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At least 181 records · Page 10

Finite difference operators on unstructured triangular meshes

A new form of the Laplace operator is derived which is shown to be second-order accurate when calculated at mesh triangle nodes if the cells corresponding to the nodes have a high degree of symmetry. It is demonstrated that the Laplace operator directly derived from Stokes' integral theorem is only zeroth-order accurate on these same cells. The construction of gradient and Laplace operators on unstructured triangular grids are discussed from the variational point of view. Two discrete representations of the Laplacian are compared to each other, and conclusions are drawn regarding their accuracy on a pointwise basis. Finally, geometric relations valid on arbitrary polygons are given for completeness in an appendix.

Erlebacher, G.↗

Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling

The technique for obtaining a subgrid model for Navier-Stokes turbulence, based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMND) equations. It is shown that a RNG treatment of the Alfven turbulence supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k yields 0, dependent on the amplitude of turbulence. The effective viscosity and resistivity become independent of the molecular quantities when the RNG analysis is augmented by the Kolmogorov argument for energy cascade. A self-contained system of equations is derived for the range of scales, k = 0-K, where K = pi/Delta is the maximum wave number for a grid size Delta. Differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities, represent in this system the resistive and viscous dissipation.

Longcope, D. W.↗

Coating Of Molded Battery Substrates

Materials applied to molds as powders, dispersions, or solutions not only enable release of molded parts from molds, but also enhance properties of surfaces of parts. Applied to casting of lead grids or other molding operations in which powdered materials adhering to molded parts improve properties of surfaces.

Larkin, Terrance M.↗

A multilevel cost-space approach to solving the balanced long transportation problem

We develop a multilevel scheme for solving the balanced long transportation problem, that is, given a set (c(sub kj)) of shipping costs from a set of M supply nodes S(sub k) to a set of N demand nodes D(sub j), we seek to find a set of flows, (x(sub kj)), that minimizes the total cost Sigma(sub k=1)(exp M) Sigma(sub j=1)(exp N) x(sub kj)c(sub kj). We require that the problem be balanced, that is, the total demand must equal the total supply. Solution techniques for this problem are well known from optimization and linear programming. We examine this problem, however, in order to develop principles that can then be applied to more intractible problems of optimization. We develop a multigrid scheme for solving the problem, defining the grids, relaxation, and intergrid operators. Numerical experimentation shows that this line of research may prove fruitful. Further research directions are suggested.

Cavanaugh, Kevin J.↗

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.

Avissar, Roni↗

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗

Space Development Grid Portal

This viewgraph presentation provides information on the development of a portal to provide secure and distributed grid computing for Payload Operations Integrated Center and Mission Control Center ground services.

Vaziri, Arsi↗

Interference Lattice-based Loop Nest Tilings for Stencil Computations

A common method for improving performance of stencil operations on structured multi-dimensional discretization grids is loop tiling. Tile shapes and sizes are usually determined heuristically, based on the size of the primary data cache. We provide a lower bound on the numbers of cache misses that must be incurred by any tiling, and a close achievable bound using a particular tiling based on the grid interference lattice. The latter tiling is used to derive highly efficient loop orderings. The total number of cache misses of a code is the sum of (necessary) cold misses and misses caused by elements being dropped from the cache between successive loads (replacement misses). Maximizing temporal locality is equivalent to minimizing replacement misses. Temporal locality of loop nests implementing stencil operations is optimized by tilings that avoid data conflicts. We divide the loop nest iteration space into conflict-free tiles, derived from the cache miss equation. The tiling involves the definition of the grid interference lattice an equivalence class of grid points whose images in main memory map to the same location in the cache-and the construction of a special basis for the lattice. Conflicts only occur on the boundaries of the tiles, unless the tiles are too thin. We show that the surface area of the tiles is bounded for grids of any dimensionality, and for caches of any associativity, provided the eccentricity of the fundamental parallelepiped (the tile spanned by the basis) of the lattice is bounded. Eccentricity is determined by two factors, aspect ratio and skewness. The aspect ratio of the parallelepiped can be bounded by appropriate array padding. The skewness can be bounded by the choice of a proper basis. Combining these two strategies ensures that pathologically thin tiles are avoided. They do not, however, minimize replacement misses per se. The reason is that tile visitation order influences the number of data conflicts on the tile boundaries. If two adjacent tiles are visited successively, there will be no replacement misses on the shared boundary. The iteration space may be covered with pencils larger than the size of the cache while avoiding data conflicts if the pencils are traversed by a scanning-face method. Replacement misses are incurred only on the boundaries of the pencils, and the number of misses is minimized by maximizing the volume of the scanning face, not the volume of the tile. We present an algorithm for constructing the most efficient scanning face for a given grid and stencil operator. In two dimensions it is based on a continued fraction algorithm. In three dimensions it follows Voronoi's successive minima algorithm. We show experimental results of using the scanning face, and compare with canonical loop orderings.

VanderWijngaart, Rob F.↗

Miniature Bipolar Electrostatic Ion Thruster

The figure presents a concept of a bipolar miniature electrostatic ion thruster for maneuvering a small spacecraft. The ionization device in the proposed thruster would be a 0.1-micron-thick dielectric membrane with metal electrodes on both sides. Small conical holes would be micromachined through the membrane and electrodes. An electric potential of the order of a volt applied between the membrane electrodes would give rise to an electric field of the order of several mega-volts per meter in the submicron gap between the electrodes. An electric field of this magnitude would be sufficient to ionize all the molecules that enter the holes. In a thruster-based on this concept, one or more propellant gases would be introduced into such a membrane ionizer. Unlike in larger prior ion thrusters, all of the propellant molecules would be ionized. This thruster would be capable of bipolar operation. There would be two accelerator grids - one located forward and one located aft of the membrane ionizer. In one mode of operation, which one could denote the forward mode, positive ions leaving the ionizer on the backside would be accelerated to high momentum by an electric field between the ionizer and an accelerator grid. Electrons leaving the ionizer on the front side would be ejected into free space by a smaller accelerating field. The equality of the ion and electron currents would eliminate the need for an additional electron- or ion-emitting device to keep the spacecraft charge-neutral. In another mode of operation, which could denote the reverse mode, the polarities of the voltages applied to the accelerator grids and to the electrodes of the membrane ionizer would be the reverse of those of the forward mode. The reversal of electric fields would cause the ion and electrons to be ejected in the reverse of their forward mode directions, thereby giving rise to thrust in the direction opposite that of the forward mode.

Hartley, Frank T.↗

Lunar Microgrid Trade Studies to Define Interface Converter Requirements

The National Aeronautics and Space Administration (NASA) is interested in developing an incremental lunar power grid to support continuous human/robotic operations under the Artemis missions and can scale to global power utilization and industrial power levels. The initial lunar surface power system will be composed primarily of assets that contain their own power generation and energy storage. These assets can be connected to form a grid, which allows power to be shared between the system’s distributed energy resources. This grid can provide backup power to existing assets as well as primary power to future assets. A trade study was conducted for an Artemis scale grid, which has identified 3 kVAC as an ideal transmission voltage. This paper documents the analysis and findings from these trade studies. These studies were used to define the operating voltage and develop a common interface for connecting lunar surface assets to the power grid. The Universal Modular Interface Converter (UMIC) connects lunar surface assets to the high voltage grid. Products from this grid definition and UMIC development work will enable highly reliable and available power for Artemis and future planetary surface missions, which is key to achieving NASA’s long-term vision of space exploration.

Planetary surface power↗

Charge-exchange erosion studies of accelerator grids in ion thrusters

A particle simulation model is developed to study the charge-exchange grid erosion in ion thrusters for both ground-based and space-based operations. Because the neutral gas downstream from the accelerator grid is different for space and ground operation conditions, the charge-exchange erosion processes are also different. Based on an assumption of now electric potential hill downstream from the ion thruster, the calculations show that the accelerator grid erosion rate for space-based operating conditions should be significantly less than experimentally observed erosion rates from the ground-based tests conducted at NASA Lewis Research Center (LeRC) and NASA Jet Propulsion Laboratory (JPL). To resolve this erosion issue completely, we believe that it is necessary to accurately measure the entire electric potential field downstream from the thruster.

Peng, Xiaohang↗

Ion Engine Grid Gap Measurements

A simple technique for measuring the grid gap of an ion engine s ion optics during startup and steady-state operation was demonstrated with beam extraction. The grid gap at the center of the ion optics assembly was measured with a long distance microscope that was focused onto an alumina pin that protruded through the center accelerator grid aperture and was mechanically attached to the screen grid. This measurement technique was successfully applied to a 30 cm titanium ion optics assembly mounted onto an NSTAR engineering model ion engine. The grid gap and each grid s movement during startup from room temperature to both full and low power were measured. The grid gaps with and without beam extraction were found to be significantly different. The grid gaps at the ion optics center were both significantly smaller than the cold grid gap and different at the two power levels examined. To avoid issues associated with a small grid gap during thruster startup with titanium ion optics, a simple method was to operate the thruster initially without beam extraction to heat the ion optics. Another possible method is to apply high voltage to the grids prior to igniting the discharge because power deposition to the grids from the plasma is lower with beam extraction than without. Further testing would be required to confirm this approach.

Soulas, Gerge C.↗

An approach to the parametric design of ion thrusters

A methodology that can be used to determine which of several physical constraints can limit ion thruster power and thrust, under various design and operating conditions, is presented. The methodology is exercised to demonstrate typical limitations imposed by grid system span-to-gap ratio, intragrid electric field, discharge chamber power per unit beam area, screen grid lifetime, and accelerator grid lifetime constraints. Limitations on power and thrust for a thruster defined by typical discharge chamber and grid system parameters when it is operated at maximum thrust-to-power are discussed. It is pointed out that other operational objectives such as optimization of payload fraction or mission duration can be substituted for the thrust-to-power objective and that the methodology can be used as a tool for mission analysis.

Wilbur, Paul J.↗

An approach to the parametric design of ion thrusters

A methodology that can be used to determine which of several physical constraints can limit ion thruster power and thrust, under various design and operating conditions, is presented. The methodology is exercised to demonstrate typical limitations imposed by grid system span-to-gap ratio, intragrid electric field, discharge chamber power per unit beam area, screen grid lifetime and accelerator grid lifetime constraints. Limitations on power and thrust for a thruster defined by typical discharge chamber and grid system parameters when it is operated at maximum thrust-to-power are discussed.

Wilbur, Paul J.↗

Plane Smoothers for Multiblock Grids: Computational Aspects

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Llorente, Ignacio M.↗

A Tool for Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D has shown that HPF provides an efficient, concise way to express parallelism and to organize data traffic. The use of HPF, as noted in the papers, requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement, and data granularity. To simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and implemented ADAPT (Automatic Data Alignment and Placement Tool). ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT, and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level, or on the application interface level. ADAPT annotates an existing CFD FORTRAN application, performing computations on single or multiple grids. On each grid the application is considered as a sequence of operators, each applied to a set of variables defined in a particular grid domain. ADAPT automatically detects implicit operators (i.e., having data dependences) and explicit operators (without data dependences). For parallelization of an explicit operator ADAPT creates a template for the operator domain, aligns arrays used in the operator with the template, distributes the template, and declares the loops over the distributed dimensions as INDEPENDENT. For parallelization of an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if the compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator, then the loop which implements the operator can be declared as INDEPENDENT. ADAPT starts with an analysis of array index expressions of the loop nests. For each pair of arrays referenced in an assignment statement, it generates an arc in the alignment graph and annotates it with an affinity relation. The template, alignment, and distribution directives for a particular loop nest are then derived from a transitive closure of the affinity relation. A compromise of data distributions in different nests and subroutines is achieved by merging annotated alignment graphs for adjacent nests/stibroutine calls in the nest/call graph of the application in the process called distribution lifting. ADAPT has been implemented as a C++ program running in conjunction with a parallelization tool called CAPTools. ADAPT uses the parse tree, interprocedural analysis and application database generated by CAPTools. It also uses the Directed Graph class, initially implemented in p2d2 (parallel debugger oi distributed programs), and some other classes supporting symbolic computations. ADAPT uses data distribution techniques described. ADAPT was tested with ARC3D and the FT benchmark and has demonstrated a code performance within a factor of 1.5 of handwritten versions.

Frumkin, Michael↗

High performance auxiliary-propulsion ion thruster with ion-machined accelerator grid

An improvement in thruster performance was achieved by reducing the diameter of the accelerator grid holes. The smaller accelerator grid holes resulted in a reduction in neutral mercury atoms escaping the discharge chamber, which in turn enhanced the discharge propellant utilization from approximately 68 percent to 92 percent. The accelerator grids were fabricated by ion machining with an 8-centimeter-diameter thruster, and the screen grid holes individually focused ion beamlets onto the blank accelerator grid. The resulting accelerator grid holes are less than 1.12 millimeters in diameter, while previously used accelerator grids had hole diameters of 1.69 millimeters. The thruster could be operated with the small-hole accelerator grid at neutralizer potential.

Hudson, W. R.↗

NEXT Ion Optics Simulation via ffx

Simulations of the erosion processes for two proposed sets of ion thruster grids for the NEXT project are presented. Structural failure and electron backstreaming due to accelerator grid erosion are discussed as two possible failure mechanisms of these grid sets. The TAG grid set was seen to outperform the NSTAR grid set both in terms of margin against electron backstreaming and accelerator grid mass loss for a variety of operating points. An investigation into the possibility of reducing the accelerator grid voltage magnitude for the TAG grid set showed improved propellant throughput capability.

Soulas, George↗