SEARCH · Engineering Papers

Results for “code verification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

Here, we present algorithms and results from Gkeyll, a full-f continuum, electromagnetic gyrokinetic code, designed to study turbulence in the edge region of fusion devices. The edge is computationally very challenging, requiring robust algorithms that can handle large-amplitude fluctuations and stable interactions with plasma sheaths. We present an energy-conserving high-order discontinuous Galerkin scheme that solves gyrokinetic equations in Hamiltonian form. Efficiency is improved by a careful choice of basis functions and automatically generated computation kernels. Previous verification tests were performed in the straight-field-line large plasma device [Shi et al., J. Plasma Phys. 83, 905830304 (2017)] and the Texas Helimak, a simple magnetized torus [Bernard et al., Phys. Plasmas 26, 042301 (2019)], including the effect of end-plate biasing on turbulence. Results for the scrape-off layer for NSTX parameters with a model helical magnetic geometry with bad curvature have been obtained [Shi et al., Phys. Plasmas 26, 012307 (2019)]. In this paper, we present algorithms for the two formulations of electromagnetic gyrokinetics: the Hamiltonian and the symplectic. We describe each formulation and show results of benchmark tests. Although our scheme works for the Hamiltonian formulation, the presence of spurious numerical modes for high-β and large $k^2_⊥ρ^2_s$ regimes shows that the symplectic formulation is more robust. We then review our recent algorithm for the symplectic formulation [Mandell et al., J. Plasma Phys. 86, 905860109 (2020)], along with example application of this new capability. Maintaining positivity of the distribution function can be challenging, and we describe a new and novel exponential recovery based algorithm to address this.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Approach to nonlinear magnetohydrodynamic simulations in stellarator geometry

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-C 1 code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-C 1 . A C 1 coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-C 1 extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approach, including simulations of the heating, destabilization, and equilibration of a stellarator plasma with strongly anisotropic thermal conductivity, and of the relaxation of stellarator equilibria to integrable and non-integrable magnetic field configurations in realistic geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Dissertation Proposal: Innovations in Pulsed Power and Plasma Science Theory Simulation and Experiment

Pulsed power and plasma physics are topics of great study at both Sandia National Laboratories (SNL or Sandia) and the University of New Mexico (UNM). The goal of this research is to further knowledge and understanding of these fields using the resources of both SNL and UNM in three ways. The first way is through the comprehension, application, and testing of theory. Reading and analytically deriving theoretical solutions of problems both real-world and simplified will allow for a fresh perspective and the furthering of the theory. One such theory is Ottinger's generalized theory for voltage measurement in magnetically insulated transmission lines (MITLs). By working through the math, a deeper understanding of the theory is gained from which one may add more physically accurate and/or more detailed physics into the theory. Additionally, understanding the theory lays a good foundation from which one can analyze, test, and compare results to the theory in the following two ways that will advance the fields of pulsed power and plasma physics. The second way is through the modeling and simulation of real-world and simplified problems that utilize and test the afore mentioned theories. Theory can be applied to a simulation domain by using the unstructured time-domain electromagnetic (UTDEM) codes EMPHASIS and EMPIRE as well as the physical modeling software CUBIT, all of which were developed at SNL. Problems such as the modeling and design of the extended MITL on HERMES III, the understanding of space-charge-limited emission from vacuum cathodes, and the interaction between a relativistic electron beam and an ideal gas can all be modeled, simulated, and analyzed with this set of codes. Here the advantage is three-fold. Firstly, theory that describes our understanding of these problems can be put to the test and advanced through iterative simulation and analysis. Secondly, the understanding of these problems will have a positive impact on national security through the advancement of the technological capability of the United States of America. Thirdly, and not unrelated to the prior advantage, is the validation and verification of EMPIRE and EMPHASIS. This segues into the third way, which is through experiment and the comparison of experiment to simulated and theoretical results. Performing experimental comparisons completes the scientific method and grounds all of the work in reality. Being able to physically test theory and simulation is necessary for any real conclusions to be drawn. Another advantage for carrying out experimental work is to advance the physical testing capabilities of SNL. Several systems will be developed and tested through the course of this work that positively impact technological advancement of Sandia National Labs. Lastly, all of the above work will converge to yield a well-rounded perspective that ties the three categories of research together.

42 ENGINEERING↗

DOE OSTI2021

Massively Parallel Capability in Sierra/SD for Simulation Vibration with Piezoelectrics

Sierra/SD is an engineering structural dynamics code that provides Sandia and other customers a tool to model structural and acoustic physics on large complex physical systems using massively parallel processing. This report provides a detailed overview on Sierra/SD’s most recent physics package: coupled electro-mechanical physics. This capability uses the finite element method to model coupled electro-mechanical physics exhibited by piezoelectric materials. This report provides an applications overview, theory overview, and verification examples demonstrating the electro-mechanical physics modeling capabilities of Sierra/SD.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIESTA a Fatigue Solution: User's and Theory Manual

This report documents the fatigue code SIESTA that has been used for recently here at Sandia National Laboratories. It is written in two parts: the first as a user manual and the second as a theory manual. Currently employed in SIESTA are stress-life cycle approaches. Clients have requested the use of standards in particular analyses; therefore, the American Society of Mechanical Engineers, Boiler Pressure Vessel Code fatigue standards have been implemented. These include an elastic, an elastic-plastic, and a weld fatigue method. All three methods use a Max-Min cycle counting method that is appropriate for non-proportional loading. A Signed von Mises method that used a Rainflow Cycle Counting Method is also implemented. The Signed von Mises with the Rainflow Cycle Counting Method is appropriate for proportional loading. Several verification examples are noted and include comparisons to experimental data.

42 ENGINEERING↗

DOE OSTI2026

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING↗

DOE OSTI2025

Reported Energy and Cost Savings from the DOE ESPC IDIQ Program: FY 2024

Energy Savings Performance Contracts (ESPCs)are a contractual mechanism that allow a federal agency to procure energy savings and facility improvements without upfront capital costs to reduce costs and resiliency. ESPCs are covered under FAR Part 23.2, and 42 USC § 8287. Section 8287(a)(2)(A) of Title 42 of the U.S. Code requires that each energy savings performance contract (ESPC) undergo an annual energy audit, resulting in a separate audit report for every project. The objective of the present report is to compile and analyze all annual ESPC audit reports issued between October 1, 2023, and September 30, 2024, for projects awarded under Generations 1, 2, and 3 of DOE’s ESPC IDIQ contracts. During this period, 205 measurement and verification (M&V) reports were produced for 200 projects; the total number of reports exceeds the number of projects because some projects generated more than one report(for example, a few projects measure savings twice per year and produce two audit reports annually, each covering a different six-month period). By aggregating the results from these individual audits, the report determines the portfolio-wide realization rate of energy and cost savings for all active ESPC projects awarded under DOE’s IDIQ program. For all 205audit reports, sufficient information was available to compare project-level estimated, reported, and guaranteed cost savings. Reported cost savings accounted for ESCO verified savings per each project’s M&V plan. The total reported cost savings for the period addressed were $\$$647.8million,compared with the total guaranteed cost savings of $\$$601.6million. On average across the reported projects: •ESPC contractors guaranteed 92.8% of the estimated cost savings• projects reported achieving 100.0% of the estimated cost savings• projects reported achieving 107.7% of the guaranteed cost savings. The M&V performed for the period indicated adjustments for government operations and maintenance impacts to savings amount to$\$$43.9millionandcould be restored with the original operational parameters for impacted projects. Accounting for this potential cost savings impact, these projects still realized 100.4% of the guaranteed cost savings. The information on estimated and reported energy savings was collected and compared for all 205of the reports examined. Based on site energy, estimated savings totaled 14.88million MMBtu, and reported savings were 15.33million MMBtu; 3.1% greater than the estimated energy savings. All of the reports examined contained sufficient information to calculate source energy savings. Based on site-adjusted source energy, total estimated energy savings were 20.90 million MMBtu, and reported savings were 21.22million MMBtu, 101.5% of the estimated energy savings. For water savings, the estimated savings were 11,539,055 kGal and the reported savings were 13,315,930 kGal. This means 1,776,875 kGal more water was saved than estimated, which is about 15% higher than the estimate. These results indicate that, overall, the reported energy savings slightly exceeded the estimated values, while estimated water savings significantly exceeded estimated values, suggesting that the projects achieved greater cost savings than originally projected. The total annual expense for the ESCOs to perform annual M&V audits and reporting was $\$$10.02million. Through this effort, $\$$647.8 million in annual cost savings was verified. The M&V results indicated that $\$$43.9 million of these verified savings reflected adjustments due to government operations A-6and maintenance impacts, which could be restored under the original operational parameters for the affected projects. These findings show the value of M&V that only costs 1.7%of the guaranteed cost savings to ensure guarantees are met.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Reported Energy and Cost Savings from the DOE ESPC IDIQ Program: FY 2024

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS2001

Progressive Fracture of Composite Structures

This report includes the results of a research in which the COmposite Durability STRuctural ANalysis (CODSTRAN) computational simulation capabilities were augmented and applied to various structures for demonstration of the new features and verification. The first chapter of this report provides an introduction to the computational simulation or virtual laboratory approach for the assessment of damage and fracture progression characteristics in composite structures. The second chapter outlines the details of the overall methodology used, including the failure criteria and the incremental/iterative loading procedure with the definitions of damage, fracture, and equilibrium states. The subsequent chapters each contain an augmented feature of the code and/or demonstration examples. All but one of the presented examples contains laminated composite structures with various fiber/matrix constituents. For each structure simulated, damage initiation and progression mechanisms are identified and the structural damage tolerance is quantified at various degradation stages. Many chapters contain the simulation of defective and defect free structures to evaluate the effects of existing defects on structural durability.

Minnetyan, Levon↗

NASA NTRS2003

Experimental Evaluation of Verification and Validation Tools on Martian Rover Software

To achieve its science objectives in deep space exploration, NASA has a need for science platform vehicles to autonomously make control decisions in a time frame that excludes intervention from Earth-based controllers. Round-trip light-time is one significant factor motivating autonomy capability, another factor is the need to reduce ground support operations cost. An unsolved problem potentially impeding the adoption of autonomy capability is the verification and validation of such software systems, which exhibit far more behaviors (and hence distinct execution paths in the software) than is typical in current deepspace platforms. Hence the need for a study to benchmark advanced Verification and Validation (V&V) tools on representative autonomy software. The objective of the study was to access the maturity of different technologies, to provide data indicative of potential synergies between them, and to identify gaps in the technologies with respect to the challenge of autonomy V&V. The study consisted of two parts: first, a set of relatively independent case studies of different tools on the same autonomy code, second a carefully controlled experiment with human participants on a subset of these technologies. This paper describes the second part of the study. Overall, nearly four hundred hours of data on human use of three different advanced V&V tools were accumulated, with a control group that used conventional testing methods. The experiment simulated four independent V&V teams debugging three successive versions of an executive controller for a Martian Rover. Defects were carefully seeded into the three versions based on a profile of defects from CVS logs that occurred in the actual development of the executive controller. The rest of the document is structured a s follows. In section 2 and 3, we respectively describe the tools used in the study and the rover software that was analyzed. In section 4 the methodology for the experiment is described; this includes the code preparation, seeding of defects, participant training and experimental setup. Next we give a qualitative overview of how the experiment went from the point of view of each technology; model checking (section 5), static analysis (section 6), runtime analysis (section 7) and testing (section 8). The find section gives some preliminary quantitative results on how the tools compared.

Brat, Guillaume↗

DOE OSTI2023

Modeling The DLOFC Accident Scenario of HTR-PM Equilibrium Core Using NEAMS Tools

High-Temperature Gas-cooled Reactors (HTGRs) have excellent characteristics in terms of safety and high thermal efficiency, and they are gaining a large interest from the industry as a candidate of Gen-IV reactors for a wide range of applications. The High Temperature gas-cooled Reactor Pebble-bed Module project (HTR-PM) is one of these designs and where helium gas is used to cool the pebble-bed region that consists of spherical fuel elements moderated with graphite. The HTR-PM design is based on the combined experience from the German pebble-bed reactor program from the 1960s through the 1990s and the HTR-10 experience in China during the 2000s. Idaho National Laboratory has a long experience in modeling of HTGRs working in developing neutronics and thermal hydraulics tools for the proper modeling of these reactors. The neutronics code Griffin has the capability to model pebble depletion . While the thermal hydraulics code Pronghorn was developed mainly to model the pebble bed reactors with the porous media assumption. In this work, an equilibrium core Multiphysics model was developed for the HTR-PM reactor to analyze the depressurized loss of forced cooling accident scenario (DLOFC). This paper is organized as follows: First, a brief description of the reactor and model specifications are provided. Then, the developed Multiphysics model is discussed. Finally, verification results of the steady-state equilibrium core and DLOFC accident are presented followed by a summary of the conclusions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Metallic fuel transient fuel-cladding interface liquefaction model assessment platform enabled by integrating BISON with databases

A novel platform has been developed within the BISON fuel performance code to assess models of fuel-cladding interface liquefaction for sodium-cooled fast reactor (SFR) metallic fuels. Here, this platform is crucial because liquefaction at the fuel-cladding interface significantly impacts fuel performance and may compromise fuel pin integrity during transient events. To ensure accurate predictions, the platform integrates data collected during the Integral Fast Reactor (IFR) program, now archived in metallic fuel databases. This integration supports verification and validation (V&V) of the models in BISON. Leveraging the extensive US experience with metallic fuel liquefaction and the collections of preserved legacy data, the platform serves as a powerful tool for evaluating existing models and advancing the development of new ones.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1996

Propellant Chemistry for CFD Applications

Current concepts for reusable launch vehicle design have created renewed interest in the use of RP-1 fuels for high pressure and tri-propellant propulsion systems. Such designs require the use of an analytical technology that accurately accounts for the effects of real fluid properties, combustion of large hydrocarbon fuel modules, and the possibility of soot formation. These effects are inadequately treated in current computational fluid dynamic (CFD) codes used for propulsion system analyses. The objective of this investigation is to provide an accurate analytical description of hydrocarbon combustion thermodynamics and kinetics that is sufficiently computationally efficient to be a practical design tool when used with CFD codes such as the FDNS code. A rigorous description of real fluid properties for RP-1 and its combustion products will be derived from the literature and from experiments conducted in this investigation. Upon the establishment of such a description, the fluid description will be simplified by using the minimum of empiricism necessary to maintain accurate combustion analyses and including such empirical models into an appropriate CFD code. An additional benefit of this approach is that the real fluid properties analysis simplifies the introduction of the effects of droplet sprays into the combustion model. Typical species compositions of RP-1 have been identified, surrogate fuels have been established for analyses, and combustion and sooting reaction kinetics models have been developed. Methods for predicting the necessary real fluid properties have been developed and essential experiments have been designed. Verification studies are in progress, and preliminary results from these studies will be presented. The approach has been determined to be feasible, and upon its completion the required methodology for accurate performance and heat transfer CFD analyses for high pressure, tri-propellant propulsion systems will be available.

Farmer, R. C.↗

NASA NTRS1999

Verification and Analysis of Formulation 4 of Langley for the Study of Noise From High Speed Surfaces

There are several approaches to the prediction of the noise from sources on high speed surfaces. Two of these are the Kirchhoff and the Ffowcs williams-Hawkings methods. It can be shown that both of these methods depend on the solution of the wave equation with mathematically similar inhomogeneous source terms. Two subsonic solutions known as Formulation 1 and 1A of Langley are simple and efficient for noise prediction. The supersonic solution known as Formulation 3 is very complicated and difficult to code. Because of the complexity of the result, the computation time is longer than the subsonic formulas. Furthermore, it is difficult to assess the accuracy of noise prediction. We have been searching for a new and simpler supersonic formulation without these shortcomings. In the last AIAA Aeroacoustics Conference in Toulouse, Farassat, Dunn and Brentner presented a paper in which such a result was presented and called Formulation 4 of Langley. In this paper we will present two analytic tests of the validity this Formulation: 1) the noise from dipole distribution on the unit circle whose strength varies radially with the square of the distance from the center and 2) the noise from dipole distribution on the unit sphere whose strength varies with the cosine of the angle from the polar axis. We will discuss the question of singularities of Formulation 4.

Farassat, F.↗

DOE OSTI2024

Photonuclear Physics in SCALE

Radiation shielding modeling involves a wide range of applications, such as power reactors, critical experiments, portable sources, linear accelerators, and fusion systems. Particle energy ranges vary from thermal energies to fast energy spectra. MAVRIC, as the radiation shielding sequence of the SCALE code system [1] developed and maintained by Oak Ridge National Laboratory, is capable of modeling both neutron and photon interactions in matter and is widely used by the US Nuclear Regulatory Commission, Department of Energy, the National Nuclear Security Administration, and radiation shielding practitioners all around the world. Although most applications don’t involve highly energetic photons that can cause photonuclear reactions and create coupled chains of high energy, ionized electrons and bremsstrahlung radiation within a material medium, when present, these reactions can have a significant impact upon the downstream particle fluxes from incident photons above 20 MeV. For example, linear accelerators used for medical isotope production are examples of applications in which high-energetic photons are generated and used for driving or controlling other components of a complex facility. Radiation shielding analyses of such a facility would require accounting for any and all significant sources of radiation. Unfortunately, MAVRIC included no data and methods to model either photonuclear reactions or the bremsstrahlung photons until this work, which enabled accounting for both. Photonuclear reaction cross sections were imported from the Evaluated Nuclear Data File libraries, and corresponding methods were implemented in the SCALE code system; see Section 2 for how the nuclear data are imported and used. Bremsstrahlung photons were modeled by assuming thick-target approximation whereby all generated electrons and positrons due to photon interactions are assumed to be absorbed within the same material in which they were born, yielding a quick particle transport simulation method by using fast lookup tables for generating subsequent gammas; see Section 4 for details. A suite of verification models was used to test implemented methods and associated data. Tests yielded satisfactory results for the new features. Enhancements will be released as part of the next major SCALE release (v7.0), which is anticipated to be deployed in 2025, with beta releases available in the interim.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2014

IKOS: A Framework for Static Analysis based on Abstract Interpretation (Tool Paper)

The RTCA standard (DO-178C) for developing avionic software and getting certification credits includes an extension (DO-333) that describes how developers can use static analysis in certification. In this paper, we give an overview of the IKOS static analysis framework that helps developing static analyses that are both precise and scalable. IKOS harnesses the power of Abstract Interpretation and makes it accessible to a larger class of static analysis developers by separating concerns such as code parsing, model development, abstract domain management, results management, and analysis strategy. The benefits of the approach is demonstrated by a buffer overflow analysis applied to flight control systems.

Abstract Interpretation↗

DOE OSTI2022

SCALE Modeling of the Fast Spectrum Heat Pipe Reactor

As part of the severe accident analysis collaboration with Sandia National Laboratories (SNL) and the Nuclear Regulatory Commission (NRC), SCALE models were developed for a fast-spectrum heat pipe reactor. These models were based on the Idaho National Laboratory (INL) Design A concept, which is an alternative design to the Los Alamos National Laboratory (LANL) Special Purpose Reactor (SPR), also known as the Megapower reactor. The model contains 1,134 heat pipes, surrounded by hexagonal fuel elements, with a potassium working fluid; the fuel is UO 2 with 19.75 wt% 235 U enrichment. The model contains axial beryllium oxide (BeO) reflectors above and below the active fuel region along with a radial alumina reflector containing 12 B 4 C control drums. The center of the core is left unfueled to make room for two shutdown control rods, one annular and one solid. The active region of the core was discretized into twenty axial and five radial zones to analyze spatial variations in power and burnup. Infinite lattice unit cell sensitivity studies were used to perform verification between the SCALE and INL models. The eigenvalue results agreed well with the reported results to within roughly 50 percent mille (pcm). Full-core model verification was performed by analyzing system eigenvalues with differing configurations of control drum and shutdown rod positions. These full core results all had eigenvalue differences less than 310 pcm. Control drum and shutdown rod worths were also compared, with differences of 3.2% or less. Using the verified model, the isotopic inventory and decay heat, as well as temperature feedback coefficients, were calculated and provided to SNL as input to the MELCOR severe accident code to analyze potential releases from this class of reactor. The results of the MELCOR analysis are provided in a different report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1982

Constitutive model development for isotropic materials

The objective is to develop a unified constitutive model for finite-element structural analysis of turbine engine hot section components. This effort constitutes a different approach for nonlinear finite-element computer codes which were heretofore based on classical inelastic methods. A unified constitutive theory will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. Model development will be directed toward isotropic, cast nickel-base alloys used for aircooled turbine blades and vanes. The contractor will select a base material for model development and an alternate material for verification purposes from a list of three alloys specified by NASA. The candidate alloys represent a cross-section of turbine blade and vane materials of interest to both large and small size engine manufacturers. Material stock for the base and alternate materials will be supplied to the Contractor by the government.

Kaufman, A.↗