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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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Brislawn, Kristi D.↗
DOE OSTI2020

ISOCS-based Extended In Situ Gamma Spectrometry Services Tool SuperISOCS for Waste Measurements - 20275

Canberra's In Situ Object Counting System (ISOCS) is an established tool used for gamma spectrometry. It allows physical representation of complex geometries and mathematical calculation of the calibration function while avoiding the need for radioisotope standards. ISOCS provides a large range of templates to generate the geometry for most nuclear waste components in nuclear facilities. Nonetheless, there are some complex geometries where the accuracy attainable is limited by the conventional ISOCS templates. An ISOCS-based extended in-situ Gamma Spectrometry service tool has been developed, based on the so-called SuperISOCS (SISOCS) software. This tool was developed to generate the most complex geometries. The principle of geometry construction is based on the composition of 8 different primitive geometries. The primitive object is able to be cut and to change a part of an object. An object is able to overlap to another one to form a more complex object. These functions refine the modelled geometry compared to the real objects and decrease the measurement systematic error because they allow the mathematical model to represent the real-life geometry more faithfully through reducing the approximations and simplifications that need to be made The algorithm of SISOCS is the same as that of standard ISOCS. A set of calculations was done in comparison with MCNP efficiency calculation and SISOCS results. 80 different models were compared between SISOCS and MCNP, with added 30 cases compared between ISOCS and SISOCS. The average differences were less than 2%, for all energy's efficiency calculations. In this paper we illustrate the benefits that this new tool can provide, in terms of improved accuracy for complex realistic geometries, through simulation of some example scenarios. Furthermore, we demonstrate, through SISOCS modelling of the real object data test, the comparison between SISOCS to ISOCS calculations for the same geometry. This paper describes the added functions that are easily employed using SISOCS. Our results show the potential application and benefit of this technique for real waste assay projects and the way to integrate the tool into the waste assay systems. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Pan, Wenxiao↗
NASA NTRS1986

Application of a full potential method for analysis of complex aircraft geometries

A supersonic potential flow solver was developed to analyze the flow over complex realistic aircraft geometries. Enhancements to the method were made to accommodate regions of subsonic flow, the effect of trailing wakes on other aircraft components, and the modeling/gridding of complete configurations. Validation of the method was demonstrated by comparisons with experimental aerodynamic force and surface pressure measurements. The predicted results are in very good agreement with the experimental data. The bibliography contains additional information on the use of the potential flow code to predict the aerodynamics of high-speed wing/body configurations, waverider concepts, TAV, and the Space Shuttle orbiter package.

Jones, Kenneth M.↗
NASA NTRS2015

Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry

The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.

Wilson, John W.↗
DOE OSTI2022

MOOSE Reactor Module Meshing Enhancements to Support Reactor Physics Analysis

The U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program develops an integrated suite of advanced reactor physics tools built upon the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Each code generally requires an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The meshing process is often burdensome for the complex geometries present in reactors due to lack of easy-to-use, open-source meshing tools. To address the bottleneck associated with meshing complex geometries found in nuclear reactors, NEAMS initiated the development of the MOOSE Reactor Module starting in FY21. The Reactor Module builds off the existing MOOSE Mesh System to include targeted meshing capabilities such as the ability to generate hexagonal pin cells, assemblies with ducts, rotating control drums, cores, peripheral zones around a core, as well as the automatic labeling (“reporting IDs”) of pin, assembly, and planar zones to simplify post-processing of results. As a Physics Module in MOOSE, the Reactor Module is open-source, available with any MOOSE installation, directly compatible with MOOSE-based tools, and can be invoked from MOOSEbased applications to generate meshes. Functionality from the Reactor Module has been applied to several advanced reactor concepts to demonstrate user workflow improvements and accuracy. The primary objective of the Reactor Module is to improve useability of MOOSEbased tools by streamlining mesh generation and output inspection processes. During FY22, the functionality of the Reactor Module (and accompanying Mesh System) has been expanded based on user needs. First, the Reactor Geometry Mesh Builder capability developed primarily in FY21 has been refactored and merged to the public MOOSE repository. This capability wraps underlying Reactor Module mesh generators into a “Pin – Assembly – Core” workflow appropriate for conventional Cartesian and hexagonal geometries, and notably assigns material IDs during mesh generation stage and generates only the minimal number of blocks needed in order to reduce computational burden. Biasing and boundary layer options have been added to the base mesh generators as required by thermal hydraulics solvers. The reporting ID functionality has been expanded to differentiate ring-wise and azimuthal sectors within a pin for use with depletion algorithms, and VectorPostProcessor and Reporter objects are now available to integrate solution variables across zones based on ID combinations. Functionality to trim hexagonal meshes along the center or periphery has been developed so users may leverage symmetry and reflective boundary conditions to reduce the mesh size. A flexible and powerful tool to fill the space between two sidesets has been introduced to the framework and can be used for transition layers such as stitching two assemblies together with different numbers of pins, or for complex geometries which do not follow conventional Cartesian/hexagonal patterns. Finally, additional verification problems were performed with NEAMS physics tools in complement with existing NEAMS work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

In this work, we propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Numerical Modeling of a Vortex Stabilized Arcjet

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Pawlas, Gary E.↗
NASA NTRSDate not supplied

LAVA Voronoi Mesher for Wall-Modeled Large-Eddy Simulations

The unstructured Voronoi mesher currently being developed within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) software framework at NASA Ames Research Center is described in detail. The discussions include, but are not limited to, the strategies used in the seeding and smoothing phases to ensure a high-quality mesh for Wall-Modeled Large-Eddy Simulations (WMLES), the methods behind the cell clipping algorithm responsible for conforming the mesh to a complex geometry, and the approach to create a global mesh from the distinct Voronoi cells. Applications and benefits of the Voronoi meshing approach are also presented. The automated meshing paradigm introduced was able to significantly reduce the time necessary to create a high-quality mesh around a complex geometry when compared against the current LAVA curvilinear overset meshing standard. For example, the task of generating a single mesh around the high-lift common research model requires the full dedication of a mesh generation expert for a period between one and two months. A family of meshes with different refinement levels up to six hundred million cells can be generated by a single engineer in a day or two. This technology has the potential for decreasing the turnaround time for conducting WMLES around complex geometries, as well as facilitating comprehensive mesh refinement studies.

Victor C B Sousa↗
NASA NTRS1994

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. These algorithms are now used in the practical engineering design of devices such as cars and airplanes as well as theoretical studies of complex phenomena such as fluid turbulence. In past years, limited computer resources have motivated the development of efficient numerical methods in computational fluid dynamics (CFD) utilizing structured meshes. These meshes are comprised of systematic arrays of quadrilateral or hexahedral cells. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Structured meshes also permit the use of highly efficient solution techniques such as alternating direction implicit (ADI) iteration schemes or multigrid. Following the dramatic improvement in computing speed in recent years, emphasis has shifted towards the design of algorithms capable of treating complex geometries. The automatic generation of structured grids about complex geometries is problematic. Unstructured grids offer one promising alternative technique for treating these general geometries. Unstructured meshes have irregular connectivity and usually contain triangles and/or quadrilaterals in two dimensions and tetrahedra and/or hexahedra in three dimensions. The generation and use of unstructured grids poses new challenges in computational fluid dynamics. This is true for both grid generation as well as for the design of algorithms for flow solution. The purpose of these notes is to present recent developments in the unstructured grid generation and flow solution technology.

Barth, T. J.↗
DOE OSTI2017

An electrostatic Particle-In-Cell code on multi-block structured meshes

We present an electrostatic Particle-In-Cell (PIC) code on multi-block, locally structured, curvilinear meshes called Curvilinear PIC (CPIC). Multi-block meshes are essential to capture complex geometries accurately and with good mesh quality, something that would not be possible with single-block structured meshes that are often used in PIC and for which CPIC was initially developed. In spite of the structured nature of the individual blocks, multi-block meshes resemble unstructured meshes in a global sense and introduce several new challenges, such as the presence of discontinuities in the mesh properties and coordinate orientation changes across adjacent blocks, and polyjunction points where an arbitrary number of blocks meet. In CPIC, these challenges have been met by an approach that features: (1) a curvilinear formulation of the PIC method: each mesh block is mapped from the physical space, where the mesh is curvilinear and arbitrarily distorted, to the logical space, where the mesh is uniform and Cartesian on the unit cube; (2) a mimetic discretization of Poisson's equation suitable for multi-block meshes; and (3) a hybrid (logical-space position/physical-space velocity), asynchronous particle mover that mitigates the performance degradation created by the necessity to track particles as they move across blocks. The numerical accuracy of CPIC was verified using two standard plasma–material interaction tests, which demonstrate good agreement with the corresponding analytic solutions. And compared to PIC codes on unstructured meshes, which have also been used for their flexibility in handling complex geometries but whose performance suffers from issues associated with data locality and indirect data access patterns, PIC codes on multi-block structured meshes may offer the best compromise for capturing complex geometries while also maintaining solution accuracy and computational efficiency.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Freeform thermoelectrics in single-step manufacturing: additive manufacturing of bismuth-telluride thermoelectrics

The project succeeded in producing crack-free Bismuth Telluride thermoelectric parts with density exceeding 98% through laser powder bed fusion (LPBF) additive manufacturing (AM). This greatly exceeded the highest previously reported density of 88% and is the highest among all semiconducting materials processed by LPBF. The additively manufactured material shows comparable Seebeck coefficient as conventional form and can be made into complex geometries with reduced material loss. On the other hand, measured properties are dramatically sensitive to the AM process parameters used, such that with identical composition, the Seebeck coefficient can be controllably tuned from +120 µV/K to -207 µV/K, which means the material switches between an n-type to a p-type semiconductor depending on processing. These changes are accompanied by significant differences in the as-processed microstructure due to rapid solidification. A machine learning protocol was developed and greatly reduced the experimental burden of the project, reducing the typical process optimization period of 2 years to 6 months. The project was fully successful in the objective of producing defect-free, complex geometry of bismuth-telluride parts through LPBF, but only partially successful in achieving performance goals. First, cost reduction of manufacturing, as measured by material waste, was successfully reduced by up to 70% compared to conventional manufacturing methods. This exceeded the proposed 30% reduction in materials waste needed to reach the 20% cost reduction goal of the project. On the other hand, the device performance, as measured by Seebeck coefficient, failed to reach the 40% improvement in efficiency. Rather, we observe comparable Seebeck coefficient between AM samples and conventionally processed counterparts. The device-level efficiency improvement does exceed 40% for complex geometry samples due to shape-induced increase in temperature gradients, but this was not the originally proposed metric. The machine learning approach developed in this project greatly accelerated the process optimization and can be adopted for fast development of AM processing parameters for other brittle and otherwise difficult-to-print materials. For the public, we deliver an efficient and widely adoptable process for incorporating waste-heat harvesting thermoelectric devices in both industrial and commercial heat exchangers. The geometric flexibility allows the capturing device to conform to the shape of the heat source to improve the system-level conversion efficiency. The technique can be deployed on any commercial LBPF systems with zero modifications, thus poses minimal adoption barrier for any manufacturer that already employed AM technology. Beyond bismuth-telluride, the machine-learning guided optimization protocol can be used in the future to reduce both the time and cost of process development for AM of other energy conversion and harvesting materials.

36 MATERIALS SCIENCE↗
DOE OSTI2019

First Annual Report on Pulsed Thermal Tomography Nondestructive Evaluation of Additively Manufactured Reactor Materials and Components: Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components

Additive manufacturing (AM, or 3D printing) for commercial nuclear energy applications is an emerging method for cost-efficient manufacturing aimed at replacing aging nuclear reactor parts and reducing costs for new construction. Because of the geometry of metallic structures of interest for nuclear applications, which consist of planar primitives with no symmetry of revolution, limited options are available for nondestructive evaluation (NDE), either during or post manufacturing. Known material flaws in AM include low-density regions consisting of non-sintered powder, which have to be detected to ensure the safety of long-term performance nuclear reactor components. As a solution to NDE of AM, we are developing pulsed thermal tomography (PTT) models and depth inversion algorithms for 3D imaging. PTT has many advantages because the method is non-contact and allows for in-service, NDE of AM nuclear reactor parts. By analyzing transients of surface temperature response due to internal thermal resistances, one can obtain 3D reconstructions of material effusivity using a unique inversion algorithm developed at Argonne. This report provides results of preliminary performance evaluation of PTT capability in detection of flaws in metallic structures, as well imaging complex geometry AM structures. Performance of PTT was investigated through modeling and experiments, Computer models of PTT were developed using COMSOL Heat Transfer module. Defects were modeled as cylindrical flat bottom holes (FBH), which is a common model of calibrated material flaws in thermal tomography experiments. Materials considered in this study include stainless steel 316 (SS316), stainless steel 304 (SS304), and Inconel 718. Theoretical analyses were conducted to validate inversion of simulated PTT data with COMSOL for a plate. Subsequently, 3D reconstructions were performed on COMSOL simulations for FBH, revealing a decrease in spatial resolution over depth due to thermal diffusion. The results of this study show that the performance of the inversion algorithm for detecting smaller defects depends strongly on the depth of the defect as well as the incident heat flux. The size of detectable defect was estimated by fitting a Gaussian function to surface temperature profile. The criteria for detectability was taken as 20mK noise equivalent temperature difference (NETD), which is currently the sensitivity limit of high-performance infrared cameras. It was determined through computer simulations that the smallest detectable FBH in SS316 has a 50µm diameter and is located 0.5mm below the plate surface. Preliminary experimental studies were performed to evaluate PTT performance in detecting calibrated flaws using metallic specimens with AM defects simulated as drilled-in FBH’s. High strength Stainless Steel 316 and Inconel 718 alloys were considered, as well as lower grade Stainless Steel 304, Nickel 200, and Hastelloy C276. Specimens investigated in this report consisted of approximately 1/4in-thick plates made out of these alloys using conventional manufacturing methods. The diameters of FBH’s varied from 1mm to 8mm, and their depths below the plate flat surface varied between 1mm and 6mm. The size of the smallest FBH was limited to 1mm because conventional mechanical drills were used for creating the holes. PTT imaging results have shown that 1mm-diameter FBH located 1mm and 2mm below the surface were detectable. Larger size FBH were detectable at greater depth. For example, 6mm-diameter FBH could be detected at 8mm depth. Image contrast varied slightly between the specimens, with the best reconstructions obtained in SS316 and C276 plates. Finally, PTT capability in imaging several AM structures fabricated from Inconel 718 (IN718) powder feedstock was investigated. The AM structures have complex geometry, but do not have calibrated internal defects. The objective is to determine PTT settings, such as the total integration time, for imaging of representative AM structures. A new FLIR X8500sc IR camera with higher spatial resolution (1280x1024 at 181Hz frame rate) was integrated into the PTT laboratory setup. Software tools were developed to ensure compatibility of new camera files with legacy effusivity reconstruction codes. The new camera was used to obtain 3-D reconstructions of AM IN718 nozzle plate and a particle filter plate. It was shown that PTT can scan through 2/3in-thick Inconel 718 plates in approximately 15s. Several modes of 3-D data visualization were explored, including using ImageJ and MATLAB software packages. The results demonstrate the capability of PTT in 3-D imaging of complex geometry AM structures. Intermediate results demonstrated in this report will be developed further to investigate detection of flaws in AM specimens.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1992

A comparative study of turbulence models for overset grids

The implementation of two different types of turbulence models for a flow solver using the Chimera overset grid method is examined. Various turbulence model characteristics, such as length scale determination and transition modeling, are found to have a significant impact on the computed pressure distribution for a multielement airfoil case. No inherent problem is found with using either algebraic or one-equation turbulence models with an overset grid scheme, but simulation of turbulence for multiple-body or complex geometry flows is very difficult regardless of the gridding method. For complex geometry flowfields, modification of the Baldwin-Lomax turbulence model is necessary to select the appropriate length scale in wall-bounded regions. The overset grid approach presents no obstacle to use of a one- or two-equation turbulence model. Both Baldwin-Lomax and Baldwin-Barth models have problems providing accurate eddy viscosity levels for complex multiple-body flowfields such as those involving the Space Shuttle.

Renze, Kevin J.↗
NASA NTRS1973

Methods of treating complex space vehicle geometry for charged particle radiation transport

Current methods of treating complex geometry models for space radiation transport calculations are reviewed. The geometric techniques used in three computer codes are outlined. Evaluations of geometric capability and speed are provided for these codes. Although no code development work is included several suggestions for significantly improving complex geometry codes are offered.

Hill, C. W.↗
DOE OSTI2023

Athena-I CUBIT Journal Files

The Monte Carlo N-Particle (MCNP)1 transport code version 6 (also known as MCNP6) has the capability for tracking particles on unstructured mesh (UM) geometry models embedded into con structive solid geometry (CSG) cells. This feature has been developed for performing calculations of complex geometry models because manually creating CSG models is a time-consuming and error prone process as the complexities of geometries increase. The UM capability was originally designed to work with UM models created with the Abaqus software and ASCII input files that it generates. The MCNP code version 6.0 and later can process UM models formatted as Abaqus input files. Starting with version 6.3, MCNP can also process HDF5 mesh input files. External codes must be used to generate Abaqus input files for MCNP UM calculations. CUBIT, the Sandia National Laboratory automated mesh generation toolkit, can generate a UM model formatted as an Abaqus input file. However, the Abaqus input files exported from CUBIT cannot be used for MCNP simulations because it lacks the proper syntax. A Python script was developed to convert an Abaqus file created by CUBIT to an Abaqus file format that MCNP can process. Creating UM models for complex geometries is not an easy task. The process of creating UM models in CUBIT for MCNP simulations is detailed in. CUBIT provides several user interface options including a graphical user interface (GUI) and a command line interface. A GUI provides an easy way to use CUBIT without learning the CUBIT command syntax. When using CUBIT with either interface option, command lines are written into an ASCII file known as a journal file; this journal file can be edited and archived so that it can be played back in CUBIT to automatically generate a UM model. This report describes the CUBIT journal files of the UM models developed for Athena-I. The Athena platform, an energy-tuning assembly, was developed to spectrally shape the National Ignition Facility (NIF) deuterium-tritium fusion neutron source to a thermonuclear (fusion) plus prompt fission neutron spectrum with capability to act as a short-pulse neutron source. MCNP6 was used for the Athena experiment design analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2003

CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method

A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.

Nemec, Marian↗