requirement of large scale solar cell fabrication is to provide low cost base material. Unconventional refining of metallurical grade silicon represents one of the most promising ways of silicon meltstock processing. The refining concept is based on an optimized combination of metallurgical treatments. Commercially available crude silicon, in this sequence, requires a first pyrometallurgical step by slagging, or, alternatively, solvent extraction by aluminum. After grinding and leaching, high purity qualtiy is gained as an advanced stage of refinement. To reach solar grade quality a final pyrometallurgical step is needed: liquid-gas extraction.

Dietl, J.