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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Multigrid Techniques for Highly Indefinite Equations

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Shapira, Yair↗
NASA NTRS2009

A Critical Study of Agglomerated Multigrid Methods for Diffusion

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.

Thomas, James L.↗
NASA NTRS2019

Computational Analysis of the External Aerodynamics of the Unpowered X-57 Mod-III Aircraft

Investigations of the external aerodynamics of the unpowered X-57 Mod-III configuration using computational fluid dynamics are presented. Two different Reynolds-averaged Navier-Stokes flow solvers were used in the analysis: the STAR-CCM+ unstructured solver using polyhedral grid topology, and the Launch Ascent Vehicle Aerodynamics (LAVA) structured curvilinear flow solver using structured overset grid topology. A grid refinement study was conducted and suitable grid resolution was determined by examining the forces and moments of the aircraft. Code-to-code comparison shows that STAR-CCM+ and LAVA are in good agreement both in quantitative values and trends. The angle-of-attack sweep and sideslip-angle sweep were performed. Results indicate that lift coefficients have a sharp drop at stall. At high angle of attack, STAR-CCM+ and LAVA show different flow separation behavior possibly due to differences in the turbulence model. The sideslip-angle sweep results show constant pitching moment from 0° to 15°, then a sharp increase between 15° and 20° sideslip angle.

Yoo, Seung Y.↗
NASA NTRSDate not supplied

Cross-Validation of Computational and Experimental Distributed Surface Pressures on the Space Launch System

This paper presents a new workflow for comparing experimental pressure-sensitive paint (PSP) data to computational fluid dynamic (CFD) simulations by way of mapping data from corresponding grids utilizing interpolation methods. In addition to generating quantitative and qualitative point-to-point comparisons between PSP and CFD data, this workflow extracts sectional loading data from both grids and generates lineload comparison charts for corresponding PSP and CFD runs. Experimental PSP data presented in this paper were taken from a 2016 NASA Ames Research Center Unitary Plan Wind Tunnel 11- by 11-Foot Transonic WindTunnel Facility test of the NASA Space Launch System. CFD simulation data for comparison purposes were generated using the FUN3D code. Overall, interpolation onto PSP grids versus CFD grids yields comparable surface pressure fields. However, lineload comparisons are easier to make on the CFD grid-mapped data due to the grid topology and the current capabilities of the lineload analysis tools at NASA Langley Research Center. This workflow is written using contemporary software (Python, Tecplot, PyTecplot), is compatible with existing tools at NASA Langley, and is developed to be adaptable depending on the situation.

SLS↗
NASA NTRSDate not supplied

Preliminary Results Cycling GEOS-JEDI with GSI-based Background Errors

The first phase of transitioning the NASA GMAO GEOS atmospheric data assimilation capabilities to JEDI involves the replacement of the Grid-point Statistical Interpolation (GSI) with a corresponding JEDI analysis. This includes taking JEDI's Unified Observation Operator (UFO), its underlying dependencies, and the JEDI solver that enables a hybrid 4DEnVar strategy similar to what is used in the current GEOS-GSI system. Variational analysis involves at least two main components associated with the observation and background cost function terms. The first is directly related to the UFO, which is being carefully validated in a joint collaboration between GMAO and NCEP to demonstrate consistency with corresponding observations usage in GSI. The second component is the background term, which in a hybrid system involves the ability to set up both a climatologically-based term and an ensemble-based term. JEDI provides the means to implement both terms through its BUMP component. Use of BUMP would require a complete re-tune of both climatological and ensemble, which is a non-trivial exercise we would prefer to avoid. As an alternative, the work here studies the results of interfacing the GSI-background error capability (GSIBEC) into JEDI through SABER. With this, the exact same background error covariance formulation used in GSI can be employed in JEDI without need for re-tuning. This brief summary covers the work done to interface GSIBEC into JEDI and shows preliminary results where the background error covariances of the control (GEOS-GSI) and experiment (GEOS-JEDI) are identical in corresponding cycling experiments. The cycling exercise is obviously preliminary and so much can be expected from GEOS-JEDI when compared to GEOS-GSI. There is still a number of features that need closer attention and although in some cases in principle ready to cycle have been intentionally either turned off or not fully exercised (e.g., VarBC is applied but not cycled). Other features are still pending implementation, one such example is the implementation of the Tangent Linear Normal Mode Constraint. Still, results are quite encouraging as hopefully the discussion here illustrates.

Ricardo Todling↗
NASA NTRS2005

Diagnostic Comparison of Meteorological Analyses during the 2002 Antarctic Winter

Several meteorological datasets, including U.K. Met Office (MetO), European Centre for Medium-Range Weather Forecasts (ECMWF), National Centers for Environmental Prediction (NCEP), and NASA's Goddard Earth Observation System (GEOS-4) analyses, are being used in studies of the 2002 Southern Hemisphere (SH) stratospheric winter and Antarctic major warming. Diagnostics are compared to assess how these studies may be affected by the meteorological data used. While the overall structure and evolution of temperatures, winds, and wave diagnostics in the different analyses provide a consistent picture of the large-scale dynamics of the SH 2002 winter, several significant differences may affect detailed studies. The NCEP-NCAR reanalysis (REAN) and NCEP-Department of Energy (DOE) reanalysis-2 (REAN-2) datasets are not recommended for detailed studies, especially those related to polar processing, because of lower-stratospheric temperature biases that result in underestimates of polar processing potential, and because their winds and wave diagnostics show increasing differences from other analyses between similar to 30 and 10 hPa (their top level). Southern Hemisphere polar stratospheric temperatures in the ECMWF 40-Yr Re-analysis (ERA-40) show unrealistic vertical structure, so this long-term reanalysis is also unsuited for quantitative studies. The NCEP/Climate Prediction Center (CPC) objective analyses give an inferior representation of the upper-stratospheric vortex. Polar vortex transport barriers are similar in all analyses, but there is large variation in the amount, patterns, and timing of mixing, even among the operational assimilated datasets (ECMWF, MetO, and GEOS-4). The higher-resolution GEOS-4 and ECMWF assimilations provide significantly better representation of filamentation and small-scale structure than the other analyses, even when fields gridded at reduced resolution are studied. The choice of which analysis to use is most critical for detailed transport studies (including polar process modeling) and studies involving synoptic evolution in the upper stratosphere. The operational assimilated datasets are better suited for most applications than the NCEP/CPC objective analyses and the reanalysis datasets.

stratosphere↗
NASA NTRS1987

Diffraction Analysis of Antennas With Mesh Surfaces

Strip-aperture model replaces wire-grid model. Far-field radiation pattern of antenna with mesh reflector calculated more accurately with new strip-aperture model than with wire-grid model of reflector surface. More adaptable than wire-grid model to variety of practical configurations and decidedly superior for reflectors in which mesh-cell width exceeds mesh thickness. Satisfies reciprocity theorem. Applied where mesh cells are no larger than tenth of wavelength. Small cell size permits use of simplifying approximation that reflector-surface current induced by electromagnetic field is present even in apertures. Approximation useful in calculating far field.

Rahmat-Samii, Yahya↗
NASA NTRS1993

Status of VGRID/USM3D aero analysis system

The topics are presented in viewgraph form and include the following: grid generation; flow solver; graphic postprocessing; dissemination; customer applications; and plans.

Neal T Frink↗
NASA NTRS1984

Application of a full potential method for computation of three-dimensional supersonic flows

A nonlinear aerodynamic analysis technique based on the full potential equation in conservative form has been modified to permit treatment of supersonic flows with embedded subsonic regions (typically near the fuselage-canopy juncture and the wing leading edge). Solution procedures for the equations do not require any specific form of geometry or physical grid system. This results in the capability to analyze easily very complex geometries provided the posed problem lies within the isentropic restrictions of the full potential theory. Characteristic signal propagation theory is used to monitor the type dependent flow and a conservative switching scheme is employed to transition from the supersonic marching algorithm to a subsonic relaxation procedure and vice versa. An implicit approximate factorization scheme is used to solve the finite-difference equations. These modifications now permit analysis of fully three-dimensional flowfields including the interference effects due to lifting surface wakes. Improved grid generation capability allows analysis of complete complex aircraft geometries (fuselage, wing, tail, wing wake, and tail wake). Results are presented showing very good correlations with experimental surface pressure data and aerodynamic force data at both design and off-design operating points. Configurations examined include several waverider concepts, an arrow wing-body with wake, an advanced tactical fighter concept, and a fighter forebody-canard configuration.

Jones, K. M.↗
NASA NTRS1993

Multi-resolution analysis for ENO schemes

Given a function u(x) which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. We apply this multi-resolution analysis to Essentially Non-oscillatory Schemes (ENO) schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one-dimensional case; this algorithm can be extended to the multi-dimensional case with cartesian grids.

Harten, Ami↗
NASA NTRS2017

Update of the NEXT Ion Thruster Service Life Assessment with Post-Test Correlation to the Long Duration Test

The service life assessment for NASA's Evolutionary Xenon Thruster is updated to incorporate the results from the successful and voluntarily early completion of the 51,184 hour long duration test which demonstrated 918 kg of total xenon throughput. The results of the numerous post-test investigations including destructive interrogations have been assessed against all of the critical known and suspected failure mechanisms to update the life and throughput expectations for each major component. Analysis results of two of the most acute failure mechanisms, namely pit-and-groove erosion and aperture enlargement of the accelerator grid, are not updated in this work but will be published at a future time after analysis completion.

ion engines↗
NASA NTRS1999

Large Eddy Simulation of Cirrus Clouds

The Regional Atmospheric Modeling System (RAMS) with mesoscale interactive nested-grids and a Large-Eddy Simulation (LES) version of RAMS, coupled to two-moment microphysics and a new two-stream radiative code were used to investigate the dynamic, microphysical, and radiative aspects of the November 26, 1991 cirrus event. Wu (1998) describes the results of that research in full detail and is enclosed as Appendix 1. The mesoscale nested grid simulation successfully reproduced the large scale circulation as compared to the Mesoscale Analysis and Prediction System's (MAPS) analyses and other observations. Three cloud bands which match nicely to the three cloud lines identified in an observational study (Mace et al., 1995) are predicted on Grid #2 of the nested grids, even though the mesoscale simulation predicts a larger west-east cloud width than what was observed. Large-eddy simulations (LES) were performed to study the dynamical, microphysical, and radiative processes in the 26 November 1991 FIRE 11 cirrus event. The LES model is based on the RAMS version 3b developed at Colorado State University. It includes a new radiation scheme developed by Harrington (1997) and a new subgrid scale model developed by Kosovic (1996). The LES model simulated a single cloud layer for Case 1 and a two-layer cloud structure for Case 2. The simulations demonstrated that latent heat release can play a significant role in the formation and development of cirrus clouds. For the thin cirrus in Case 1, the latent heat release was insufficient for the cirrus clouds to become positively buoyant. However, in some special cases such as Case 2, positively buoyant cells can be embedded within the cirrus layers. These cells were so active that the rising updraft induced its own pressure perturbations that affected the cloud evolution. Vertical profiles of the total radiative and latent heating rates indicated that for well developed, deep, and active cirrus clouds, radiative cooling and latent heating could be comparable in magnitude in the cloudy layer. This implies that latent heating cannot be neglected in the construction of a cirrus cloud model. The probability density function (PDF) of w was analyzed to assist in the parameterization of cloud-scale velocities in large-scale models. For the more radiatively-driven, thin cirrus case, the PDFs are approximately Gaussian. However, in the interior of the deep, convectively unstable case, the PDFs of w are multi-modal and very broad, indicating that parameterizing cloud-scale motions for such clouds can be very challenging. The results of this research are described in detail in a paper submitted to the Journal of Atmospheric Science (Wu and Cotton, 1999), which is enclosed as Appendix 2. Using soundings extracted from a mesoscale simulation of the November 26, 1991 cirrus event, the radiative effects on vapor deposition/sublimation of ice crystals was studied using a two-dimensional cloud-resolving model (CRM) version of RAMS, coupled to an explicit bin-resolving microphysics. The CRM simulations of the November 26, 1991 cirrus event demonstrate that the radiative impact on the diffusional growth (or sublimation) of ice crystals is significant. In this case, the ice particles experienced radiative warming. Model results show that radiative feedbacks in the diffusional growth of ice particles can be very complex. Radiative warming of an ice particle will restrict the particle's diffusional growth. In the case of radiative warming, ice particles larger than a certain size will experience so much radiative warming that surface ice saturation vapor pressures become large enough to cause sublimation of the larger crystals, while smaller crystals are growing by vapor deposition. However, ice mass production can be enhanced in the case of radiative cooling of an ice particle. For the November 26, 1991 cirrus event, radiative feedback results in significant reduction in the total ice mass, especially in the production of large ice crystals, and consequently, both radiative and dynamic properties of the cirrus cloud are significantly affected. A complete description of this research has been submitted as a paper to the Journal of Atmospheric Science (Wu et al., 1999), and included as Appendix 3.

Wu, Ting↗
NASA NTRS2003

Development of a Flexible Framework of Common Hypersonic Navier-Strokes Meshes for the Space Shuttle Orbiter

A flexible framework for the development of block structured volume grids for hypersonic Navier-Stokes flow simulations was developed for analysis of the Shuttle Orbiter Columbia. The development of the flexible framework, resulted in an ability to quickly generate meshes to directly correlate solutions contributed by participating groups on a common surface mesh, providing confidence for the extension of the envelope of solutions and damage scenarios. The framework draws on the experience of NASA Langely and NASA Ames Research Centers in structured grid generation, and consists of a grid generation process that is implemented through a division of responsibilities. The nominal division of labor consisted of NASA Johnson Space Center coordinating the damage scenarios to be analyzed by the Aerothermodynamics Columbia Accident Investigation (CAI) team, Ames developing the surface grids that described the computational volume about the orbiter, and Langely improving grid quality of Ames generated data and constructing the final volume grids. Distributing the work among the participants in the Aerothermodynamic CIA team resulted in significantly less time required to construct complete meshes than possible by any individual participant. The approach demonstrated that the One-NASA grid generation team could sustain the demand for new meshes to explore new damage scenarios within a aggressive timeline.

Alter, Stephen J.↗
NASA NTRS2016

Evaluation of NASA's MERRA Precipitation Product in Reproducing the Observed Trend and Distribution of Extreme Precipitation Events in the United States

This study evaluates the performance of NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA) precipitation product in reproducing the trend and distribution of extreme precipitation events. Utilizing the extreme value theory, time-invariant and time-variant extreme value distributions are developed to model the trends and changes in the patterns of extreme precipitation events over the contiguous United States during 1979-2010. The Climate Prediction Center (CPC) U.S.Unified gridded observation data are used as the observational dataset. The CPC analysis shows that the eastern and western parts of the United States are experiencing positive and negative trends in annual maxima, respectively. The continental-scale patterns of change found in MERRA seem to reasonably mirror the observed patterns of change found in CPC. This is not previously expected, given the difficulty in constraining precipitation in reanalysis products. MERRA tends to overestimate the frequency at which the 99th percentile of precipitation is exceeded because this threshold tends to be lower in MERRA, making it easier to be exceeded. This feature is dominant during the summer months. MERRA tends to reproduce spatial patterns of the scale and location parameters of the generalized extreme value and generalized Pareto distributions. However, MERRA underestimates these parameters, particularly over the Gulf Coast states, leading to lower magnitudes in extreme precipitation events. Two issues in MERRA are identified: 1) MERRA shows a spurious negative trend in Nebraska and Kansas, which is most likely related to the changes in the satellite observing system over time that has apparently affected the water cycle in the central United States, and 2) the patterns of positive trend over the Gulf Coast states and along the East Coast seem to be correlated with the tropical cyclones in these regions. The analysis of the trends in the seasonal precipitation extremes indicates that the hurricane and winter seasons are contributing the most to these trend patterns in the southeastern United States. In addition, the increasing annual trend simulated by MERRA in the Gulf Coast region is due to an incorrect trend in winter precipitation extremes.

MERRA↗
NASA NTRS1982

Analysis of atmosphere-sea ice interactions in the Arctic basin using ESMR microwave data

Data from the Electrically Scanning Microwave Radiometer (ESMR) on Nimbus-5 are used to determine the spatial and temporal patterns of change in microwave brightness signatures of Arctic sea ice during a full annual cycle (1973/74). Interactions of ice conditions with the atmosphere are examined using grid point data for surface air temperature and atmospheric pressure. Principal components analysis is used to examine the major elements present in the microwave and atmospheric data. Component scores from these analyses are then used in a canonical correlation analysis to determine interassociations present between the ice and atmosphere in the Beaufort Sea and the European sectors on a synoptic time scale. The synoptic weather conditions associated with the pattern of snow melt on the ice in spring 1974 are described, and a clarification of possible alternative interpretations of features identified as polynyi occurring at 80-85 deg N during the late summer 1974 is presented.

Crane, R. G.↗
NASA NTRS1995

Algorithms for parallel flow solvers on message passing architectures

The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those immediately adjacent to them, then the first processor in the pipeline will receive a computational load that is less than that of subsequent processors, magnifying the pipeline slowdown effect. Extra compensation is needed for grid boundary effects, even if all grid blocks are equally sized.

Vanderwijngaart, Rob F.↗
NASA NTRS2004

Transonic Drag Prediction on a DLR-F6 Transport Configuration Using Unstructured Grid Solvers

A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to inves- tigate the code-to-code uncertainty. address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver. FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. For the wingbody, the total drag predicted for a constant-lift transonic cruise condition showed a decrease in code-to-code variation with grid refinement as expected. For the same flight condition, the wing/body/nacelle/pylon total drag and the nacelle/pylon drag increment predicted showed an increase in code-to-code variation with grid refinement. Although the range in total drag for the wingbody fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wingbody or the wing/body/nacelle pylon configuration. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within plus or minus 3 counts of the experimental data. The correlation with experimental incremental drag was not significantly changed by specifying transition. Although the sources of code-to-code variation in force and moment predictions for the three unstructured grid codes have not yet been identified, the current study reinforces the necessity of applying multiple codes to the same application to assess uncertainty.

Lee-Rausch, E. M.↗