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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Use of a Hybrid Edge Node-Centroid Node Approach to Thermal Modeling

A recent proposal submitted for an ESA mission required that models be delivered in ESARAD/ESATAN formats. ThermalDesktop was the preferable analysis code to be used for model development with a conversion done as the final step before delivery. However, due to some differences between the capabilities of the two codes, a unique approach was developed to take advantage of the edge node capability of ThermalDesktop while maintaining the centroid node approach used by ESARAD. In essence, two separate meshes were used: one for conduction and one for radiation. The conduction calculations were eliminated from the radiation surfaces and the capacitance and radiative calculations were eliminated from the conduction surfaces. The resulting conduction surface nodes were coincident with all nodes of the radiation surface and were subsequently merged, while the nodes along the edges remained free. Merging of nodes on the edges of adjacent surfaces provided the conductive links between surfaces. Lastly, all nodes along edges were placed into the subnetwork and the resulting supernetwork included only the nodes associated with radiation surfaces. This approach had both benefits and disadvantages. The use of centroid, surface based radiation reduces the overall size of the radiation network, which is often the most computationally intensive part of the modeling process. Furthermore, using the conduction surfaces and allowing ThermalDesktop to calculate the conduction network can save significant time by not having to manually generate the couplings. Lastly, the resulting GMM/TMM models can be exported to formats which do not support edge nodes. One drawback, however, is the necessity to maintain two sets of surfaces. This requires additional care on the part of the analyst to ensure communication between the conductive and radiative surfaces in the resulting overall network. However, with more frequent use of this technique, the benefits of this approach can far outweigh the additional effort.

Peabody, Hume L.↗
NASA NTRS2010

Use of a Hybrid Edge Node-Centroid Node Approach to Thermal Modeling

A recent proposal submitted for an ESA mission required that models be delivered in ESARAD/ESAT AN formats. ThermalDesktop was the preferable analysis code to be used for model development with a conversion done as the final step before delivery. However, due to some differences between the capabilities of the two codes, a unique approach was developed to take advantage of the edge node capability of ThermalDesktop while maintaining the centroid node approach used by ESARAD. In essence, two separate meshes were used: one for conduction and one for radiation. The conduction calculations were eliminated from the radiation surfaces and the capacitance and radiative calculations were eliminated from the conduction surfaces. The resulting conduction surface nodes were coincident with all nodes of the radiation surface and were subsequently merged, while the nodes along the edges remained free. Merging of nodes on the edges of adjacent surfaces provided the conductive links between surfaces. Lastly, all nodes along edges were placed into the subnetwork and the resulting supernetwork included only the nodes associated with radiation surfaces. This approach had both benefits and disadvantages. The use of centroid, surface based radiation reduces the overall size of the radiation network, which is often the most computationally intensive part of the modeling process. Furthermore, using the conduction surfaces and allowing ThermalDesktop to calculate the conduction network can save significant time by not having to manually generate the couplings. Lastly, the resulting GMM/TMM models can be exported to formats which do not support edge nodes. One drawback, however, is the necessity to maintain two sets of surfaces. This requires additional care on the part of the analyst to ensure communication between the conductive and radiative surfaces in the resulting overall network. However, with more frequent use of this technique, the benefits of this approach can far outweigh the additional effort.

Peabody, Hume L.↗
NASA NTRSDate not supplied

Implementation of a Hybrid Edge Node-Centroid Node Approach for the Generation of Reduced Thermal Models

Reduced thermal models are often required for delivery to organizations that manage observatory or launch models at the highest levels of assembly. However, the effort to generate reduced models, and verify against their detailed counterparts, is a challenge that has not yet been conclusively solved. Higher level organizations often place a limit on the number of nodes for delivered models with the assumption that smaller models generally result in less computation time. However, the burden of producing and verifying the accuracy of the reduced models is placed primarily on the lower-level organizations, which in turn consumes resources needed to produce these models. Limiting the total number of allowable nodes may also prevent users from taking full advantage of software capabilities that allow for faster generation of models, such as finite elements, which generally require more nodes than older centroid based models. A methodology using Thermal Desktop was described in 2010 which used: (1) finite elements and edge nodes for a conduction matrix, (2) centroid nodes for capacitance and radiative computations, and (3) the super network feature to produce a conduction matrix based only on the centroid nodes. At that time, the methodology was clear, but the implementation would have had to be done manually; however, with the inclusion of the OpenTD Application Programming Interface, this methodology can now be implemented programmatically and for the first time, be a viable approach for the generation of reduced models. The approach was implemented and developed at the NASA Goddard Space Flight Center (GSFC) for the Capture, Containment, and Return System (CCRS) payload on the Earth Return Orbiter (ERO) as part of the Mars Sample Return mission, resulting in the TCYEE tool. ERO features a spacecraft bus provided by Airbus through the European Space Agency with node limitations on the delivered CCRS model provided by GSFC. TCYEE was used to generate the reduced model for this delivery and the predictions compared favorably to the detailed model currently in use for the thermal performance evaluation. Furthermore, TCYEE is being explored for potential use on the Roman Space Telescope (RST) for the generation of reduced models for delivery to the launch provider, which also has node limit requirements on the RST observatory model for use in launch simulation analyses. This paper describes the methodology, its implementation, and compares the performance of reduced models generated by TCYEE to their detailed counterparts.

Thermal Desktop↗
NASA NTRSDate not supplied

Implementation of a Hybrid Edge Node-Centroid Node Approach for the Generation of Reduced Thermal Models

Reduced thermal models are often required for delivery to organizations that manage observatory or launch models at the highest levels of assembly. However, the effort to generate reduced models, and verify against their detailed counterparts, is a challenge that has not yet been conclusively solved. Higher level organizations often place a limit on the number of nodes for delivered models with the assumption that smaller models generally result in less computation time. However, the burden of producing and verifying the accuracy of the reduced models is placed primarily on the lower-level organizations, which in turn consumes resources needed to produce these models. Limiting the total number of allowable nodes may also prevent users from taking full advantage of software capabilities that allow for faster generation of models, such as finite elements, which generally require more nodes than older centroid based models. A methodology using Thermal Desktop was described in 2010 which used: (1) finite elements and edge nodes for a conduction matrix, (2) centroid nodes for capacitance and radiative computations, and (3) the super network feature to produce a conduction matrix based only on the centroid nodes. At that time, the methodology was clear, but the implementation would have had to be done manually; however, with the inclusion of the OpenTD API, this methodology can now be implemented programmatically and for the first time, be a viable approach for the generation of reduced models. The approach was implemented and developed at the NASA Goddard Space Flight Center (GSFC) for the Capture, Containment, and Return System (CCRS) payload on the Earth Return Orbiter (ERO) as part of the Mars Sample Return (MSR) mission, resulting in the TCYEE tool. ERO features a spacecraft bus provided by Airbus through the European Space Agency (ESA) with node limitations on the delivered CCRS model provided by GSFC. TCYEE was used to generate the reduced model for this delivery and the predictions compared favorably to the detailed model currently in use for the thermal performance evaluation. Furthermore, TCYEE is being explored for potential use on the Roman Space Telescope (RST) for the generation of reduced models for delivery to the launch provider, which also has node limit requirements on the RST observatory model for use in launch simulation analyses. This paper describes the methodology, its implementation, and compares the performance of reduced models generated by TCYEE to their detailed counterparts.

Thermal desktop↗
NASA NTRSDate not supplied

Implementation of a Hybrid Edge Node-Centroid Node Approach for the Generation of Reduced Thermal Models

Reduced thermal models are often required for delivery to organizations that manage observatory or launch models at the highest levels of assembly. However, the effort to generate reduced models, and verify against their detailed counterparts, is a challenge that has not yet been conclusively solved. Higher level organizations often place a limit on the number of nodes for delivered models with the assumption that smaller models generally result in less computation time. However, the burden of producing and verifying the accuracy of the reduced models is placed primarily on the lower-level organizations, which in turn consumes resources needed to produce these models. Limiting the total number of allowable nodes may also prevent users from taking full advantage of software capabilities that allow for faster generation of models, such as finite elements, which generally require more nodes than older centroid based models. A methodology using Thermal Desktop was described in 2010 which used: (1) finite elements and edge nodes for a conduction matrix, (2) centroid nodes for capacitance and radiative computations, and (3) the super network feature to produce a conduction matrix based only on the centroid nodes. At that time, the methodology was clear, but the implementation would have had to be done manually; however, with the inclusion of the OpenTD API, this methodology can now be implemented programmatically and for the first time, be a viable approach for the generation of reduced models. The approach was implemented and developed at the NASA Goddard Space Flight Center (GSFC) for the Capture, Containment, and Return System (CCRS) payload on the Earth Return Orbiter (ERO) as part of the Mars Sample Return (MSR) mission, resulting in the TCYEE tool. ERO features a spacecraft bus provided by Airbus through the European Space Agency (ESA) with node limitations on the delivered CCRS model provided by GSFC. TCYEE was used to generate the reduced model for this delivery and the predictions compared favorably to the detailed model currently in use for the thermal performance evaluation. Furthermore, TCYEE is being explored for potential use on the Roman Space Telescope (RST) for the generation of reduced models for delivery to the launch provider, which also has node limit requirements on the RST observatory model for use in launch simulation analyses. This paper describes the methodology, its implementation, and compares the performance of reduced models generated by TCYEE to their detailed counterparts.

Hume L. Peabody↗
NASA NTRSDate not supplied

Implementation of a Hybrid Edge Node-Centroid Node Approach for the Generation of Reduced Thermal Models

Reduced thermal models are often required for delivery to organizations that manage models at the highest levels of assembly. The effort to generate/verify these models against their detailed counterparts is a challenge not yet conclusively solved. Higher level organizations often place a limit on the node count for delivered models, assuming smaller models result in faster computation. The burden of producing and verifying the accuracy of reduced models is primarily on the lower-level organizations, which consumes resources to produce these models. Limiting the number of allowable nodes may prevent users from taking full advantage of software capabilities that allow for faster generation of models, such as finite elements, which require more nodes than centroid based models. A methodology using Thermal Desktop was described in 2010 using: (1) finite elements and edge nodes for the conduction matrix, (2) centroid nodes for capacitance and radiative computations, and (3) the super network feature to produce a conduction matrix based only on the centroid nodes. While the methodology was clear, the implementation would have had to be done manually; with the inclusion of the OpenTD Application Programming Interface, this methodology can now be implemented programmatically and be a viable approach for the generation of reduced models. The approach was implemented at NASA-Goddard for the Capture-Containment-and-Return-System (CCRS) payload, resulting in the TCYEE tool. CCRS requires delivery with node limitations through the European Space Agency to its contractors. TCYEE generated the reduced model for delivery and the predictions compared favorably to the detailed model. Furthermore, TCYEE is being explored for potential use on the Roman Space Telescope (RST) for the generation of reduced models for delivery to the launch provider, which also has node limit requirements. This paper describes the methodology, implementation, and the performance of reduced models compared to their detailed counterparts.

Computer Programming and Software↗
NASA NTRS2004

A Six-Node Curved Triangular Element and a Four-Node Quadrilateral Element for Analysis of Laminated Composite Aerospace Structures

Mathematical development and some computed results are presented for Mindlin plate and shell elements, suitable for analysis of laminated composite and sandwich structures. These elements use the conventional 3 (plate) or 5 (shell) nodal degrees of freedom, have no communicable mechanisms, have no spurious shear energy (no shear locking), have no spurious membrane energy (no membrane locking) and do not require arbitrary reduction of out-of-plane shear moduli or under-integration. Artificial out-of-plane rotational stiffnesses are added at the element level to avoid convergence problems or singularity due to flat spots in shells. This report discusses a 6-node curved triangular element and a 4-node quadrilateral element. Findings show that in regular rectangular meshes, the Martin-Breiner 6-node triangular curved shell (MB6) is approximately equivalent to the conventional 8-node quadrilateral with integration. The 4-node quadrilateral (MB4) has very good accuracy for a 4-node element, and may be preferred in vibration analysis because of narrower bandwidth. The mathematical developments used in these elements, those discussed in the seven appendices, have been applied to elements with 3, 4, 6, and 10 nodes and can be applied to other nodal configurations.

Martin, C. Wayne↗
NASA NTRS2011

Connecting node and method for constructing a connecting node

A connecting node comprises a polyhedral structure comprising a plurality of panels joined together at its side edges to form a spherical approximation, wherein at least one of the plurality of panels comprises a faceted surface being constructed with a passage for integrating with one of a plurality of elements comprising a docking port, a hatch, and a window that is attached to the connecting node. A method for manufacturing a connecting node comprises the steps of providing a plurality of panels, connecting the plurality of panels to form a spherical approximation, wherein each edge of each panel of the plurality is joined to another edge of another panel, and constructing at least one of the plurality of panels to include a passage for integrating at least one of a plurality of elements that may be attached to the connecting node.

Johnson, Christopher J.↗
DOE OSTI2025

Comparing cross-platform performance via node-to-node scaling studies

Due to the increasing diversity of high-performance computing architectures, researchers and practitioners are increasingly interested in comparing a code’s performance and scalability across different platforms. However, there is a lack of available guidance on how to actually set up and analyze such cross-platform studies. In this paper, we contend that the natural base unit of computing for such studies is a single compute node on each platform and offer guidance in setting up, running, and analyzing node-to-node scaling studies. In conclusion, we propose templates for presenting scaling results of these studies and provide several case studies highlighting the benefits of this approach.

cross-platform studies↗
DOE OSTI2024

Generic and ML Workloads in an HPC Datacenter: Node Energy, Job Failures, and Node-Job Analysis

HPC datacenters offer a backbone to the modern digital society. Increasingly, they run Machine Learning (ML) jobs next to generic, compute-intensive workloads, supporting science, business, and other decision-making processes. However, understanding how ML jobs impact the operation of HPC datacenters, relative to generic jobs, remains desirable but understudied. In this work, we leverage long-term operational data, collected from a national-scale production HPC datacenter, and statistically compare how ML and generic jobs can impact the performance, failures, resource utilization, and energy consumption of HPC datacenters. Our study provides key insights, e.g., ML-related power usage causes GPU nodes to run into temperature limitations, median/mean runtime and failure rates are higher for ML jobs than for generic jobs, both ML and generic jobs exhibit highly variable arrival processes and resource demands, significant amounts of energy are spent on unsuccessfully terminating jobs, and concurrent jobs tend to terminate in the same state. We open-source our cleaned-up data traces on Zenodo (https://doi. org/10.5281/zenodo.13685426), and provide our analysis toolkit as software hosted on GitHub (https://github.com/atlarge-research/2024-icpads-hpc-workload-characterization). This study offers multiple benefits for data center administrators, who can improve operational efficiency, and for researchers, who can further improve system designs, scheduling techniques, etc.

crossanalysis↗
NASA NTRS1997

Planetary Data System Spaceborne Thermal Data Sub-Node of the Geosciences Node

The objectives of this proposal were: (1) to assemble the existing spacecraft thermal-infrared data and to place these data into a uniform format as specified by the PDS; (2) to develop a standardized software package, user interface, and catalog database to support the access and analysis of existing and planned thermal infrared datasets in order to provide wide community access to these data; (3) to support the distribution of Thermal SubNode data to users as requested; (4) to incorporate future spacecraft thermal observations into the Thermal SubNode; and (5) to sponsor workshops on the applications of Thermal SubNode data.

Christensen, Philip R.↗
NASA NTRS2010

Node 3 Relocation Environmental Control and Life Support System Modification Kit Verification and Updated Status

Node 1 (Unity) flew to International Space Station (ISS) on Flight 2A. Node 1 was the first module of the United States On-Orbit Segment (USOS) launched to ISS. The Node 1 ISS Environmental Control and Life Support (ECLS) design featured limited ECLS capability. The main purpose of Node 1 was to provide internal storage by providing four stowage rack locations within the module and to allow docking of multiple modules and a truss segment to it. The ECLS subsystems inside Node 1 were routed through the element prior to launch to allow for easy integration of the attached future elements, particularly the Habitation Module which was planned to be located at the nadir docking port of Node 1. After Node I was on-orbit, the Program decided not to launch the Habitation Module and instead, to replace it with Node 3 (Tranquility). In 2007, the Program became concerned with a potential Russian docking port approach issue for the Russian FGB nadir docking port after Node 3 is attached to Node 1. To solve this concern the Program decided to relocate Node 3 from Node I nadir to Node 1 port. To support the movement of Node 3 the Program decided to build a modification kit for Node 1, an on-orbit feedthrough leak test device, and new vestibule jumpers to support the ECLS part of the relocation. This paper provides a design overview of the modification kit for Node 1, a summary of the Node 1 ECLS re-verification to support the Node 3 relocation from Node 1 nadir to Node 1 port, and a status of the ECLS modification kit installation into Node 1.

Williams, David E.↗
NASA NTRS2009

Node 3 Relocation Environmental Control and Life Support System Modification Kit Verification and Updated Status

Node 1 (Unity) flew to International Space Station (ISS) on Flight 2A. Node 1 was the first module of the United States On-Orbit Segment (USOS) launched to ISS. The Node 1 ISS Environmental Control and Life Support (ECLS) design featured limited ECLS capability. The main purpose of Node 1 was to provide internal storage by providing four stowage rack locations within the module and to allow docking of multiple modules and a truss segment to it. The ECLS subsystems inside Node 1 were routed through the element prior to launch to allow for easy integration of the attached future elements, particularly the Habitation Module which was planned to be located at the nadir docking port of Node 1. After Node 1 was on-orbit, the Program decided not to launch the Habitation Module and instead, to replace it with Node 3 (Tranquility). In 2007, the Program became concerned with a potential Russian docking port approach issue for the Russian FGB nadir docking port after Node 3 is attached to Node 1. To solve this concern the Program decided to relocate Node 3 from Node 1 nadir to Node 1 port. To support the movement of Node 3 the Program decided to build a modification kit for Node 1, an on-orbit feedthrough leak test device, and new vestibule jumpers to support the ECLS part of the relocation. This paper provides a design overview of the modification kit, a summary of the Node 1 ECLS re-verification to support the Node 3 relocation from Node 1 nadir to Node 1 port, and a status of the ECLS modification kit installation into Node 1.

Williams, David E.↗
NASA NTRS1992

Seawifs Technical Report Series. Volume 2: Analysis of Orbit Selection for Seawifs: Ascending Versus Descending Node

Due to range safety considerations, the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument may be required to be launched into a near-noon descending node, as opposed to the ascending node used by the predecessor sensor, the Coastal Zone Color Scanner (CZCS). The relative importance of ascending versus descending near-noon orbits was assessed here to determine if descending node will meet the scientific requirements of SeaWiFS. Analyses focused on ground coverage, local times of coverage, solar and viewing geometries (zenith and azimuth angles), and sun glint. Differences were found in the areas covered by individual orbits, but were not important when taken over a 16 day repeat time. Local time of coverage was also different: for ascending node orbits the Northern Hemisphere was observed in the morning and the Southern Hemisphere in the afternoon, while for descending node orbits the Northern Hemisphere was observed in the afternoon and the Southern in the morning. There were substantial differences in solar azimuth and spacecraft azimuth angles both at equinox and at the Northern Hemisphere summer solstice. Negligible differences in solar and spacecraft zenith angles, relative azimuth angles, and sun glint were obtained at the equinox. However, large differences were found in solar zenith angles, relative azimuths, and sun glint for the solstice. These differences appeared to compensate across the scan, however, an increase in sun glint in descending node over that in ascending node on the western part of the scan was compensated by a decrease on the eastern part of the scan. Thus, no advantage or disadvantage could be conferred upon either ascending node or descending node for noon orbits. Analyses were also performed for ascending and descending node orbits that deviated from a noon equator crossing time. For ascending node, afternoon orbits produced the lowest mean solar zenith angles in the Northern Hemisphere, and morning orbits produced the lowest angles for the Southern Hemisphere. For descending node, morning orbits produced the lowest mean solar zenith angles for the Northern Hemisphere; afternoon orbits produced the lowest angles for the Southern Hemisphere.

Hooker, Stanford B.↗
NASA NTRS2023

Alternate Approach to Multi Layer Insulation Modeling to Reduce Node Count

For models with a limitation on the overall node count, the typical approach to Multi-Layer Insulation (MLI) modeling may generate nodes that are necessary for the analysis, but do not represent components of particular interest. This leaves fewer nodes that can be utilized to model components of greater importance than the MLI. A common approach to modeling MLI is to include a separate MLI node representing the outer layer of the insulation and a radiative coupling based on the area multiplied by an effective emissivity. Therefore, wherever insulation is included, one node is needed for the underlying surface and another node for the insulation. Since many spacecraft and instruments include MLI covering a sizable portion of their designs, this may result in a considerable number of nodes being used for MLI. An alternate method to MLI modeling was developed that eliminates the MLI node, while still preserving the effect of the insulation for the underlying surface, thereby increasing the available nodes that could be used elsewhere in the model. This approach relies on preserving the baseline reflectivity, while reducing the absorptivity (based on the blanket effective emittance) and including a transparency. An inactive second surface is placed just behind the base surface that fully absorbs any energy that is transmitted without including its effect in the model. In essence, this approach applies only the energy that makes it through the blanket to the underlying surface. This method was tested out on the Roman Space Telescope model in local areas in preparation for its use in the generation of a launch model, which is constrained in the allowable node count. This paper documents the performance of the method and presents a comparison between the One-Node MLI method and the traditional two node MLI approach.

Thermal↗
NASA NTRS1997

Operation of the Planetary Plasma Interactions Node of the Planetary Data System

Five years ago NASA selected the Planetary Plasma Interactions (PPI) Node at UCLA to help the scientific community locate, access and preserve particles and fields data from planetary missions. We propose to continue to serve for 5 more years. During the first five years we have served the scientific community by providing them with high quality data products. We worked with missions and individual scientists to secure the highest quality data possible and to thoroughly document it. We validated the data, placed it on long lasting media and made sure it was properly archived for future use. So far we have prepared and archived over 10(exp 11) bytes of data from 26 instruments on 4 spacecraft. We have produced 106 CD-ROMs with peer reviewed data. In so doing, we have developed an efficient system to prepare and archive the data and thereby have been able to steadily increase the rate at which the data are produced. Although we produced a substantial archive during the initial five years, we have an even larger amount of work in progress. This includes preparing CD-ROM data sets with all of the Voyager, Pioneer and Ulysses data at Jupiter and Saturn. We will have the Jupiter data ready for the Galileo encounter in December, 1995. We are also completing the Pioneer Venus data restoration. The Galileo Venus archive and radio science data from Magellan will be prepared early in the next period. We are assisting the Small Bodies Node of PDS in the preparation of comet data and will be archiving the asteroid data from Galileo. We will be moving in several new directions as well. We will archive the PPI Node's first Earth based data with data from the International Jupiter Watch and Hubble data taken in support of Ulysses particles and field observations. We will work with the Cassini mission in archive planning efforts. For the inner planets we will begin an archive of Mars data starting with Phobos data and will support the US and Russian Mars missions in the late 1990's. We will restore the Mercury data from Mariner 10 and prepare the lunar data from Clementine in time for the lunar data analysis program in 1995. We will work with the Discovery mission teams to plan their archive and have already started with one, NEAR. Finally we will begin archiving our first heliospheric data from Voyager, Galileo, and Mars observers. We will continue to serve the science community by providing access to the data products. During the past 19 months we have filled nearly 6000 requests for on-line and CD-ROM data. The data delivered directly by the PPI Node has been - 5 x 10(exp 11) bytes. In addition to providing the data, we have provided users with software tools to manage and read the data which are computer, operating system and format independent. We have developed scalable systems so that the same software we use to manage and access the data for the entire PPI Node can be used by individual investigators to manage the data on a single CD-ROM, thereby greatly reducing the software development effort for both the PPI Node and users. We deliver this software with the disks. Recent technical advances have made it possible for us to serve a broader community than before. In the next five year period we plan to extend our outreach to the general public and in particular to increase our support for education. Since planetary plasma data are varied and require expertise in many areas the PPI Node will continue to be distributed. In addition to the primary node at UCLA, the PPI Node has three subnodes with an Outer Planets Subnode at the University of Iowa, an Inner Planets Subnode at UCLA, and a Radio Science Subnode at Stanford University. During the first two years of the renewal period there will be a Radio Astronomy Data Node at GSFC. These organizations will provide scientific expertise on the data, participate in node data selection activities and help with data restoration and mission activities.

Walker, Raymond J.↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Diskin, Boris↗