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At least 343 records · Page 19

Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction

Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.

Sockol, Peter M.↗

Mapping robust parallel multigrid algorithms to scalable memory architectures

The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.

Overman, Andrea↗

Modelling TOVS radiances of synoptic systems

Two operational analysis models, produced by ECMWF and NMC, are compared against observed satellite radiances by converting the analyzed variables into synthetic radiances using a radiative transfer model (RTM). Observed TOVS satellite radiances are used as a ground truth, since they are the only source of continuous, synoptic-scale resolution observations available over the data-sparse tropical Pacific Ocean. It is assumed that if the analysis models correctly simulate atmospheric conditions, the observed and modelled radiance fields will have similar patterns and magnitudes. In each of seven TOVS channels examined, the mean temperature difference between the models was small, but the differences between the models and the observations were large. The mean temperature difference within each channel was larger than the standard deviation in most cases. The moisture channels of the RTM were sensitive to changes in moisture content, but none of the channels were significantly affected by changes in temperature. Single-day modelled radiance analyses contain synoptic information similar to the satellite observations. ECMWF is often too noisy, producing features not verified by the satellite; NMC is often too smooth. NMC more closely resembles the TOVS contours. Modelled water vapor channel analyses resemble observed monthly and composited observations well, but do not accurately reproduce the highly-variable single-day fields. ECMWF generally has more accurate gradients. Neither model simulates the tropics well. The water vapor channels, especially channel eleven (weighted at 700 mb), most closely resembled the tropical plume composite described by McGuirk and Ulsh. The only plume evidence found in the thermal or microwave channels, in either the observations or the models, was a composite trough situated in the correct location, extending from the mid-latitudes into the subtropics. This feature was not readily discernable until the definition and mature stages. Additional information besides the modelled temperatures would be required to produce an accurate forecast for the tropics. Model patterns more closely resembled the observations in the quiescent atmosphere, though the magnitudes were not any closer. ECMWF simulates the TOVS quiescent state better than NMC. The moisture channels continue to present the most realistic patterns. The models contained more detail in the tropics than was verified by the satellite observations, apparently trying to force an active ITCZ. Lag correlations showed TOVS to be more persistent than the models. TOVS also showed a smoother lag trend, but all products appeared to have adequate ability to react to changes in the atmosphere over time.

Coe, Thomas Eddy↗

A comparison of TSS and TRASYS in form factor calculation

As the workstation and personal computer become more popular than a centralized mainframe to perform thermal analysis, the methods for space vehicle thermal analysis will change. Already, many thermal analysis codes are now available for workstations, which were not in existence just five years ago. As these changes occur, some organizations will adopt the new codes and analysis techniques, while others will not. This might lead to misunderstandings between thermal shops in different organizations. If thermal analysts make an effort to understand the major differences between the new and old methods, a smoother transition to a more efficient and more versatile thermal analysis environment will be realized.

Golliher, Eric↗

Improved solution accuracy for TDRSS-based TOPEX/Poseidon orbit determination

Orbit determination results are obtained by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) using a batch-least-squares estimator available in the Goddard Trajectory Determination System (GTDS) and an extended Kalman filter estimation system to process Tracking and Data Relay Satellite (TDRS) System (TDRSS) measurements. GTDS is the operational orbit determination system used by the FDD in support of the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft navigation and health and safety operations. The extended Kalman filter was implemented in an orbit determination analysis prototype system, closely related to the Real-Time Orbit Determination System/Enhanced (RTOD/E) system. In addition, the Precision Orbit Determination (POD) team within the GSFC Space Geodesy Branch generated an independent set of high-accuracy trajectories to support the TOPEX/Poseidon scientific data. These latter solutions use the geodynamics (GEODYN) orbit determination system with laser ranging and Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) tracking measurements. The TOPEX/Poseidon trajectories were estimated for November 7 through November 11, 1992, the timeframe under study. Independent assessments were made of the consistencies of solutions produced by the batch and sequential methods. The batch-least-squares solutions were assessed based on the solution residuals, while the sequential solutions were assessed based on primarily the estimated covariances. The batch-least-squares and sequential orbit solutions were compared with the definitive POD orbit solutions. The solution differences were generally less than 2 meters for the batch-least-squares and less than 13 meters for the sequential estimation solutions. After the sequential estimation solutions were processed with a smoother algorithm, position differences with POD orbit solutions of less than 7 meters were obtained. The differences among the POD, GTDS, and filter/smoother solutions can be traced to differences in modeling and tracking data types, which are being analyzed in detail.

Doll, C. E.↗

Improved solution accuracy for Landsat-4 (TDRSS-user) orbit determination

This paper presents the results of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft, Landsat-4, obtained using a Prototype Filter Smoother (PFS), with the accuracy of an established batch-least-squares system, the Goddard Trajectory Determination System (GTDS). The results of Landsat-4 orbit determination will provide useful experience for the Earth Observing System (EOS) series of satellites. The Landsat-4 ephemerides were estimated for the January 17-23, 1991, timeframe, during which intensive TDRSS tracking data for Landsat-4 were available. Independent assessments were made of the consistencies (overlap comparisons for the batch case and convariances for the sequential case) of solutions produced by the batch and sequential methods. The filtered and smoothed PFS orbit solutions were compared with the definitive GTDS orbit solutions for Landsat-4; the solution differences were generally less than 15 meters.

Oza, D. H.↗

System concept definition of the Grumman superconducting Electromagnetic Suspension (EMS) Maglev design

Grumman, under contract to the Army Corps of Engineers, completed a System Concept Definition (SCD) study to design a high-speed 134 m/s (300 m.p.h.) magnetically levitated (Maglev) transportation system. The primary development goals were to design a Maglev that is safe, reliable, environmentally acceptable, and low-cost. The cost issue was a predominant one, since previous studies have shown that an economically viable Maglev system (one that is attractive to investors for future models of passenger and/or freight transportation) requires a cost that is about $12.4 M/km ($20 Million per mile). The design is based on the electromagnetic suspension (EMS) system using superconducting iron-core magnets mounted along both sides of the vehicle. The EMS system has several advantages compared to the electrodynamic suspension (EDS) Maglev systems such as low stray magnetic fields in the passenger cabin and the surrounding areas, uniform load distribution along the full length of the vehicle, and small pole pitch for smoother propulsion and ride comfort. It is also levitated at all speeds and incorporates a wrap-around design of safer operation. The Grumman design has all the advantages of an EMS system identified above, while eliminating (or significantly improving) drawbacks associated with normal magnet powered EMS systems. Improvements include larger gap clearance, lighter weight, lower number of control servos, and higher off line switching speeds. The design also incorporates vehicle tilt (plus or minus 9 deg) for higher coordinated turn and turn out speed capability.

Proise, M.↗

A Hubble Space Telescope ultraviolet spectrum of SN 1993J

We obtained a Hubble Space Telescope (HST) ultraviolet spectrum of the Type II supernova SN 1993J in M81 on 1993 April 15. The approximately 1650-2900 A region is smoother than observed for SN 1987A and SN 1992A and lacks strong P Cygni absorptions caused by iron peak element lines. Synthetic spectra calculated using a parameterized Local Thermodynamic Equilibrium (LTE) procedure and a simple model atmosphere do not fit the UV region. Radio observations suggest that SN 1993J is embedded in a thick circumstellar envelope. The UV spectra of other supernovae that are believed to have thick circumstellar envelopes also have approximately 1650-2900 A regions lacking in strong P Cygni absorptions. Interaction of supernova ejecta and circumstellar matter may cause the smooth UV spectrum. If so, UV observations of supernovae will provide insight into the circumstellar environment of the supernova progenitors.

Jeffery, David J.↗

Bell Regio, Venus: Integration of remote sensing data and terrestrial analogs for geologic analysis

The geology and surface morphology of Bell Regio (18-42 deg N, 32-58 deg E) are investigated using a combination of Magellan, Venera, and analogous terrestrial data. The properties of surface units are compared to either direct terrestrial analog measurements or to the behaviors predicted by theoretical models. Five major volcanic sources are identified from geologic mapping (Tepev Mons, Nefertiti corona, a large shield volcano east of Tepev, and two small edifices southeast of Tepev). The volcano Api Mons lies northeast of the main Bell uplift. The oldest volcanic units are associated with an extensive low shield volcano east of Tepev Mons and a small edifice southeast of Tepev. The annular flow apron of Tepev Mons formed next, with volcanism at a second small edifice on the southeast flank of Tepev Mons producing the youngest flow units. Comparisons between Magellan data, terrestrial radar images, and field topography profiles suggest that only three units resemble terrestrial a'a flows; the remainder are consistent with smoother pahoehoe-type surfaces. This suggests that most of the flow units were erupted at relatively low volume effusion rates (less than 100 cu m/sec) over long periods of time or had very low viscosities

Campbell, Bruce A.↗

Space and time aliasing structure is monthly mean polar-orbiting satellite data

Monthly mean wind fields from the European Remote Sensing Satellite (ERS1) scatterometer are presented. A banded structure which resembles the satellite subtrack is clearly and consistently apparent in the isotachs as well as the u and v components of the routinely produced fields. The structure also appears in the means of data from other polar-orbiting satellites and instruments. An experiment is designed to trace the cause of the banded structure. The European Centre for Medium-Range Weather Forecast (ECMWF) gridded surface wind analyses are used as a control set. These analyses are also sampled with the ERS1 temporal-spatial samplig pattern to form a simulated scatterometer wind set. Both sets are used to create monthly averages. The banded structures appear in the monthly mean simulated data but do not appear in the control set. It is concluded that the source of the banded structure lies in the spatial and temporal sampling of the polar-orbiting satellite which results in undersampling. The problem involves multiple timescales and space scales, oversampling and under-sampling in space, aliasing in the time and space domains, and preferentially sampled variability. It is shown that commonly used spatial smoothers (or filters), while producing visually pleasing results, also significantly bias the true mean. A three-dimensional spatial-temporal interpolator is designed and used to determine the mean field. It is found to produce satisfactory monthly means from both simulated and real ERS1 data. The implications to climate studies involving polar-orbiting satellite data are discussed.

Zeng, Lixin↗

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗

Controlling Flows Of Two Ingredients For Spraying

Closed-loop servo control subsystem incorporated, as modification, into system controlling flows of two ingredients mixed and sprayed to form thermally insulating foams on large tanks. Provides steady flows at specified rates. Foams produced smoother and of higher quality. Continued use of system results in substantial reduction in cost stemming from close control of application of foam and consequent reduced use of material.

Chandler, Huel H.↗

A far-field non-reflecting boundary condition for two-dimensional wake flows

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

Danowitz, Jeffrey S.↗

Design, Implementation, and Verification of the Reliable Multicast Protocol

This document describes the Reliable Multicast Protocol (RMP) design, first implementation, and formal verification. RMP provides a totally ordered, reliable, atomic multicast service on top of an unreliable multicast datagram service. RMP is fully and symmetrically distributed so that no site bears an undue portion of the communications load. RMP provides a wide range of guarantees, from unreliable delivery to totally ordered delivery, to K-resilient, majority resilient, and totally resilient atomic delivery. These guarantees are selectable on a per message basis. RMP provides many communication options, including virtual synchrony, a publisher/subscriber model of message delivery, a client/server model of delivery, mutually exclusive handlers for messages, and mutually exclusive locks. It has been commonly believed that total ordering of messages can only be achieved at great performance expense. RMP discounts this. The first implementation of RMP has been shown to provide high throughput performance on Local Area Networks (LAN). For two or more destinations a single LAN, RMP provides higher throughput than any other protocol that does not use multicast or broadcast technology. The design, implementation, and verification activities of RMP have occurred concurrently. This has allowed the verification to maintain a high fidelity between design model, implementation model, and the verification model. The restrictions of implementation have influenced the design earlier than in normal sequential approaches. The protocol as a whole has matured smoother by the inclusion of several different perspectives into the product development.

Montgomery, Todd L.↗

A Genuinely Two-Dimensional Scheme for the Compressible Euler Equations

We present a new genuinely multidimensional discretization for the compressible Euler equations. It is the only high-resolution scheme known to us where Gauss-Seidel relaxation is stable when applied as a smoother directly to the resulting high-resolution scheme. This allows us to construct a very simple and highly efficient multigrid steady-state solver. The scheme is formulated on triangular (possibly unstructured) meshes.

Sidilkover, David↗

A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations

The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.

Borzi, A.↗

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

High Performance Parallel Multigrid Algorithms for Unstructured Grids

We describe a high performance parallel multigrid algorithm for a rather general class of unstructured grid problems in two and three dimensions. The algorithm PUMG, for parallel unstructured multigrid, is related in structure to the parallel multigrid algorithm PSMG introduced by McBryan and Frederickson, for they both obtain a higher convergence rate through the use of multiple coarse grids. Another reason for the high convergence rate of PUMG is its smoother, an approximate inverse developed by Baumgardner and Frederickson.

Frederickson, Paul O.↗