Explicitly computing geodetic coordinates from Cartesian coordinates
NASA Astrophysics Data System (ADS)
Zeng, Huaien
2013-04-01
This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.
Stable boundary conditions for Cartesian grid calculations
NASA Technical Reports Server (NTRS)
Berger, M. J.; Leveque, R. J.
1990-01-01
The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.
The 3D Euler solutions using automated Cartesian grid generation
NASA Technical Reports Server (NTRS)
Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.
1993-01-01
Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.
NASA Astrophysics Data System (ADS)
Polkowski, Marcin
2016-04-01
Seismic wave travel time calculation is the most common numerical operation in seismology. The most efficient is travel time calculation in 1D velocity model - for given source, receiver depths and angular distance time is calculated within fraction of a second. Unfortunately, in most cases 1D is not enough to encounter differentiating local and regional structures. Whenever possible travel time through 3D velocity model has to be calculated. It can be achieved using ray calculation or time propagation in space. While single ray path calculation is quick it is complicated to find the ray path that connects source with the receiver. Time propagation in space using Fast Marching Method seems more efficient in most cases, especially when there are multiple receivers. In this presentation a Python module pySeismicFMM is presented - simple and very efficient tool for calculating travel time from sources to receivers. Calculation requires regular 2D or 3D velocity grid either in Cartesian or geographic coordinates. On desktop class computer calculation speed is 200k grid cells per second. Calculation has to be performed once for every source location and provides travel time to all receivers. pySeismicFMM is free and open source. Development of this tool is a part of authors PhD thesis. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.
Transonic airfoil design using Cartesian coordinates
NASA Technical Reports Server (NTRS)
Carlson, L. A.
1976-01-01
A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.
Errors of Remapping of Radar Estimates onto Cartesian Coordinates
NASA Astrophysics Data System (ADS)
Sharif, H. O.; Ogden, F. L.
2014-12-01
Recent upgrades to operational radar rainfall products in terms of quality and resolution call for re-examination of the factors that contribute to the uncertainty of radar rainfall estimation. Remapping or gridding of radar polar observations onto Cartesian coordinates is implemented using various methods, and is often applied when radar estimates are compared against rain gauge observations, in hydrologic applications, or for merging data from different radars. However, assuming perfect radar observations, many of the widely used remapping methodologies do not conserve mass for the rainfall rate field. Research has suggested that optimal remapping should select all polar bins falling within or intersecting a Cartesian grid and assign them weights based on the proportion of each individual bin's area falling within the grid. However, to reduce computational demand practitioners use a variety of approximate remapping approaches. The most popular approximate approaches used are those based on extracting information from radar bins whose centers fall within a certain distance from the center of the Cartesian grid. This paper introduces a mass-conserving method for remapping, which we call "precise remapping", and evaluates it by comparing against two other commonly used remapping methods based on areal weighting and distance. Results show that the choice of the remapping method can lead to large errors in grid-averaged rainfall accumulations.
Conversion of Cartesian coordinates from and to Generalized Balanced Ternary addresses
van Roessel, Jan W.
1988-01-01
Hexagonal grids have several advantages over square grids, such as a greater angular resolution and unambiguous connectivity. The Generalized Balanced Ternary (GBT) system is a spatial addressing method for hexagonal grids in which the hexagons are arranged in hierarchical aggregates, and which accommodates vector operations in GBT space. Efficient algorithms for converting Cartesian coordinates from and to GBT addresses are based on the dual representation of the hexagonal tessellation. The GBT-to-Cartesian algorithm is an order of magnitude faster than the Cartesian-to-GBT algorithm, the latter requiring interpolation and GBT addition for each digit of the generated GBT address.
On differential transformations between Cartesian and curvilinear (geodetic) coordinates
NASA Technical Reports Server (NTRS)
Soler, T.
1976-01-01
Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.
Efficient Fluid Dynamic Design Optimization Using Cartesian Grids
NASA Technical Reports Server (NTRS)
Dadone, A.; Grossman, B.; Sellers, Bill (Technical Monitor)
2004-01-01
This report is subdivided in three parts. The first one reviews a new approach to the computation of inviscid flows using Cartesian grid methods. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, which satisfies the normal momentum equation and the non-penetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we call the Ghost Body-Cell Method (GBCM). In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells which complicate other Cartesian mesh methods.
A Cartesian grid approach with hierarchical refinement for compressible flows
NASA Technical Reports Server (NTRS)
Quirk, James J.
1994-01-01
Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)
2002-01-01
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Topology preserving advection of implicit interfaces on Cartesian grids
NASA Astrophysics Data System (ADS)
Qin, Zhipeng; Delaney, Keegan; Riaz, Amir; Balaras, Elias
2015-06-01
Accurate representation of implicit interface topology is important for the numerical computation of two phase flow on Cartesian grids. A new method is proposed for the construction of signed distance function by geometrically projecting interface topology onto the Cartesian grid using a multi-level projection framework. The method involves a stepwise improvement in the approximation to the signed distance function based on pointwise, piecewise and locally smooth reconstructions of the interface. We show that this approach provides accurate representation of the projected interface and its topology on the Cartesian grid, including the distance from the interface and the interface normal and curvature. The projected interface can be in the form of either a connected set of marker particles that evolve with Lagrangian advection, or a discrete set of points associated with an implicit interface that evolves with the advection of a scalar function. The signed distance function obtained with geometric projection is independent of the details of the scaler field, in contrast to the conventional approach where advection and reinitialization cannot be decoupled. As a result, errors introduced by reinitialization do not amplify advection errors, which leads to substantial improvement in both volume conservation and topology representation.
Nested Cartesian grid method in incompressible viscous fluid flow
NASA Astrophysics Data System (ADS)
Peng, Yih-Ferng; Mittal, Rajat; Sau, Amalendu; Hwang, Robert R.
2010-09-01
In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow-structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier-Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively
Cartesian to geodetic coordinates conversion on a triaxial ellipsoid
NASA Astrophysics Data System (ADS)
Ligas, Marcin
2012-04-01
A new method of transforming Cartesian to geodetic (or planetographic) coordinates on a triaxial ellipsoid is presented. The method is based on simple reasoning coming from essentials of vector calculus. The reasoning results in solving a nonlinear system of equations for coordinates of the point being the projection of a point located outside or inside a triaxial ellipsoid along the normal to the ellipsoid. The presented method has been compared to a vector method of Feltens (J Geod 83:129-137, 2009) who claims that no other methods are available in the literature. Generally, our method turns out to be more accurate, faster and applicable to celestial bodies characterized by different geometric parameters. The presented method also fits to the classical problem of converting Cartesian to geodetic coordinates on the ellipsoid of revolution.
NASA Astrophysics Data System (ADS)
Civicioglu, Pinar
2012-09-01
In order to solve numerous practical navigational, geodetic and astro-geodetic problems, it is necessary to transform geocentric cartesian coordinates into geodetic coordinates or vice versa. It is very easy to solve the problem of transforming geodetic coordinates into geocentric cartesian coordinates. On the other hand, it is rather difficult to solve the problem of transforming geocentric cartesian coordinates into geodetic coordinates as it is very hard to define a mathematical relationship between the geodetic latitude (φ) and the geocentric cartesian coordinates (X, Y, Z). In this paper, a new algorithm, the Differential Search Algorithm (DS), is presented to solve the problem of transforming the geocentric cartesian coordinates into geodetic coordinates and its performance is compared with the performances of the classical methods (i.e., Borkowski, 1989; Bowring, 1976; Fukushima, 2006; Heikkinen, 1982; Jones, 2002; Zhang, 2005; Borkowski, 1987; Shu, 2010 and Lin, 1995) and Computational-Intelligence algorithms (i.e., ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES). The statistical tests realized for the comparison of performances indicate that the problem-solving success of DS algorithm in transforming the geocentric cartesian coordinates into geodetic coordinates is higher than those of all classical methods and Computational-Intelligence algorithms used in this paper.
GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows
NASA Technical Reports Server (NTRS)
2003-01-01
With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.
3D Euler flow solutions using unstructured Cartesian and prismatic grids
NASA Technical Reports Server (NTRS)
Melton, John E.; Pandya, Shishir A.; Steger, Joseph L.
1993-01-01
A hyperbolic prismatic grid generation technique is combined with a background Cartesian grid for the study of inviscid three-dimensional flows. The mathematics of the hyperbolic prismatic grid generation algorithm are described, and some simple inviscid demonstration cases are presented. By combining the simplicity of the Cartesian background grid with the geometric flexibility and computational efficiencies inherent to prismatic grids, this approach shows promise for improving computational aerodynamic simulations.
On NUFFT-based gridding for non-Cartesian MRI
NASA Astrophysics Data System (ADS)
Fessler, Jeffrey A.
2007-10-01
For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI.
On NUFFT-based gridding for non-Cartesian MRI.
Fessler, Jeffrey A
2007-10-01
For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI. PMID:17689121
On NUFFT-based gridding for non-Cartesian MRI
Fessler, Jeffrey A.
2007-01-01
For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [1] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI. PMID:17689121
A multilevel Cartesian non-uniform grid time domain algorithm
Meng Jun; Boag, Amir; Lomakin, Vitaliy; Michielssen, Eric
2010-11-01
A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N{sub s} observation locations from N{sub s} collocated sources for N{sub t} discrete time instances scales as O(N{sub t}N{sub s}logN{sub s}) and O(N{sub t}N{sub s}log{sup 2}N{sub s}) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.
A general time element for orbit integration in Cartesian coordinates
NASA Technical Reports Server (NTRS)
Janin, G.; Bond, V. R.
1981-01-01
Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the in-track error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.
OTAHAL,THOMAS J.; GALLIS,MICHAIL A.; BARTEL,TIMOTHY J.
2000-06-27
This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.
Choi, Cheol Ho
2004-02-22
A new way of generating the multipole moments of Cartesian Gaussian functions in spherical polar coordinates has been established, bypassing the intermediary of Cartesian moment tensors. A new set of recurrence relations have also been derived for the resulting analytic integral values. The new method furnishes a conceptually simple and numerically efficient evaluation procedure for the multipole moments. The advantages over existing methods are documented. The results are relevant for the linear scaling quantum theories based on the fast multipole method. PMID:15268515
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2011-01-01
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
Development and application of a 3D Cartesian grid Euler method
NASA Technical Reports Server (NTRS)
Melton, John E.; Aftosmis, Michael J.; Berger, Marsha J.; Wong, Michael D.
1995-01-01
This report describes recent progress in the development and application of 3D Cartesian grid generation and Euler flow solution techniques. Improvements to flow field grid generation algorithms, geometry representations, and geometry refinement criteria are presented, including details of a procedure for correctly identifying and resolving extremely thin surface features. An initial implementation of automatic flow field refinement is also presented. Results for several 3D multi-component configurations are provided and discussed.
NASA Astrophysics Data System (ADS)
Rhee, Young Min
2000-10-01
A modified method to construct an accurate potential energy surface by interpolation is presented. The modification is based on the use of Cartesian coordinates in the weighting function. The translational and rotational invariance of the potential is incorporated by a proper definition of the distance between two Cartesian configurations. A numerical algorithm to find the distance is developed. It is shown that the present method is more exact in describing a planar system compared to the previous methods with weightings in internal coordinates. The applicability of the method to reactive systems is also demonstrated by performing classical trajectory simulations on the surface.
An adaptive discretization of compressible flow using a multitude of moving Cartesian grids
NASA Astrophysics Data System (ADS)
Qiu, Linhai; Lu, Wenlong; Fedkiw, Ronald
2016-01-01
We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.
Geometry optimization for peptides and proteins: comparison of Cartesian and internal coordinates.
Koslover, Elena F; Wales, David J
2007-12-21
We present the results of several benchmarks comparing the relative efficiency of different coordinate systems in optimizing polypeptide geometries. Cartesian, natural internal, and primitive internal coordinates are employed in quasi-Newton minimization for a variety of biomolecules. The peptides and proteins used in these benchmarks range in size from 16 to 999 residues. They vary in complexity from polyalanine helices to a beta-barrel enzyme. We find that the relative performance of the different coordinate systems depends on the parameters of the optimization method, the starting point for the optimization, and the size of the system studied. In general, internal coordinates were found to be advantageous for small peptides. For larger structures, Cartesians appear to be more efficient for empirical potentials where the energy and gradient can be evaluated relatively quickly compared to the cost of the coordinate transformations. PMID:18154373
Geometry optimization for peptides and proteins: Comparison of Cartesian and internal coordinates
NASA Astrophysics Data System (ADS)
Koslover, Elena F.; Wales, David J.
2007-12-01
We present the results of several benchmarks comparing the relative efficiency of different coordinate systems in optimizing polypeptide geometries. Cartesian, natural internal, and primitive internal coordinates are employed in quasi-Newton minimization for a variety of biomolecules. The peptides and proteins used in these benchmarks range in size from 16 to 999 residues. They vary in complexity from polyalanine helices to a β-barrel enzyme. We find that the relative performance of the different coordinate systems depends on the parameters of the optimization method, the starting point for the optimization, and the size of the system studied. In general, internal coordinates were found to be advantageous for small peptides. For larger structures, Cartesians appear to be more efficient for empirical potentials where the energy and gradient can be evaluated relatively quickly compared to the cost of the coordinate transformations.
NASA Technical Reports Server (NTRS)
Finley, Dennis B.
1995-01-01
This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
Schwartz, Peter; Barad, Michael; Colella, Phillip; Ligocki, Terry
2004-11-02
We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60-85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60-85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.
Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates
NASA Astrophysics Data System (ADS)
Briggs, Andrew; Camblong, Horacio E.; Ordóñez, Carlos R.
2013-06-01
The path integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat space-time geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.
Grid-coordinate generation program
Cosner, Oliver J.; Horwich, Esther
1974-01-01
This program description of the grid-coordinate generation program is written for computer users who are familiar with digital aquifer models. The program computes the coordinates for a variable grid -used in the 'Pinder Model' (a finite-difference aquifer simulator), for input to the CalComp GPCP (general purpose contouring program). The program adjusts the y-value by a user-supplied constant in order to transpose the origin of the model grid from the upper left-hand corner to the lower left-hand corner of the grid. The user has the options of, (1.) choosing the boundaries of the plot; (2.) adjusting the z-values (altitudes) by a constant; (3.) deleting superfluous z-values and (4.) subtracting the simulated surfaces from each other to obtain the decline. Output of this program includes the fixed format CNTL data cards and the other data cards required for input to GPCP. The output from GPCP then is used to produce a potentiometric map or a decline map by means of the CalComp plotter.
Cartesian grid simulations of gas-solids flow systems with complex geometry
Dietiker, Jean-Francois; Li, Tingwen; Garg, Rahul; Shahnam, Mehrdad
2013-02-01
Complex geometries encountered in many applications of gas–solids flow need special treatment in most legacy multiphase flow solvers with Cartesian numerical grid. This paper briefly outlines the implementation of a cut cell technique in the open-source multiphase flow solver—MFIX for accurate representation of complex geometries. Specifically, applications of the Cartesian cut cell method to different gas–solids fluidization systems including a small scale bubbling fluidized bed with submerged tube bundle and a complete pilot-scale circulating fluidized bed will be presented. In addition to qualitative predictions on the general flow behaviors inside each system, quantitative comparison with the available experimental data will be presented. Furthermore, some results on extending the current cut-cell technique to Lagrangian–Eulerian simulations will be presented.
On the new analytical solution for a well in Cartesian coordinates with MODFLOW comparisons.
Batu, Vedat
2014-01-01
In this paper, the comparison process of Batu (2012) generalized three-dimensional well hydraulics solution for confined aquifers in Cartesian coordinates with MODFLOW is presented. First, a brief description of Batu (2012) solution along with the governing equations and some of its key features are described. The final average drawdown expression in an observation well is given with the conversion expressions from Cartesian to radial coordinates. A generalized comparison using Batu (2012), Hantush (1964), and MODFLOW (Harbaugh et al. 2000), for vertical wells in horizontally isotropic aquifers, that is, ayx = Ky /Kx = 1, is presented. Comparisons are also presented with Batu (2012) and MODFLOW for horizontally anisotropic aquifers, that is, ayx ≠ 1. After that comparisons are presented for horizontal wells between Batu (2012) and MODFLOW. PMID:24236933
Mackie, Cameron J; Candian, Alessandra; Huang, Xinchuan; Lee, Timothy J; Tielens, Alexander G G M
2015-06-28
A full derivation of the analytic transformation of the quadratic, cubic, and quartic force constants from normal coordinates to Cartesian coordinates is given. Previous attempts at this transformation have resulted in non-linear transformations; however, for the first time, a simple linear transformation is presented here. Two different approaches have been formulated and implemented, one of which does not require prior knowledge of the translation-rotation eigenvectors from diagonalization of the Hessian matrix. The validity of this method is tested using two molecules H2O and c-C3H2D(+). PMID:26133410
NASA Astrophysics Data System (ADS)
Noda, N.; Ashida, F.; Okumura, I. A.
1992-07-01
In the present paper we propose a new general solution technique for transient thermoelastic problems of transversely isotropic solids in Cartesian coordinates. The solution technique consists of five fundamental solutions. By considering the relations among the material constants of transverse isotropy, the solution technique is classified into five groups. One among those corresponds to Goodier's thermoelastic potential function as well as the generalized Boussinesq solutions and the Michell function. For an application of the solution technique, an inverse problem of transient thermoelasticity in a transversely isotropic semi-infinite solid is analyzed.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
Khoromskij, B.N. Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-09-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h{sup 3}) convergence in the grid-size h=O(n{sup -1}). Moreover, this requires O(3rn+r{sup 3}) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH{sub 4} molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10{sup -6} hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
NASA Astrophysics Data System (ADS)
Zhang, Y.; Chen, C.; Du, J.; Sun, S.; Liang, Q.
2015-12-01
In the study of the inversion of gravity and magnetic data, the discretization of underground space is usually achieved by the use of structured grids. For instance, using the regular block as the module unit to divide model space in Cartesian coordinate system and the tesseroid in spherical coordinate system. Structured grids show clear spatial structures and mathematical properties. However, the block can only provide a rough approximation to the given terrain and using the tesseroid to approximate the terrain even seems impracticable. These shape determining errors cause the reduction of forward modeling precision. Moreover, the precision decreases again while using the tesseroid as no analytical algorithm has been acquired. On the other hand, since most terrain data has a limited resolution, unstructured grids, based on the polyhedron or tetrahedron, could fill the space completely, which allows us to reduce errors in shape determination to the minima. In addition, the analytical algorithms for polyhedron have been proposed. In our study, we use the tetrahedron as the module unit to divide the underground space. Moreover, based on the former researches, we supplement new analytical algorithms for tetrahedron to forward modeling gravity and magnetic fields and their gradient tensors in both Cartesian and spherical coordinate systems. The algorithm is testified by comparing the forward gravity and magnetic data of a block with the data obtained using the existed algorithms. The absolute difference between these two data is under 10e-9 mGal. Our approach is suitable for the inversion of gravity and magnetic data in both Cartesian and spherical coordinate systems.This study is supported by Natural Science Fund of Hubei Province (Grant No.: 2015CFB361) and International Cooperation Project in Science and Technology of China (Grant No.: 2010DFA24580).
A Cartesian grid embedded boundary method for the heat equation on irregular domains
McCorquodale, Peter; Colella, Phillip; Johansen, Hans
2001-03-14
We present an algorithm for solving the heat equation on irregular time-dependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (J. Comput. Phys. 147(2):60--85) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative. This leads to a method that is second-order accurate in space and time. For the case where the boundary is moving, we convert the moving-boundary problem to a sequence of fixed-boundary problems, combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves. We find that, in the moving boundary case, the use of Crank--Nicolson time discretization is unstable, requiring us to use the L{sub 0}-stable implicit Runge--Kutta method of Twizell, Gumel, and Arigu.
Cartesian-Grid Simulations of a Canard-Controlled Missile with a Free-Spinning Tail
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Kwak, Dochan (Technical Monitor)
2002-01-01
The proposed paper presents a series of simulations of a geometrically complex, canard-controlled, supersonic missile with free-spinning tail fins. Time-dependent simulations were performed using an inviscid Cartesian-grid-based method with results compared to both experimental data and high-resolution Navier-Stokes computations. At fixed free stream conditions and canard deflections, the tail spin rate was iteratively determined such that the net rolling moment on the empennage is zero. This rate corresponds to the time-asymptotic rate of the free-to-spin fin system. After obtaining spin-averaged aerodynamic coefficients for the missile, the investigation seeks a fixed-tail approximation to the spin-averaged aerodynamic coefficients, and examines the validity of this approximation over a variety of freestream conditions.
A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids.
Boschitsch, Alexander H; Fenley, Marcia O
2011-05-10
An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous
NASA Astrophysics Data System (ADS)
Chen, XinJian
2012-12-01
This paper presents an application of a three-dimensional unstructured Cartesian grid model (Chen, 2011) to a real-world case, namely the Crystal River/Kings Bay system located on the Gulf coast of the Florida peninsula of the United States. Crystal River/Kings Bay is a spring-fed estuarine system which is believed to be the largest natural refuge in the United States for manatees during the coldest days in winter because of the existence of a large amount of discharge out of numerous spring vents at the bottom of Kings Bay. The unstructured Cartesian grid model was used to simulate hydrodynamics, including salinity transport processes and thermodynamics, in the estuary during a 34-month period from April 2007 to February 2010. Although there are some unidentified uncertainties in quantifying flow rates from the spring vents and salinity variations in spring flows, simulated water elevations, salinities, temperatures, and cross-sectional flux all match well or very well with measured real-time field data. This suggests that the unstructured Cartesian grid model can adequately simulate hydrodynamics in a complex shallow water system such as Crystal River/Kings Bay and the numerical theory for the unstructured Cartesian grid model works properly. The successful simulation of hydrodynamics in the estuarine system also suggests that an empirical formula that relates the spring discharge with the water level in Kings Bay and the groundwater level measured in a nearby well is reasonable.
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
NASA Astrophysics Data System (ADS)
English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald
2013-12-01
We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.
NASA Technical Reports Server (NTRS)
Finley, Dennis B.; Karman, Steve L., Jr.
1996-01-01
The objective of the second phase of the Euler Technology Assessment program was to evaluate the ability of Euler computational fluid dynamics codes to predict compressible flow effects over a generic fighter wind tunnel model. This portion of the study was conducted by Lockheed Martin Tactical Aircraft Systems, using an in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaption of the volume grid during the solution to resolve high-gradient regions. The SPLITFLOW code predictions of configuration forces and moments are shown to be adequate for preliminary design, including predictions of sideslip effects and the effects of geometry variations at low and high angles-of-attack. The transonic pressure prediction capabilities of SPLITFLOW are shown to be improved over subsonic comparisons. The time required to generate the results from initial surface data is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2000-01-01
Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.; Nixon, David (Technical Monitor)
1998-01-01
The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.
Features of CPB: A Poisson-Boltzmann Solver that Uses an Adaptive Cartesian Grid
Harris, Robert C.; Mackoy, Travis
2014-01-01
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other PBE solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software. PMID:25430617
Features of CPB: a Poisson-Boltzmann solver that uses an adaptive Cartesian grid.
Fenley, Marcia O; Harris, Robert C; Mackoy, Travis; Boschitsch, Alexander H
2015-02-01
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software. PMID:25430617
The Dirac equation in external fields: Variable separation in Cartesian coordinates
Shishkin, G.V.; Cabos, W.D. )
1991-11-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors (J. Math. Phys. {bold 30}, 2132 (1989)) is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational (Theor. Math. Phys. {bold 70}, 204 (1987)) or vector fields (J. Math. Phys. {bold 30}, 2132 (1989)), permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper.
The Dirac equation in external fields: Variable separation in Cartesian coordinates
NASA Astrophysics Data System (ADS)
Shishkin, German V.; Cabos, William D.
1991-11-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper.
NASA Astrophysics Data System (ADS)
Sawada, Ryohto; Sato, Takeshi; Ishikawa, Kenichi L.
2016-02-01
We report a three-dimensional numerical implementation of the multiconfiguration time-dependent Hartree-Fock method based on a multiresolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation of H2 and H2O . The present implementation will open a way to the first-principles theoretical study of intense-field- and attosecond-pulse-induced ultrafast phenomena in general molecules.
NASA Astrophysics Data System (ADS)
Sato, Norikazu; Takeuchi, Shintaro; Kajishima, Takeo; Inagaki, Masahide; Horinouchi, Nariaki
2016-09-01
A new discretization scheme on Cartesian grids, namely, a "consistent direct discretization scheme", is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object. The Navier-Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid-solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.
Modelling rapid mass movements using the shallow water equations in Cartesian coordinates
NASA Astrophysics Data System (ADS)
Hergarten, S.; Robl, J.
2015-03-01
We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application - an almost horizontal fluid table - is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this study we present the mathematical formulation of these correction terms and their implementation in the open-source flow solver GERRIS. This novel approach is evaluated by simulating avalanches on synthetic and finally natural topographies and the widely used Voellmy flow resistance law. Testing the results against analytical solutions and the proprietary avalanche model RAMMS, we found a very good agreement. As the GERRIS flow solver is freely available and open source, it can be easily extended by additional fluid models or source areas, making this model suitable for simulating several types of rapid mass movements. It therefore provides a valuable tool for assisting regional-scale natural hazard studies.
NASA Astrophysics Data System (ADS)
Miao, Sha; Hendrickson, Kelli; Liu, Yuming; Subramani, Hariprasad
2015-11-01
This work presents a novel and efficient Cartesian-grid based simulation capability for the study of an incompressible, turbulent gas layer over a liquid flow with disparate Reynolds numbers in two phases. This capability couples a turbulent gas-flow solver and a liquid-layer based on a second-order accurate Boundary Data Immersion Method (BDIM) at the deformable interface. The turbulent gas flow solver solves the incompressible Navier-Stokes equations via direct numerical simulation or through turbulence closure (unsteady Reynolds-Averaged Navier-Stokes Models) for Reynolds numbers O(106). In this application, a laminar liquid layer solution is obtained from depth-integrated Navier-Stokes equations utilizing shallow water wave assumptions. The immersed boundary method (BDIM) enforces the coupling at the deformable interface, the boundary conditions to turbulence closure equations and defines the domain geometry on the Cartesian grid. Validations are made for the turbulent gas channel flow over high-viscosity liquid. This simulation capability can be applied to problems in the oil and industrial sector such as channel and pipe flows with heavy oils as well as wind wave generation in shallow waters. Sponsored by the Chevron Energy Technology Company.
NASA Astrophysics Data System (ADS)
Chung, Eric T.; Ciarlet, Patrick; Yu, Tang Fei
2013-02-01
In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee’s scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. Numerical results are shown to confirm our theoretical statements, and applications to problems in unbounded domains with the use of PML are presented. A comparison of our staggered method and non-staggered method is carried out and shows that our method has better accuracy and efficiency.
Vandewalle, Kristof; Festjens, Nele; Plets, Evelyn; Vuylsteke, Marnik; Saeys, Yvan; Callewaert, Nico
2015-01-01
Reverse genetics research approaches require the availability of methods to rapidly generate specific mutants. Alternatively, where these methods are lacking, the construction of pre-characterized libraries of mutants can be extremely valuable. However, this can be complex, expensive and time consuming. Here, we describe a robust, easy to implement parallel sequencing-based method (Cartesian Pooling-Coordinate Sequencing or CP-CSeq) that reports both on the identity as well as on the location of sequence-tagged biological entities in well-plate archived clone collections. We demonstrate this approach using a transposon insertion mutant library of the Mycobacterium bovis BCG vaccine strain, providing the largest resource of mutants in any strain of the M. tuberculosis complex. The method is applicable to any entity for which sequence-tagged identification is possible. PMID:25960123
NASA Astrophysics Data System (ADS)
Le Chenadec, Vincent; Bay, Yong Yi
2015-11-01
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods also introduce new challenges, in that the formulation of accurate and well-posed discrete operators is not trivial. A cut-cell method for the solution of the incompressible Navier-Stokes equation is proposed for staggered Cartesian grids. In both scalar and vector cases, the emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, different forms are proposed (divergence, advective and skew-symmetric), and shown to be equivalent when the discrete continuity equation is satisfied. This ensures mass, momentum and kinetic energy conservation. For diffusive transport, conservative and symmetric operators are proposed for both Dirichlet and Neumann boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The accuracy of method is finally assessed in standard test cases.
NASA Astrophysics Data System (ADS)
Tran, L. B.; Udaykumar, H. S.
2004-01-01
An Eulerian, sharp interface, Cartesian grid method is developed for the numerical simulation of the response of materials to impact, shocks and detonations. The mass, momentum, and energy equations are solved along with evolution equations for deviatoric stresses and equivalent plastic strain. These equations are cast in Eulerian conservation law form. The Mie-Grüneisen equation of state is used to obtain pressure and the material is modeled as a Johnson-Cook solid. The ENO scheme is employed to capture shocks in combination with a hybrid particle level set technique to evolve sharp immersed boundaries. The numerical technique is able to handle collisions between multiple materials and can accurately compute the dynamics of the immersed boundaries. Results of calculations for axisymmetric Taylor bar impact and penetration of a Tungsten rod into steel plate show good agreement with moving finite element solutions and experimental results. Qualitative agreement with theory is shown for the void collapse phenomenon in an impacted material containing a spherical void.
Relationship between Students' Understanding of Functions in Cartesian and Polar Coordinate Systems
ERIC Educational Resources Information Center
Montiel, Mariana; Vidakovic, Draga; Kabael, Tangul
2009-01-01
The present study was implemented as a prelude to a study on the generalization of the single variable function concept to multivariate calculus. In the present study we analyze students' mental processes and adjustments, as they are being exposed to single variable calculus with polar coordinates. The results show that there appears to be a…
Katz, Jessica; Denholm, Paul; Cochran, Jaquelin
2015-06-01
Greening the Grid provides technical assistance to energy system planners, regulators, and grid operators to overcome challenges associated with integrating variable renewable energy into the grid. Coordinating balancing area operation can promote more cost and resource efficient integration of variable renewable energy, such as wind and solar, into power systems. This efficiency is achieved by sharing or coordinating balancing resources and operating reserves across larger geographic boundaries.
A topological coordinate system for the diamond cubic grid.
Čomić, Lidija; Nagy, Benedek
2016-09-01
Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis. PMID:27580205
Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates
NASA Technical Reports Server (NTRS)
Deane, Anil E.
1996-01-01
Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.
Crockett, Robert; Graves, Daniel; Colella, Phillip
2009-10-23
We present a method for solving Poisson and heat equations with discon- tinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materi- als, as described in Johansen& Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 106, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.
NASA Astrophysics Data System (ADS)
Trost, Nico; Jiménez, Javier; Imke, Uwe; Sanchez, Victor
2014-06-01
TWOPORFLOW is a thermo-hydraulic code based on a porous media approach to simulate single- and two-phase flow including boiling. It is under development at the Institute for Neutron Physics and Reactor Technology (INR) at KIT. The code features a 3D transient solution of the mass, momentum and energy conservation equations for two inter-penetrating fluids with a semi-implicit continuous Eulerian type solver. The application domain of TWOPORFLOW includes the flow in standard porous media and in structured porous media such as micro-channels and cores of nuclear power plants. In the latter case, the fluid domain is coupled to a fuel rod model, describing the heat flow inside the solid structure. In this work, detailed profiling tools have been utilized to determine the optimization potential of TWOPORFLOW. As a result, bottle-necks were identified and reduced in the most feasible way, leading for instance to an optimization of the water-steam property computation. Furthermore, an OpenMP implementation addressing the routines in charge of inter-phase momentum-, energy- and mass-coupling delivered good performance together with a high scalability on shared memory architectures. In contrast to that, the approach for distributed memory systems was to solve sub-problems resulting by the decomposition of the initial Cartesian geometry. Thread communication for the sub-problem boundary updates was accomplished by the Message Passing Interface (MPI) standard.
An efficient game for vehicle-to-grid coordination problems in smart grids
NASA Astrophysics Data System (ADS)
Shi, Xingyu; Ma, Zhongjing
2015-11-01
Emerging plug-in electric vehicles (PEVs), as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grids, like frequency and voltage regulations, by coordinating their active and reactive power rates. However, due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviours among these units in a distributed way. In this paper, we formulate the underlying coordination problems as a novel class of Vickrey-Clarke-Groves style (VCG-style) auction games where players, power grids and PEVs do not report a full cost or valuation function but only a multidimensional bid signal: the maximum active and reactive power quantities that a power grid wants and the maximum per unit prices it is willing to pay, and the maximum active and reactive power quantities that a PEV can provide and the minimum per unit prices it asks for. We show the existence of the efficient Nash equilibrium (NE) for the underlying auction games, though there may exist other inefficient NEs. In order to deal with large-scale PEVs, we design games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extend the so-called quantised-progressive second price mechanism to the underlying auction games to implement the efficient NE.
Akçakaya, Mehmet; Nam, Seunghoon; Basha, Tamer A.; Kawaji, Keigo; Tarokh, Vahid; Nezafat, Reza
2014-01-01
Background Non-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability. Methods We sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate. Results Both CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time. Conclusions The proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity. PMID:25215945
NASA Astrophysics Data System (ADS)
Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.
2014-09-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.
NASA Astrophysics Data System (ADS)
Kapahi, A.; Sambasivan, S.; Udaykumar, H. S.
2013-05-01
This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson-Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.
Federal Register 2010, 2011, 2012, 2013, 2014
2012-09-20
... From the Federal Register Online via the Government Publishing Office NATIONAL SCIENCE FOUNDATION Large Scale Networking (LSN); Middleware and Grid Interagency Coordination (MAGIC) Team AGENCY: The... to the Large Scale Networking (LSN) Coordinating Group (CG). Public Comments: The government...
78 FR 7464 - Large Scale Networking (LSN)-Middleware And Grid Interagency Coordination (MAGIC) Team
Federal Register 2010, 2011, 2012, 2013, 2014
2013-02-01
... From the Federal Register Online via the Government Publishing Office NATIONAL SCIENCE FOUNDATION Large Scale Networking (LSN)--Middleware And Grid Interagency Coordination (MAGIC) Team AGENCY: The... Team reports to the Large Scale Networking (LSN) Coordinating Group (CG). Public Comments:...
Recognizing Patterns In Log-Polar Coordinates
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1992-01-01
Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.
Coordinated grid and place cell replay during rest.
Ólafsdóttir, H Freyja; Carpenter, Francis; Barry, Caswell
2016-06-01
Hippocampal replay has been hypothesized to underlie memory consolidation and navigational planning, yet the involvement of grid cells in replay is unknown. During replay we found grid cells to be spatially coherent with place cells, encoding locations 11 ms delayed relative to the hippocampus, with directionally modulated grid cells and forward replay exhibiting the greatest coherence with the CA1 area of the hippocampus. This suggests grid cells are engaged during the consolidation of spatial memories to the neocortex. PMID:27089021
Electronic Absolute Cartesian Autocollimator
NASA Technical Reports Server (NTRS)
Leviton, Douglas B.
2006-01-01
An electronic absolute Cartesian autocollimator performs the same basic optical function as does a conventional all-optical or a conventional electronic autocollimator but differs in the nature of its optical target and the manner in which the position of the image of the target is measured. The term absolute in the name of this apparatus reflects the nature of the position measurement, which, unlike in a conventional electronic autocollimator, is based absolutely on the position of the image rather than on an assumed proportionality between the position and the levels of processed analog electronic signals. The term Cartesian in the name of this apparatus reflects the nature of its optical target. Figure 1 depicts the electronic functional blocks of an electronic absolute Cartesian autocollimator along with its basic optical layout, which is the same as that of a conventional autocollimator. Referring first to the optical layout and functions only, this or any autocollimator is used to measure the compound angular deviation of a flat datum mirror with respect to the optical axis of the autocollimator itself. The optical components include an illuminated target, a beam splitter, an objective or collimating lens, and a viewer or detector (described in more detail below) at a viewing plane. The target and the viewing planes are focal planes of the lens. Target light reflected by the datum mirror is imaged on the viewing plane at unit magnification by the collimating lens. If the normal to the datum mirror is parallel to the optical axis of the autocollimator, then the target image is centered on the viewing plane. Any angular deviation of the normal from the optical axis manifests itself as a lateral displacement of the target image from the center. The magnitude of the displacement is proportional to the focal length and to the magnitude (assumed to be small) of the angular deviation. The direction of the displacement is perpendicular to the axis about which the
Discretization formulas for unstructured grids
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.
1988-01-01
The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.
78 FR 70076 - Large Scale Networking (LSN)-Middleware and Grid Interagency Coordination (MAGIC) Team
Federal Register 2010, 2011, 2012, 2013, 2014
2013-11-22
... From the Federal Register Online via the Government Publishing Office NATIONAL SCIENCE FOUNDATION Large Scale Networking (LSN)--Middleware and Grid Interagency Coordination (MAGIC) Team AGENCY: The... and responsibility for middleware, Grid, and cloud projects. The MAGIC Team reports to the Large...
NASA Technical Reports Server (NTRS)
Dulikravich, D. S.
1982-01-01
A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.
Gai, Jiading; Obeid, Nady; Holtrop, Joseph L.; Wu, Xiao-Long; Lam, Fan; Fu, Maojing; Haldar, Justin P.; Hwu, Wen-mei W.; Liang, Zhi-Pei; Sutton, Bradley P.
2013-01-01
Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code. PMID:23682203
Multi-agent coordination algorithms for control of distributed energy resources in smart grids
NASA Astrophysics Data System (ADS)
Cortes, Andres
Sustainable energy is a top-priority for researchers these days, since electricity and transportation are pillars of modern society. Integration of clean energy technologies such as wind, solar, and plug-in electric vehicles (PEVs), is a major engineering challenge in operation and management of power systems. This is due to the uncertain nature of renewable energy technologies and the large amount of extra load that PEVs would add to the power grid. Given the networked structure of a power system, multi-agent control and optimization strategies are natural approaches to address the various problems of interest for the safe and reliable operation of the power grid. The distributed computation in multi-agent algorithms addresses three problems at the same time: i) it allows for the handling of problems with millions of variables that a single processor cannot compute, ii) it allows certain independence and privacy to electricity customers by not requiring any usage information, and iii) it is robust to localized failures in the communication network, being able to solve problems by simply neglecting the failing section of the system. We propose various algorithms to coordinate storage, generation, and demand resources in a power grid using multi-agent computation and decentralized decision making. First, we introduce a hierarchical vehicle-one-grid (V1G) algorithm for coordination of PEVs under usage constraints, where energy only flows from the grid in to the batteries of PEVs. We then present a hierarchical vehicle-to-grid (V2G) algorithm for PEV coordination that takes into consideration line capacity constraints in the distribution grid, and where energy flows both ways, from the grid in to the batteries, and from the batteries to the grid. Next, we develop a greedy-like hierarchical algorithm for management of demand response events with on/off loads. Finally, we introduce distributed algorithms for the optimal control of distributed energy resources, i
NASA Technical Reports Server (NTRS)
Eriksson, L. E.
1980-01-01
A direct algebraic method was developed and applied to generate three dimensional grids around wing-body configurations. The method used is a generalized transfinite interpolation method which generates the desired coordinate transformation using geometric data only on the boundaries of the domain of interest. The geometric data that can be specified includes not only coordinates on the boundaries but also out-of-surface parametric derivatives that give a very precise control over the transformation in the vicinity of the surface. In addition to this, the method gives good control over the stretching of the mesh between different boundaries.
The adaptive, cut-cell Cartesian approach (warts and all)
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.
1995-01-01
Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.
A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh
NASA Astrophysics Data System (ADS)
Byerly, Zachary D.; Adelstein-Lelbach, Bryce; Tohline, Joel E.; Marcello, Dominic C.
2014-06-01
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable nonaxisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios and on quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows such as accretion disks and mass-transferring binary systems.
Blodwell, J.F.
1987-10-01
It is argued that the point structure of space and time must be constructed from the primitive extensional character of space and time. A procedure for doing this is laid down and applied to one-dimensional and two-dimensional systems of abstract extensions. Topological and metrical properties of the constructed point systems, which differ nontrivially from the usual R and R/sup 2/ models, are examined. Briefly, constructed points are associated with directions and the Cartesian point is split. In one-dimension each point splits into a point pair compatible with the linear ordering. An application to one-dimensional particle motion is given, with the result that natural topological assumptions force the number of left point, right point transitions to remain locally finite in a continuous motion. In general, Cartesian points are seen to correspond to certain filters on a suitable Boolean algebra. Constructed points correspond to ultrafilters. Thus, point construction gives a natural refinement of the Cartesian systems.
Inverting x,y grid coordinates to obtain latitude and longitude in the vanderGrinten projection
NASA Technical Reports Server (NTRS)
Rubincam, D. P.
1980-01-01
The latitude and longitude of a point on the Earth's surface are found from its x,y grid coordinates in the vanderGrinten projection. The latitude is a solution of a cubic equation and the longitude a solution of a quadratic equation. Also, the x,y grid coordinates of a point on the Earth's surface can be found if its latitude and longitude are known by solving two simultaneous quadratic equations.
Curvilinear grids for sinuous river channels
NASA Technical Reports Server (NTRS)
Tatom, F. B.; Waldrop, W. R.; Smith, S. R.
1980-01-01
In order to effectively analyze the flow in sinuous river channels, a curvilinear grid system was developed for use in the appropriate hydrodynamic code. The CENTERLINE program was designed to generate a two dimensional grid for this purpose. The Cartesian coordinates of a series of points along the boundaries of the sinuous channel represent the primary input to CENTERLINE. The program calculates the location of the river centerline, the distance downstream along the centerline, and both radius of curvature and channel width as a function of such distance downstream. These parameters form the basis for the generation of the curvilinear grid. Based on input values for longitudinal and lateral grid spacing, the corresponding grid system is generated and a file is created containing the appropriate parameters for use in the associated explicit finite difference hydrodynamic programs. Because of the option for a nonuniform grid, grid spacing can be concentrated in areas containing the largest flow gradients.
NASA Astrophysics Data System (ADS)
Takenaka, H.; Komatsu, M.; Toyokuni, G.; Nakamura, T.; Okamoto, T.
2015-12-01
A simple and efficient finite-difference scheme is developed to compute seismic wave propagation for a partial spherical shell model of a three-dimensionally (3-D) heterogeneous global earth structure. This new scheme solves the elastodynamic equations in the "quasi-Cartesian" coordinate system similar to a local Cartesian one, instead of the spherical coordinate system, with a staggered-grid finite-difference method in time domain (FDTD) which is one of the most popular numerical methods in seismic motion simulations for local to regional scale models. The proposed scheme may be useful for modeling seismic wave propagation in a very large region of sub-global scale beyond regional and less than global ones, where the effects of roundness of earth cannot be ignored. In "quasi-Cartesian" coordinates, x, y, and z are set to be locally in directions of latitude, longitude and depth, respectively. The stencil for each of the x-derivatives then depends on the depth coordinate at the evaluation point, while the stencil for each of the y-derivatives varies with both coordinates of the depth and latitude. In order to reduce lateral variations of the horizontal finite-difference stencils over the computational domain, we move the target area to a location around the equator of the computational spherical coordinate system using a way similar to the conversion from equatorial coordinates to ecliptic coordinates. The developed scheme can be easily implemented in 3-D Cartesian FDTD codes for local to regional scale modeling by changing a very small part of the codes. Our scheme may be able to open a window for multi-scale modeling of seismic wave propagation in scales from sub-global to local one.
NASA Technical Reports Server (NTRS)
Chen, Chaing
1991-01-01
This study presents a nested-grid nonhydrostatic and elastic model using a terrain-following coordinate transformation as well as a unique application of grid-nesting techniques to the time-splitting elastic model. A simulation of the 10-m-high Witch of Agnesi Mountain provides the control to test this new model. The results show that the model produces the same solution as that derived from a simple linear analytic model. It is demonstrated that the new nested-grid model improves model resolution without resorting to the costly method of placing a fine-resolution grid over the entire domain. Since the wave reflection from the boundaries of the fine-grid model is well controlled, the boundary of the nested fine-grid model can be located even at the wave-active region. The model can be used to simulate various weather systems in which scale interactions are important.
Development and Applications of 3D Cartesian CFD Technology
NASA Technical Reports Server (NTRS)
Melton, John E.; Berger, Marsha J.; VanDalsem, William (Technical Monitor)
1994-01-01
The urgent need for dramatic reductions in aircraft design cycle time is focusing scrutiny upon all aspects of computational fluid dynamics (CFD). These reductions will most likely come not from increased reliance upon user-interactive (and therefore time-expensive) methods, but instead from methods that can be fully automated and incorporated into 'black box' solutions. In comparison with tetrahedral methods, three-dimensional Cartesian grid approaches are in relative infancy, but initial experiences with automated Cartesian techniques are quite promising. Our research is targeted at furthering the development of Cartesian methods so that they can become key elements of a completely automatic grid generation/flow solution procedure applicable to the Euler analysis of complex aircraft geometries.
Flexible Two-Dimensional Square-Grid Coordination Polymers: Structures and Functions
Kajiro, Hiroshi; Kondo, Atsushi; Kaneko, Katsumi; Kanoh, Hirofumi
2010-01-01
Coordination polymers (CPs) or metal-organic frameworks (MOFs) have attracted considerable attention because of the tunable diversity of structures and functions. A 4,4′-bipyridine molecule, which is a simple, linear, exobidentate, and rigid ligand molecule, can construct two-dimensional (2D) square grid type CPs. Only the 2D-CPs with appropriate metal cations and counter anions exhibit flexibility and adsorb gas with a gate mechanism and these 2D-CPs are called elastic layer-structured metal-organic frameworks (ELMs). Such a unique property can make it possible to overcome the dilemma of strong adsorption and easy desorption, which is one of the ideal properties for practical adsorbents. PMID:21152303
Software for Automated Generation of Cartesian Meshes
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Melton, John E.; Berger, Marshal J.
2006-01-01
Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.
A Cartesian embedded boundary method for hyperbolic conservation laws
Sjogreen, B; Petersson, N A
2006-12-04
The authors develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. They show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, they discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
1988-08-01
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Rapid Structured Volume Grid Smoothing and Adaption Technique
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
2006-01-01
A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reductions in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.
Rapid Structured Volume Grid Smoothing and Adaption Technique
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
2004-01-01
A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reduction in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.
Yin-Yang-Zhong grid: An overset grid system for a sphere
NASA Astrophysics Data System (ADS)
Hayashi, Hiroshi; Kageyama, Akira
2016-01-01
For numerical simulations inside a sphere, an overset grid system, Yin-Yang-Zhong grid, is proposed. The Yin-Yang-Zhong grid is an extension of the Yin-Yang grid, which is widely used in various simulations in spherical shell geometry. The Yin-Yang grid is itself an overset grid system with two component grids, and a new component grid called Zhong is placed at the center of the Yin-Yang grid. The Zhong grid component is constructed on Cartesian coordinates. Parallelization is intrinsically embedded in the Yin-Yang-Zhong grid system because the Zhong grid points are defined with cuboid blocks that are decomposed domains for parallelization. The computational efficiency approaches the optimum as the process number increases. Quantitative test simulations are performed for a diffusion problem in a sphere with the Yin-Yang-Zhong grid. Correct decay rates are obtained by the simulations. Two other tests in magnetohydrodynamics (MHD) in a sphere are also performed. One is an MHD dynamo simulation, and the other is an MHD relaxation simulation in a sphere.
Lalonde, R; Hayzoun, K; Selimi, F; Mariani, J; Strazielle, C
2003-11-01
Grid2(ho/ho) is a loss of function gene mutation resulting in abnormal dendritic arborizations of Purkinje cells. These mutants were compared in a series of motor coordination tests requiring balance and equilibrium to nonataxic controls (Grid2(ho/+)) and to a double mutant (Grid2(ho/Lc)) with an inserted Lc mutation. The performance of Grid2(ho/ho) mutant mice was poorer than that of controls on stationary beam, coat hanger, unsteady platform, and rotorod tests. Grid2(ho/Lc) did not differ from Grid2(Lc/+) mice. However, the insertion of the Lc mutation in Grid2(ho/Lc) potentiated the deficits found in Grid2(ho/ho) in stationary beam, unsteady platform, and rotorod tests. These results indicate a deleterious effect of the Lc mutation on Grid2-deficient mice. PMID:14637233
ERIC Educational Resources Information Center
Planinsic, G.; Kos, M.; Jerman, R.
2004-01-01
It is quite easy to make a version of the well known Cartesian diver experiment that uses two immiscible liquids. This allows students to test their knowledge of density and pressure in explaining the diver's behaviour. Construction details are presented here together with a mathematical model to explain the observations.
Cartesian control of redundant robots
NASA Technical Reports Server (NTRS)
Colbaugh, R.; Glass, K.
1989-01-01
A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.
NASA Astrophysics Data System (ADS)
Zhang, Li; Jabbari, Faryar; Brown, Tim; Samuelsen, Scott
2014-12-01
Plug-in electric vehicles (PEVs) shift energy consumption from petroleum to electricity for the personal transportation sector. This work proposes a decentralized charging protocol for PEVs with grid operators updating the cost signal. Each PEV calculates its own optimal charging profile only once based on the cost signal, after it is plugged in, and sends the result back to the grid operators. Grid operators only need to aggregate charging profiles and update the load and cost. The existing PEV characteristics, national household travel survey (NHTS), California Independent System Operator (CAISO) demand, and estimates for future renewable generation in California are used to simulate PEV operation, PEV charging profiles, grid demand, and grid net load (demand minus renewable). Results show the proposed protocol has good performance for overnight net load valley filling if the costs to be minimized are proportional to the net load. Annual results are shown in terms of overnight load variation and comparisons are made with grid level valley filling results. Further, a target load can be approached in the same manner by using the gap between current load and the target load as the cost. The communication effort involved is quite modest.
Irreducible Cartesian tensors of highest weight, for arbitrary order
NASA Astrophysics Data System (ADS)
Mane, S. R.
2016-03-01
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.
Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing.
Si, Weijian; Qu, Xinggen; Qu, Zhiyu
2015-01-01
This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods. PMID:26343658
Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing
Si, Weijian; Qu, Xinggen; Qu, Zhiyu
2015-01-01
This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods. PMID:26343658
Tao, Liang; McCurdy, C.W.; Rescigno, T.N.
2008-11-25
We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.
76 FR 70721 - Voltage Coordination on High Voltage Grids; Notice of Staff Workshop
Federal Register 2010, 2011, 2012, 2013, 2014
2011-11-15
... software could improve reliability and market efficiency. The workshop will address how entities currently coordinate economic dispatch and voltage control and the capability of existing and emerging software to... interested in better understanding the interaction between voltage control, reliability, and...
The cancer cell 'energy grid': TGF-β1 signaling coordinates metabolism for migration.
Jiang, Lei; Deberardinis, Ralph; Boothman, David A
2015-01-01
Cancer cells have an increased reliance on lipogenesis, which is required for uncontrolled cell division. We recently reported transcriptional and functional 'reprogramming' of the cellular energy grid, allowing cancer cells to divert metabolism from biosynthesis to bioenergetic pathways and thus supplying enhanced mobility during epithelial-mesenchymal transition (EMT) induced by transforming growth factor β (TGF-β1) (Fig. 1). PMID:27308459
NASA Technical Reports Server (NTRS)
Lopez, Isaac; Follen, Gregory J.; Gutierrez, Richard; Foster, Ian; Ginsburg, Brian; Larsson, Olle; Martin, Stuart; Tuecke, Steven; Woodford, David
2000-01-01
This paper describes a project to evaluate the feasibility of combining Grid and Numerical Propulsion System Simulation (NPSS) technologies, with a view to leveraging the numerous advantages of commodity technologies in a high-performance Grid environment. A team from the NASA Glenn Research Center and Argonne National Laboratory has been studying three problems: a desktop-controlled parameter study using Excel (Microsoft Corporation); a multicomponent application using ADPAC, NPSS, and a controller program-, and an aviation safety application running about 100 jobs in near real time. The team has successfully demonstrated (1) a Common-Object- Request-Broker-Architecture- (CORBA-) to-Globus resource manager gateway that allows CORBA remote procedure calls to be used to control the submission and execution of programs on workstations and massively parallel computers, (2) a gateway from the CORBA Trader service to the Grid information service, and (3) a preliminary integration of CORBA and Grid security mechanisms. We have applied these technologies to two applications related to NPSS, namely a parameter study and a multicomponent simulation.
Coordinating the Global Information Grid Initiative with the NG9-1-1 Initiative
Michael Schmitt
2008-05-01
As the Department of Defense develops the Global Information Grid, the Department of Transportation develops the Next Generation 9-1-1 system. Close examinations of these initiatives show that the two are similar in architectures, applications, and communications interoperability. These similarities are extracted from the lowest user level to the highest commander rank that will be involved in each network. Once the similarities are brought into perspective, efforts should be made to collaborate between the two departments.
Adjoint Formulation for an Embedded-Boundary Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
2004-01-01
Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code
Dimbylow, Peter
2011-07-21
This paper sets out to explore the effects of voxel resolution, from 2 mm down to 0.1 mm for Cartesian co-ordinates and the differences between Cartesian and spherical polar co-ordinates for a standardized test-bed model of the eye. This model was taken from the work of Yoriyaz et al (2005 Radiat. Prot. Dosim. 115 316-9) who have developed a detailed geometric description of the eye including choroid, retina, sclera, lens, cornea, anterior chamber, vitreous humour and optic nerve for ophthalmic brachytherapy. The spherical co-ordinate model has radial and angular steplengths of 0.1 mm and 0.25°, respectively. The current density averaged over 1 cm(2) and the 99th percentile value of the induced electric field have been calculated in the retina and central nervous system for uniform magnetic fields. The Cartesian co-ordinate calculations proceed in a sequence of grids at 2, 1, 0.5, 0.2 and 0.1 mm resolution with the potentials from the previous calculation at a coarser grid providing the boundary conditions on the finer grid. The 0.2 mm grid provides the boundary conditions for the spherical polar calculations. Comparisons are made with the International Commission on Non-Ionizing Radiation Protection reference levels. PMID:21725142
A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID
Feng, Xueshang; Zhang, Man; Zhou, Yufen
2014-09-01
In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.
CUDA accelerated uniform re-sampling for non-Cartesian MR reconstruction.
Feng, Chaolu; Zhao, Dazhe
2015-01-01
A grid-driven gridding (GDG) method is proposed to uniformly re-sample non-Cartesian raw data acquired in PROPELLER, in which a trajectory window for each Cartesian grid is first computed. The intensity of the reconstructed image at this grid is the weighted average of raw data in this window. Taking consider of the single instruction multiple data (SIMD) property of the proposed GDG, a CUDA accelerated method is then proposed to improve the performance of the proposed GDG. Two groups of raw data sampled by PROPELLER in two resolutions are reconstructed by the proposed method. To balance computation resources of the GPU and obtain the best performance improvement, four thread-block strategies are adopted. Experimental results demonstrate that although the proposed GDG is more time consuming than traditional DDG, the CUDA accelerated GDG is almost 10 times faster than traditional DDG. PMID:26406102
NASA Technical Reports Server (NTRS)
Smith, R. E.
1981-01-01
A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.
Rabow, A. A.; Scheraga, H. A.
1996-01-01
We have devised a Cartesian combination operator and coding scheme for improving the performance of genetic algorithms applied to the protein folding problem. The genetic coding consists of the C alpha Cartesian coordinates of the protein chain. The recombination of the genes of the parents is accomplished by: (1) a rigid superposition of one parent chain on the other, to make the relation of Cartesian coordinates meaningful, then, (2) the chains of the children are formed through a linear combination of the coordinates of their parents. The children produced with this Cartesian combination operator scheme have similar topology and retain the long-range contacts of their parents. The new scheme is significantly more efficient than the standard genetic algorithm methods for locating low-energy conformations of proteins. The considerable superiority of genetic algorithms over Monte Carlo optimization methods is also demonstrated. We have also devised a new dynamic programming lattice fitting procedure for use with the Cartesian combination operator method. The procedure finds excellent fits of real-space chains to the lattice while satisfying bond-length, bond-angle, and overlap constraints. PMID:8880904
On automating domain connectivity for overset grids
NASA Technical Reports Server (NTRS)
Chiu, Ing-Tsau
1994-01-01
An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximated body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian Systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems.
NASA Astrophysics Data System (ADS)
Rousseau, Guy; Gay, David; Piché, Michel
2006-09-01
A recent analysis [G. Rousseau, D. Gay and M. Piché, One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams, J. Opt. Soc. Am. A, 22 (2005) 1274] has shown that any cylindrically symmetric laser beam can be synthesized from a single wave called a constituent wave. This representation allows the introduction of one-dimensional Cartesian root-mean-square (rms) parameters to describe the conical structure of cylindrically symmetric laser beams. In this paper, we compare the rms characterization of Bessel-Gauss beams in polar coordinates with that of their respective constituent waves in Cartesian coordinates. Numerical results reveal an asymptotic correspondence between polar and Cartesian rms parameters of Bessel-Gauss beams propagating in a nondiffracting regime. Such a correspondence eliminates misleading interpretations about the propagation factor and the Rayleigh range of nondiffracting Bessel-type beams characterized in terms of polar rms parameters.
A Cartesian cut cell method for rarefied flow simulations around moving obstacles
NASA Astrophysics Data System (ADS)
Dechristé, G.; Mieussens, L.
2016-06-01
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kinds of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including a 3D unsteady simulation of the Crookes radiometer.
Parameter Studies, time-dependent simulations and design with automated Cartesian methods
NASA Technical Reports Server (NTRS)
Aftosmis, Michael
2005-01-01
Over the past decade, NASA has made a substantial investment in developing adaptive Cartesian grid methods for aerodynamic simulation. Cartesian-based methods played a key role in both the Space Shuttle Accident Investigation and in NASA's return to flight activities. The talk will provide an overview of recent technological developments focusing on the generation of large-scale aerodynamic databases, automated CAD-based design, and time-dependent simulations with of bodies in relative motion. Automation, scalability and robustness underly all of these applications and research in each of these topics will be presented.
Minimization of deviations of gear real tooth surfaces determined by coordinate measurements
NASA Technical Reports Server (NTRS)
Litvin, F. L.; Kuan, C.; Wang, J.-C.; Handschuh, R. F.; Masseth, J.; Maruyama, N.
1992-01-01
The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.
Turing instabilities on Cartesian product networks
Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-01-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory. PMID:26245138
Turing instabilities on Cartesian product networks
NASA Astrophysics Data System (ADS)
Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-08-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory.
Turing instabilities on Cartesian product networks.
Asllani, Malbor; Busiello, Daniel M; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
2015-01-01
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory. PMID:26245138
Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids
NASA Technical Reports Server (NTRS)
Vinokur, Marcel; Yee H. C.; Koga, Dennis (Technical Monitor)
2000-01-01
The efficient low dissipative high order schemes proposed by Yee et al. is formulated for 3-D curvilinear moving grids. These schemes consists of a high order base schemes combined with nonlinear characteristic filters. The amount of numerical dissipation is minimized by applying the schemes to the entropy splitting form of the inviscid flux derivatives. The analysis is given for a thermally perfect gas. The main difficulty in the extension of higher order schemes that were formulated in Cartesian coordinates to curvilinear moving grids is the higher order transformed metric evaluations. The higher order numerical evaluation of the transformed metric terms to insure freestream preservation is done in a coordinate invariant manner. The formulation is an improvement over existing formulation of high order scheme in curvilinear moving grids.
Moment Closures on Two-Dimensional Cartesian Grids
Energy Science and Technology Software Center (ESTSC)
2015-07-31
Some moment methods for kinetic equations are complicated and take time to develop. Over the course of a couple years, this software was developed to test different closures on standard test problems in the literature. With this software, researchers in the field of moment closures will be able to rapidly test new methods.
A Laplacian Equation Method for Numerical Generation of Boundary-Fitted 3D Orthogonal Grids
NASA Astrophysics Data System (ADS)
Theodoropoulos, T.; Bergeles, G. C.
1989-06-01
A sethod for generating boundary fitted orthogonal curvilinear grids in 3-dimensional space is described. The mapping between the curvilinear coordinates and the Cartesian coordinates is provided by a set of Laplace equations which, expressed in curvilinear coordinates, involve the components of the metric tensor and are therefore non-linear and coupled. An iterative algorithm is described, which achieves a numerical solution. Grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery, and for other engineering applications can be constructed using the proposed method. Various examples are presented and plotted in perspective, and data for the assessment of the properties of the resulting meshes is provided.
NASA Astrophysics Data System (ADS)
Melaaen, M. C.
1992-02-01
Tensor calculus is presently employed to furnish both necessary coordinate and velocity transformations in the present use of two different finite-volume methods for discretization of conservation equations in 3D curvilinear nonorthogonal coordinates. While one method is based on the nonstaggered grid arrangement and employs Cartesian velocity components as dependent variables in the momentum equations, the other combines a staggered grid arrangement with physical covariant velocity projections in a locally fixed coordinate system. In the second part of this work, a comparative evaluation of the two methods indicates that while results of comparable accuracy are achieved after a similar number of iterations, the staggered method may be recommended for curvilinear nonorthogonal coordinate problems due to its reduced memory and computational requirements.
NASA Astrophysics Data System (ADS)
Liu, Guang-Zhen; Li, Xiao-Dong; Xin, Ling-Yun; Li, Xiao-Ling; Wang, Li-Ya
2013-07-01
Diverse (4,4) grid layers are exemplified in five two-dimensional coordination polymers with dual μ2-bridged ligands, namely, {[Zn(cbaa)(bpp)]·H2O}n (1), [Zn2(cbaa)2(bpy)]n (2), [Co2(cbaa)2(bpp)2]n (3), [Co(cbaa)(bpp)]n (4), and [Co(bdaa)(bpp)(H2O)2]n (5) (H2cbaa=4-carboxybenzeneacetic acid, bpp=1,3-di(4-pyridyl)propane, bpy=4,4‧-bipyridyl, and H2bdaa=1,4-benzenediacrylic acid). For 1, two (4,4) grid layers with [ZnN2O2] tetrahedron as the node are held together by lattice water forming a H-bonding bilayer. Individual (4,4) grid layer in 2 is based on {Zn2(OCO)4} paddlewheel unit as the node. Two (4,4) grid layers with {Co2O(OCO)2} dimer as the node are covalently interconnected by organic ligands affording a thick bilayer of 3 with new framework topology. The different entanglements between two coincident (4,4) grid layers with [CoN2O4] octahedron as the node leads to two 2D→2D interpenetrated structures for 4 and 5. Furthermore, fluorescent properties of 1 and 2 as well as magnetic properties of 3 are investigated.
Maintain rigid structures in Verlet based Cartesian molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Tao, Peng; Wu, Xiongwu; Brooks, Bernard R.
2012-10-01
An algorithm is presented to maintain rigid structures in Verlet based Cartesian molecular dynamics (MD) simulations. After each unconstrained MD step, the coordinates of selected particles are corrected to maintain rigid structures through an iterative procedure of rotation matrix computation. This algorithm, named as SHAPE and implemented in CHARMM program suite, avoids the calculations of Lagrange multipliers, so that the complexity of computation does not increase with the number of particles in a rigid structure. The implementation of this algorithm does not require significant modification of propagation integrator, and can be plugged into any Cartesian based MD integration scheme. A unique feature of the SHAPE method is that it is interchangeable with SHAKE for any object that can be constrained as a rigid structure using multiple SHAKE constraints. Unlike SHAKE, the SHAPE method can be applied to large linear (with three or more centers) and planar (with four or more centers) rigid bodies. Numerical tests with four model systems including two proteins demonstrate that the accuracy and reliability of the SHAPE method are comparable to the SHAKE method, but with much more applicability and efficiency.
Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1996-01-01
A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
Near-Body Grid Adaption for Overset Grids
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2016-01-01
A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.
Liu, Guang-Zhen; Li, Xiao-Dong; Xin, Ling-Yun; Li, Xiao-Ling; Wang, Li-Ya
2013-07-15
Diverse (4,4) grid layers are exemplified in five two-dimensional coordination polymers with dual µ{sub 2}-bridged ligands, namely, ([Zn(cbaa)(bpp)]·H{sub 2}O){sub n} (1), [Zn{sub 2}(cbaa){sub 2}(bpy)]{sub n} (2), [Co{sub 2}(cbaa){sub 2}(bpp){sub 2}]{sub n} (3), [Co(cbaa)(bpp)]{sub n} (4), and [Co(bdaa)(bpp)(H{sub 2}O){sub 2}]{sub n} (5) (H{sub 2}cbaa=4-carboxybenzeneacetic acid, bpp=1,3-di(4-pyridyl)propane, bpy=4,4′-bipyridyl, and H{sub 2}bdaa=1,4-benzenediacrylic acid). For 1, two (4,4) grid layers with [ZnN{sub 2}O{sub 2}] tetrahedron as the node are held together by lattice water forming a H-bonding bilayer. Individual (4,4) grid layer in 2 is based on (Zn{sub 2}(OCO){sub 4}) paddlewheel unit as the node. Two (4,4) grid layers with (Co{sub 2}O(OCO){sub 2}) dimer as the node are covalently interconnected by organic ligands affording a thick bilayer of 3 with new framework topology. The different entanglements between two coincident (4,4) grid layers with [CoN{sub 2}O{sub 4}] octahedron as the node leads to two 2D→2D interpenetrated structures for 4 and 5. Furthermore, fluorescent properties of 1 and 2 as well as magnetic properties of 3 are investigated. - Graphical abstract: Diverse assemblies of the (4,4) grid layers with different network nodes forms five coordination polymers that are well characterized by IR, TGA, element analysis, fluorescent and magnetic measurement. - Highlights: • Diverse assemblies of the (4,4) grid layers with different structural units as the nodes. • A new topology type with the uninodal 6-connected net of (4{sup 12}.5{sup 2}.6) is found. • Intense fluorescence emissions with a rare blue-shift of 55 nm compared to free carboxylate ligand.
Adventures in Coordinate Space
NASA Astrophysics Data System (ADS)
Chambers, J. E.
2003-08-01
A variety of coordinate systems have been used to study the N-body problem for cases involving a dominant central mass. These include the traditional Keplerian orbital elements and the canonical Delaunay variables, which both incorporate conserved quantities of the two-body problem. Recently, Cartesian coordinate systems have returned to favour with the rise of mixed-variable symplectic integrators, since these coordinates prove to be more efficient than using orbital elements. Three sets of canonical Cartesian coordinates are well known, each with its own advantages and disadvantages. Inertial coordinates (which include barycentric coordinates as a special case) are the simplest and easiest to implement. However, they suffer from the disadvantage that the motion of the central body must be calculated explicitly, leading to relatively large errors in general. Jacobi coordinates overcome this problem by replacing the coordinates and momenta of the central body with those of the system as a whole, so that momentum is conserved exactly. This leads to substantial improvements in accuracy, but has the disadvantage that every object is treated differently, and interactions between each pair of bodies are now expressed in a complicated manner involving the coordinates of many bodies. Canonical heliocentric coordinates (also known as democratic heliocentric coordinates) treat all bodies equally, and conserve the centre of mass motion, but at the cost of introducing momentum cross terms into the kinetic energy. This complicates the development of higher order symplectic integrators and symplectic correctors, as well as the development of methods used to resolve close encounters with the central body. Here I will re-examine the set of possible canonical Cartesian coordinate systems to determine if it is possible to (a) conserve the centre of mass motion, (b) treat all bodies equally, and (c) eliminate the momentum cross terms. I will demonstrate that this is indeed possible
A spectral element shallow water model on spherical geodesic grids
NASA Astrophysics Data System (ADS)
Giraldo, Francis X.
2001-04-01
The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained from the generalized icosahedral grid introduced previously (Giraldo FX. Lagrange-Galerkin methods on spherical geodesic grids: the shallow water equations. Journal of Computational Physics 2000; 160: 336-368). The equations are written in Cartesian co-ordinates that introduce an additional momentum equation, but the pole singularities disappear. This paper represents a departure from previously published work on solving the shallow water equations on the sphere in that the equations are all written, discretized, and solved in three-dimensional Cartesian space. Because the equations are written in a three-dimensional Cartesian co-ordinate system, the algorithm simplifies into the integration of surface elements on the sphere from the fully three-dimensional equations. A mapping (Song Ch, Wolf JP. The scaled boundary finite element method - alias consistent infinitesimal finite element cell method - for diffusion. International Journal for Numerical Methods in Engineering 1999; 45: 1403-1431) which simplifies these computations is described and is shown to contain the Eulerian version of the method introduced previously by Giraldo (Journal of Computational Physics 2000; 160: 336-368) for the special case of triangular elements. The significance of this mapping is that although the equations are written in Cartesian co-ordinates, the mapping takes into account the curvature of the high-order spectral elements, thereby allowing the elements to lie entirely on the surface of the sphere. In addition, using this mapping simplifies all of the three-dimensional spectral-type finite element surface integrals because any of the typical two-dimensional planar finite element or spectral element basis functions found in any textbook (for example, Huebner et al
Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.
NASA Technical Reports Server (NTRS)
Rumsey, Christopher Lockwood
1991-01-01
A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.
Schäfer, Bernhard; Greisch, Jean-François; Faus, Isabelle; Bodenstein, Tilmann; Šalitroš, Ivan; Fuhr, Olaf; Fink, Karin; Schünemann, Volker; Kappes, Manfred M; Ruben, Mario
2016-08-26
The coordination of iron(II) ions by a homoditopic ligand L with two tridentate chelates leads to the tautomerism-driven emergence of complexity, with isomeric tetramers and trimers as the coordination products. The structures of the two dominant [Fe(II) 4 L4 ](8+) complexes were determined by X-ray diffraction, and the distinctness of the products was confirmed by ion-mobility mass spectrometry. Moreover, these two isomers display contrasting magnetic properties (Fe(II) spin crossover vs. a blocked Fe(II) high-spin state). These results demonstrate how the coordination of a metal ion to a ligand that can undergo tautomerization can increase, at a higher hierarchical level, complexity, here expressed by the formation of isomeric molecular assemblies with distinct physical properties. Such results are of importance for improving our understanding of the emergence of complexity in chemistry and biology. PMID:27411212
A Cartesian Adaptive Level Set Method for Two-Phase Flows
NASA Technical Reports Server (NTRS)
Ham, F.; Young, Y.-N.
2003-01-01
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
Inflow-outflow boundary conditions along arbitrary directions in Cartesian lake models
NASA Astrophysics Data System (ADS)
Ramón, C. L.; Cortés, A.; Rueda, F. J.
2015-01-01
Specifying point sources and sinks of water near boundaries is presented as a flexible approach to prescribe inflows and outflows along arbitrary directions in Cartesian grid lake models. Implementing the approach involves a straightforward modification of the governing equations, to include a first order source term in the continuity and momentum equations. The approach is implemented in a Cartesian grid model and applied to several test cases. First, the flow along a straight flat bottom channel with its axis forming different angles with the grid directions is simulated and the results are compared against well-known analytical solutions. Point-sources are then used to simulate unconfined inflows into a reservoir (a small river entering a reservoir in a jet-like manner), which occur at an angle with the grid directions. The model results are assessed in terms of a mixing ratio between lake and river water, evaluated at a cross section downstream of the inflow boundary. Those results are particularly sensitive to changes in the inflow angle. It is argued that differences in mixing rates near the inflow sections could affect the fate of river-borne substances in model simulations.
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
Structured background grids for generation of unstructured grids by advancing front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1991-01-01
A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.
Chassin, David P.; Kiesling, Lynne
2008-10-15
The project highlights the idea that technology-enabled decentralized coordination can achieve the same, or better, economic and reliability benefits when compared to utility-focused centralized physical and economic control. Among the design's unique features was a retail double auction with five-minute market-clearing intervals that included residential customers as direct, active market participants. (author)
NASA Astrophysics Data System (ADS)
Indrani, Murugan; Ramasubramanian, Ramasamy; Fronczek, Frank R.; Vasanthacharya, N. Y.; Kumaresan, Sudalaiandi
2009-08-01
Three distinct coordination complexes, viz., [Co(imi) 2(tmb) 2] ( 1) [where imi = imidazole], {[Ni(tmb) 2(H 2O) 3]·2H 2O} n ( 2) and [Cu 2(μ-tmb) 4(CH 3OH) 2] ( 3), have been synthesized hydrothermally by the reactions of metal acetates, 2,4,6-trimethylbenzoic acid (Htmb) and with or without appropriate amine. The Ni analogue of 1 and the Co analogue of 2 have also been synthesized. X-ray single-crystal diffraction suggests that complex 1 represents discrete mononuclear species and complex 2 represents a 1D chain coordination polymer in which the Ni(II) ions are connected by the bridging water molecules. Complex 3 represents a neutral dinuclear complex. In 1, the central metal ions are associated by the carboxylate moiety and imidazole ligands, whereas the central metal atom is coordinated to the carboxylate moiety and the respective solvent molecules in 2 and 3. In 3, the four 2,4,6-trimethylbenzoate moieties act as a bridge connecting two copper (II) ions and the O atoms of methanol coordinate in an anti arrangement to form a square pyramidal geometry, with the methanol molecule at the apical position. In all the three structures the central metal atom sits on a crystallographic inversion centre. In all the cases, the coordination entities are further organized via hydrogen bonding interactions to generate multifarious supramolecular networks. Complexes 1, 2 and 3 have also been characterized by spectroscopic (UV/Vis and IR) and thermal analysis (TGA). In addition, the complexes were found to exhibit antimicrobial activity.The magnetic susceptibility measurements, measured from 8 to 300 K, revealed antiferromagnetic interactions between the Co(II) ions in compound 1 and the Ni(II) ions in 1a, respectively.
NASA Technical Reports Server (NTRS)
Moore, Reagan W.; Jagatheesan, Arun; Rajasekar, Arcot; Wan, Michael; Schroeder, Wayne
2004-01-01
The "Grid" is an emerging infrastructure for coordinating access across autonomous organizations to distributed, heterogeneous computation and data resources. Data grids are being built around the world as the next generation data handling systems for sharing, publishing, and preserving data residing on storage systems located in multiple administrative domains. A data grid provides logical namespaces for users, digital entities and storage resources to create persistent identifiers for controlling access, enabling discovery, and managing wide area latencies. This paper introduces data grids and describes data grid use cases. The relevance of data grids to digital libraries and persistent archives is demonstrated, and research issues in data grids and grid dataflow management systems are discussed.
Tao, Liang; McCurdy, Bill; Rescigno, Tom
2010-06-10
Our previously developed finite-element/ discrete variable representation in prolate spheroidal coordinates is extended to two-electron systems with a study of double ionization of H$_2$ with fixed-nuclei. Particular attention is paid to the development of fast and accurate methods for treating the electron-electron interaction. The use of exterior complex scaling in the implementation offers a simple way of enforcing Coulomb boundary conditions for the electronic double continuum. While the angular distributions calculated in this study are found to be completely consistent with our earlier treatments that employed single-center expansions in spherical coordinates, we find that the magnitude of the integrated cross sections are sensitive to small changes in the initial-state wave function. The present formulation offers significant advantages with respect to convergence and efficiency and opens the way to calculations on more complicated diatomic targets.
A Two-dimensional Cartesian and Axisymmetric Study of Combustion-acoustic Interaction
NASA Technical Reports Server (NTRS)
Hood, Caroline; Frendi, Abdelkader
2006-01-01
This paper describes a study of a lean premixed (LP) methane-air combustion wave in a two-dimensional Cartesian and axisymmetric coordinate system. Lean premixed combustors provide low emission and high efficiency; however, they are susceptible to combustion instabilities. The present study focuses on the behavior of the flame as it interacts with an external acoustic disturbance. It was found that the flame oscillations increase as the disturbance amplitude is increased. Furthermore, when the frequency of the disturbance is at resonance with a chamber frequency, the instabilities increase. For the axisymmetric geometry, the flame is found to be more unstable compared to the Cartesian case. In some cases, these instabilities were severe and led to flame extinction. In the axisymmetric case, several passive control devices were tested to assess their effectiveness. It is found that an acoustic cavity is better able at controlling the pressure fluctuations in the chamber.
On automating domain connectivity for overset grids
NASA Technical Reports Server (NTRS)
Chiu, Ing-Tsau; Meakin, Robert L.
1995-01-01
An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.
Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.
Electrostatic PIC with adaptive Cartesian mesh
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert
2016-05-01
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.
An adaptive Cartesian control scheme for manipulators
NASA Technical Reports Server (NTRS)
Seraji, H.
1987-01-01
A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.
NASA Technical Reports Server (NTRS)
Swinbank, Richard; Purser, James
2006-01-01
Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.
NASA Astrophysics Data System (ADS)
Lamer, K.; Tatarevic, A.; Jo, I.; Kollias, P.
2013-11-01
The Scanning ARM Cloud Radars (SACR's) provide continuous atmospheric observations aspiring to capture the 3-D cloud-scale structure. Sampling clouds in 3-D is challenging due to their temporal-spatial scales, the need to sample the sky at high elevations and cloud radar limitations. Thus, a common scan strategy is to repetitively slice the atmosphere from horizon to horizon as clouds advect over the radar (Cross-Wind Range Height Indicator - CWRHI). Here, the processing and gridding of the SACR CW-RHI scans are presented. First, the SACR sample observations from the ARM Oklahoma (SGP) and Cape-Cod (PVC) sites are post-processed (detection mask, velocity de-aliasing and gaseous attenuation correction). The resulting radial Doppler moment fields are then mapped to Cartesian coordinates with time as one of the dimension. The Cartesian-gridded Doppler velocity fields are next decomposed into the horizontal wind velocity contribution and the vertical Doppler velocity component. For validation purposes, all gridded and retrieved fields are compared to collocated zenith pointing ARM cloud radar measurements. We consider that the SACR sensitivity loss with range, the cloud type observed and the research purpose should be considered in determining the gridded domain size. Our results also demonstrate that the gridded SACR observations resolve the main features of low and high stratiform clouds. It is established that the CW-RHI observations complemented with processing techniques could lead to robust 3-D clouds dynamical representations up to 25-30° off zenith. The proposed gridded products are expected to advance our understanding of 3-D cloud morphology, dynamics, anisotropy and lead to more realistic 3-D radiative transfer calculations.
NASA Astrophysics Data System (ADS)
Lamer, K.; Tatarevic, A.; Jo, I.; Kollias, P.
2014-04-01
The scanning Atmospheric Radiation Measurement (ARM) cloud radars (SACRs) provide continuous atmospheric observations aspiring to capture the 3-D cloud-scale structure. Sampling clouds in 3-D is challenging due to their temporal-spatial scales, the need to sample the sky at high elevations and cloud radar limitations. Thus, a suggested scan strategy is to repetitively slice the atmosphere from horizon to horizon as clouds advect over the radar (Cross-Wind Range-Height Indicator - CW-RHI). Here, the processing and gridding of the SACR CW-RHI scans are presented. First, the SACR sample observations from the ARM Southern Great Plains and Cape Cod sites are post-processed (detection mask, gaseous attenuation correction, insect filtering and velocity de-aliasing). The resulting radial Doppler moment fields are then mapped to Cartesian coordinates with time as one of the dimensions. Next the Cartesian-gridded Doppler velocity fields are decomposed into the horizontal wind velocity contribution and the vertical Doppler velocity component. For validation purposes, all gridded and retrieved fields are compared to collocated zenith-pointing ARM cloud radar measurements. We consider that the SACR sensitivity loss with range, the cloud type observed and the research purpose should be considered in determining the gridded domain size. Our results also demonstrate that the gridded SACR observations resolve the main features of low and high stratiform clouds. It is established that the CW-RHI observations complemented with processing techniques could lead to robust 3-D cloud dynamical representations up to 25-30 degrees off zenith. The proposed gridded products are expected to advance our understanding of 3-D cloud morphology, dynamics and anisotropy and lead to more realistic 3-D radiative transfer calculations.
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1994-01-01
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.
Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Martí, José María; Müller, Ewald
2015-12-01
An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates.
NASA Astrophysics Data System (ADS)
Lin, Dejun
2015-09-01
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2004-01-01
Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2005-01-01
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
Visual Methods for Model and Grid Validation
NASA Technical Reports Server (NTRS)
Pang, Alex
1998-01-01
This joint research interchange proposal allowed us to contribute in two directions that are of interest to NASA. These are: (a) data level comparative visualization of experimental and computational fluid flow, and (b) visualization tools for analysis of adaptively refined Cartesian grids.
OVERGRID: A Unified Overset Grid Generation Graphical Interface
NASA Technical Reports Server (NTRS)
Chan, William M.; Akien, Edwin W. (Technical Monitor)
1999-01-01
This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.
Biangular Coordinates Redux: Discovering a New Kind of Geometry
ERIC Educational Resources Information Center
Winkel, Brian; Naylor, Michael
2010-01-01
Biangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the…
Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers
Zanchi, Marta G.; Pauly, John M.; Scott, Greig C.
2010-01-01
A modified Cartesian feedback method called “frequency-offset Cartesian feedback” and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems. In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200–1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback. In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems. PMID:20814450
Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers.
Zanchi, Marta G; Pauly, John M; Scott, Greig C
2010-05-01
A modified Cartesian feedback method called "frequency-offset Cartesian feedback" and based on polyphase difference amplifiers is described that significantly reduces the problems associated with quadrature errors and DC-offsets in classic Cartesian feedback power amplifier control systems.In this method, the reference input and feedback signals are down-converted and compared at a low intermediate frequency (IF) instead of at DC. The polyphase difference amplifiers create a complex control bandwidth centered at this low IF, which is typically offset from DC by 200-1500 kHz. Consequently, the loop gain peak does not overlap DC where voltage offsets, drift, and local oscillator leakage create errors. Moreover, quadrature mismatch errors are significantly attenuated in the control bandwidth. Since the polyphase amplifiers selectively amplify the complex signals characterized by a +90° phase relationship representing positive frequency signals, the control system operates somewhat like single sideband (SSB) modulation. However, the approach still allows the same modulation bandwidth control as classic Cartesian feedback.In this paper, the behavior of the polyphase difference amplifier is described through both the results of simulations, based on a theoretical analysis of their architecture, and experiments. We then describe our first printed circuit board prototype of a frequency-offset Cartesian feedback transmitter and its performance in open and closed loop configuration. This approach should be especially useful in magnetic resonance imaging transmit array systems. PMID:20814450
Configuration space representation in parallel coordinates
NASA Technical Reports Server (NTRS)
Fiorini, Paolo; Inselberg, Alfred
1989-01-01
By means of a system of parallel coordinates, a nonprojective mapping from R exp N to R squared is obtained for any positive integer N. In this way multivariate data and relations can be represented in the Euclidean plane (embedded in the projective plane). Basically, R squared with Cartesian coordinates is augmented by N parallel axes, one for each variable. The N joint variables of a robotic device can be represented graphically by using parallel coordinates. It is pointed out that some properties of the relation are better perceived visually from the parallel coordinate representation, and that new algorithms and data structures can be obtained from this representation. The main features of parallel coordinates are described, and an example is presented of their use for configuration space representation of a mechanical arm (where Cartesian coordinates cannot be used).
A Cartesian parametrization for the numerical analysis of material instability
Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; Ostien, Jakob T.; Lai, Zhengshou
2016-02-25
We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less
Applications of Space-Filling-Curves to Cartesian Methods for CFD
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.
2003-01-01
The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.
Applications of Space-Filling-Curves to Cartesian Methods for CFD
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Murman, S. M.; Berger, M. J.
2003-01-01
This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.
Branduardi, Davide; Faraldo-Gómez, José D
2013-09-10
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID
Implicit Approaches for Moving Boundaries in a 3-D Cartesian Method
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan
2003-01-01
This work considers numerical simulation of three-dimensional flows with time-evolving boundaries. Such problems pose a variety of challenges for numerical schemes, and have received a substantial amount of attention in the recent literature. Since such simulations are unsteady, time-accurate solution of the governing equations is required. In special cases, the body motion can be treated by a uniform rigid motion of the computational domain. For the more general situation of relative-body motion, however, this simplification is unavailable and the simulations require a mechanism for ensuring that the mesh evolves with the moving boundaries. This involves a "remeshing" of the computational domain (either localized or global) at each physical timestep, and places a premium on both the speed and robustness of the remeshing algorithms. This work presents a method which includes unsteady flow simulation, rigid domain motion, and relative body motion using a time-evolving Cartesian grid system in three dimensions.
NASA Astrophysics Data System (ADS)
Gilmanov, Anvar; Sotiropoulos, Fotis
2005-08-01
A numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics. The governing equations are discretized on a hybrid staggered/non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual-time-stepping, artificial compressibility iteration scheme. Unstructured, triangular meshes are employed to discretize complex immersed boundaries. The nodes of the surface mesh constitute a set of Lagrangian control points used to track the motion of the flexible body. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. Grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity, which show that the method is second-order accurate. The method is validated by applying it to calculate flow in a Cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing. The ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish-like body and flow past an anatomically realistic planktonic copepod performing an escape-like maneuver.
The Cartesian Diver as an Aid for Teaching Respiratory Physiology
ERIC Educational Resources Information Center
Fitch, Greg K.
2004-01-01
The mechanism by which air enters the mammalian lung is difficult for many students of physiology. In particular, some students have trouble seeing how pressure can be transmitted through a fluid such as the intrapleural fluid and how the magnitude of that pressure can change. A Cartesian diver, an old-time child's toy, may be used as a visual aid…
The Cartesian Diver, Surface Tension and the Cheerios Effect
ERIC Educational Resources Information Center
Chen, Chi-Tung; Lee, Wen-Tang; Kao, Sung-Kai
2014-01-01
A Cartesian diver can be used to measure the surface tension of a liquid to a certain extent. The surface tension measurement is related to the two critical pressures at which the diver is about to sink and about to emerge. After sinking because of increasing pressure, the diver is repulsed to the centre of the vessel. After the pressure is…
A Lot of Good Physics in the Cartesian Diver
ERIC Educational Resources Information Center
De Luca, Roberto; Ganci, Salvatore
2011-01-01
The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…
Lin, Dejun
2015-09-21
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green’s function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4–16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
Lin, Dejun
2015-09-21
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A
A grid spacing control technique for algebraic grid generation methods
NASA Technical Reports Server (NTRS)
Smith, R. E.; Kudlinski, R. A.; Everton, E. L.
1982-01-01
A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.
Grid Interaction Technical Team Roadmap
2013-06-01
The mission of the Grid Interaction Technical Team (GITT) is to support a transition scenario to large scale grid-connected vehicle charging with transformational technology, proof of concept and information dissemination. The GITT facilitates technical coordination and collaboration between vehicle-grid connectivity and communication activities among U.S. DRIVE government and industry partners.
A finite volume Fokker-Planck collision operator in constants-of-motion coordinates
NASA Astrophysics Data System (ADS)
Xiong, Z.; Xu, X. Q.; Cohen, B. I.; Cohen, R.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G.; Nevins, W. M.; Rognlien, T.
2006-04-01
TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy E and the magnetic moment μ, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a Fokker-Planck collision operator directly in (E,μ) space usin g a finite volume approach. The (E, μ) grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and non-physical zones. The resulting cut-cells are treated by a cell-mergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples.
Duality between coordinates and Dirac field
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; Gadelha, A. L.; Vancea, I. V.
2000-07-01
The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order.
Polar versus Cartesian velocity models for maneuvering target tracking with IMM
NASA Astrophysics Data System (ADS)
Laneuville, Dann
This paper compares various model sets in different IMM filters for the maneuvering target tracking problem. The aim is to see whether we can improve the tracking performance of what is certainly the most widely used model set in the literature for the maneuvering target tracking problem: a Nearly Constant Velocity model and a Nearly Coordinated Turn model. Our new challenger set consists of a mixed Cartesian position and polar velocity state vector to describe the uniform motion segments and is augmented with the turn rate to obtain the second model for the maneuvering segments. This paper also gives a general procedure to discretize up to second order any non-linear continuous time model with linear diffusion. Comparative simulations on an air defence scenario with a 2D radar, show that this new approach improves significantly the tracking performance in this case.
Plasticity of Intermediate Mechanics Students' Coordinate System Choice
ERIC Educational Resources Information Center
Sayre, Eleanor C.; Wittman, Michael C.
2008-01-01
We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their…
Simulations of 6-DOF Motion with a Cartesian Method
NASA Technical Reports Server (NTRS)
Murman, Scott M.; Aftosmis, Michael J.; Berger, Marsha J.; Kwak, Dochan (Technical Monitor)
2003-01-01
Coupled 6-DOF/CFD trajectory predictions using an automated Cartesian method are demonstrated by simulating a GBU-32/JDAM store separating from an F-18C aircraft. Numerical simulations are performed at two Mach numbers near the sonic speed, and compared with flight-test telemetry and photographic-derived data. Simulation results obtained with a sequential-static series of flow solutions are contrasted with results using a time-dependent flow solver. Both numerical methods show good agreement with the flight-test data through the first half of the simulations. The sequential-static and time-dependent methods diverge over the last half of the trajectory prediction. after the store produces peak angular rates. A cost comparison for the Cartesian method is included, in terms of absolute cost and relative to computing uncoupled 6-DOF trajectories. A detailed description of the 6-DOF method, as well as a verification of its accuracy, is provided in an appendix.
Conservation equations of gasdynamics in curvilinear coordinate systems
NASA Technical Reports Server (NTRS)
Vinokur, M.
1974-01-01
Description of a new method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms. It is thus possible to readily apply difference schemes derived for Cartesian coordinates which conserve mass, momentum, and energy in the total flow field. The method is derived for orthogonal coordinates, and then extended to cover the most general class of coordinate transformations, using general tensor analysis. Several special features of the equations are discussed.
Quality-based generation of weather radar Cartesian products
NASA Astrophysics Data System (ADS)
Osrodka, K.; Szturc, J.
2015-05-01
Weather radar data volumes are commonly processed to obtain various 2-D Cartesian products based on the transfer from polar to Cartesian representations through a certain interpolation method. In this research an algorithm of the spatial interpolation of polar reflectivity data employing quality index data is applied to find the Cartesian reflectivity as plan position indicator products. On this basis, quality-based versions of standard algorithms for the generation of the following products have been developed: ETOP (echo top), MAX (maximum of reflectivity), and VIL (vertically integrated liquid water). Moreover, as an example of a higher-level product, a CONVECTION (detection of convection) has been defined as a specific combination of the above-listed standard products. A corresponding quality field is determined for each generated product, taking into account the quality of the pixels from which a given product was determined and how large a fraction of the investigated heights was scanned. Examples of such quality-based products are presented in the paper.
Frequency-offset Cartesian feedback for MRI power amplifier linearization.
Zanchi, Marta G; Stang, Pascal; Kerr, Adam; Pauly, John M; Scott, Greig C
2011-02-01
High-quality magnetic resonance imaging (MRI) requires precise control of the transmit radio-frequency (RF) field. In parallel excitation applications such as transmit SENSE, high RF power linearity is essential to cancel aliased excitations. In widely-employed class AB power amplifiers, gain compression, cross-over distortion, memory effects, and thermal drift all distort the RF field modulation and can degrade image quality. Cartesian feedback (CF) linearization can mitigate these effects in MRI, if the quadrature mismatch and dc offset imperfections inherent in the architecture can be minimized. In this paper, we present a modified Cartesian feedback technique called "frequency-offset Cartesian feedback" (FOCF) that significantly reduces these problems. In the FOCF architecture, the feedback control is performed at a low intermediate frequency rather than dc, so that quadrature ghosts and dc errors are shifted outside the control bandwidth. FOCF linearization is demonstrated with a variety of typical MRI pulses. Simulation of the magnetization obtained with the Bloch equation demonstrates that high-fidelity RF reproduction can be obtained even with inexpensive class AB amplifiers. Finally, the enhanced RF fidelity of FOCF over CF is demonstrated with actual images obtained in a 1.5 T MRI system. PMID:20959264
Frequency-Offset Cartesian Feedback for MRI Power Amplifier Linearization
Zanchi, Marta Gaia; Stang, Pascal; Kerr, Adam; Pauly, John Mark; Scott, Greig Cameron
2011-01-01
High-quality magnetic resonance imaging (MRI) requires precise control of the transmit radio-frequency field. In parallel excitation applications such as transmit SENSE, high RF power linearity is essential to cancel aliased excitations. In widely-employed class AB power amplifiers, gain compression, cross-over distortion, memory effects, and thermal drift all distort the RF field modulation and can degrade image quality. Cartesian feedback (CF) linearization can mitigate these effects in MRI, if the quadrature mismatch and DC offset imperfections inherent in the architecture can be minimized. In this paper, we present a modified Cartesian feedback technique called “frequency-offset Cartesian feedback” (FOCF) that significantly reduces these problems. In the FOCF architecture, the feedback control is performed at a low intermediate frequency rather than DC, so that quadrature ghosts and DC errors are shifted outside the control bandwidth. FOCF linearization is demonstrated with a variety of typical MRI pulses. Simulation of the magnetization obtained with the Bloch equation demonstrates that high-fidelity RF reproduction can be obtained even with inexpensive class AB amplifiers. Finally, the enhanced RF fidelity of FOCF over CF is demonstrated with actual images obtained in a 1.5 T MRI system. PMID:20959264
SU-E-I-41: Non-Cartesian MR Image Reconstruction with Integrated Gradient Non-Linearity Correction
Tao, S; Trzasko, JD; Polley, TW; Shu, Y; Bernstein, MA
2014-06-01
Purpose: Nonlinearities in the spatial encoding gradients of MRI systems cause geometric distortion in images. Typically, this is retrospectively corrected via image-domain interpolation (a.k.a., “gradwarp”) albeit with a loss of spatial resolution. For non-Cartesian MRI, the latter problem is exaggerated by noise and undersampling artifact. In this study, we describe a novel correction strategy that accounts for gradient nonlinearities during — rather than after — non-Cartesian MRI reconstruction, and demonstrate that this approach mitigates the resolution loss that can occur with standard methods. Methods: To test the proposed method, the American College of Radiology (ACR) quality control phantom was scanned on at 1.5 T (General Electric, v16.0, “zoom” gradient) using a 1.6x undersampled 3D non- Cartesian Shells trajectory (GRE, FOV=24 cm3, 120 shells, 16552 shots, 512 readout, matrix=2403). Image reconstruction was first performed via standard k-space density-compensated gridding and retrospectively corrected via cubic spline interpolation. Image reconstruction was then separately performed using a k-space and image-domain densitycompensated type-3 non-uniform fast Fourier transform (NUFFT), which provides a direct mapping between non-Cartesian k-space samples and warped image space voxel locations. Thus, no separate distortion correction procedure is needed for the proposed approach. The gradient distortion field was determined using vendor provided calibration data. Results: Phantom scan results show that both processing approaches successfully correct geometric distortion. However, visual inspection of the ACR phantom spatial resolution inserts shows that the proposed strategy preserves the resolution of the nominal (uncorrected) reconstruction while “gradwarp” imparts marked spatial blurring (especially for the 1.0 and 1.1 mm inserts) and thus resolution loss. Conclusion: We've presented a novel reconstruction strategy for non-Cartesian MRI
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.
Claes Hellerström and Cartesian diver microrespirometry
Welsh, Michael
2016-01-01
Cartesian diver microrespirometry was introduced by Claes Hellerström at the Department of Histology/Medical Cell Biology at Uppsala University, Sweden, to determine rates of oxygen consumption in islets of Langerhans. The theory behind this method is touched upon and the main findings described. Glucose-stimulated beta cell respiration significantly contributes to increased ATP generation, which is a prerequisite for stimulated insulin secretion and synthesis. This has had major implications for understanding the beta cell stimulus–secretion coupling. PMID:27181825
NASA Astrophysics Data System (ADS)
Wu, C. S.; Young, D. L.; Chiu, C. L.
2013-12-01
This article aims to develop a Cartesian-grid-based numerical model to study the interaction between free-surface flow and stationary or oscillating immersed obstacle in a viscous fluid. To incorporate the effect of the free surface motion, an arbitrary Lagrangian-Eulerian (ALE) scheme is employed to accurately capture the configuration of free surface. To deal with the complex submerged obstacle in the fluid, a hybrid Cartesian/immersed boundary (HCIB) method is adopted, which allows easy implementation of the solid boundary conditions for a fixed structured grid. The two numerical techniques are combined to study the wave-structure interaction problems. The major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients, while the immersed body can move arbitrarily through the Cartesian grid. The meshes deform smoothly over the solid and free-surface boundaries, especially for representing sharp interface. There is no re-meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation. Some numerical examples are displayed respectively to validate the robustness and accuracy of the HCIB method, the ALE based finite-element scheme and their combinations. In addition, the other two numerical applications are carried out to simulate the wave-structure interaction with stationary and moving immersed body. In case studies some physical characteristics are also discussed for a range of amplitude of free-surface wave, Reynolds numbers and the proximity of structure under the liquid surface. The feasibility of the developed novel numerical model is shown through five numerical experiments.
NASA Astrophysics Data System (ADS)
Pathak, Harshavardhana S.; Shukla, Ratnesh K.
2016-08-01
A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of
Compact-range coordinate system established using a laser tracker.
Gallegos, Floyd H.; Bryce, Edwin Anthony
2006-12-01
Establishing a Cartesian coordinate reference system for an existing Compact Antenna Range using the parabolic reflector is presented. A SMX (Spatial Metrix Corporation) M/N 4000 laser-based coordinate measuring system established absolute coordinates for the facility. Electric field characteristics with positional movement correction are evaluated. Feed Horn relocation for alignment with the reflector axis is also described. Reference points are established for follow-on non-laser alignments utilizing a theodolite.
[Cartesian misunderstanding as a cause of therapeutic failure].
Isler, H
1986-01-01
Headache patients disassociate themselves from their own automatic responses, relying on the traditional separation of body and mind. On the other hand, patients who obtain voluntary control of automatic functions by biofeedback training modify not only vegetative but also voluntary behaviour patterns, losing "neurotic" traits. The basic misconception of the separation of body and mind, Cartesian dualism, is now ingrained in our culture. In the 17th century Descartes asserted that concepts applied to the soul must be entirely different from those used for the body in order to improve comprehension of the immortality of the soul. This dualism also led to "enlightenment" and to many later social and philosophical developments. But his basic neurophysiology was obsolete when he wrote it down. Other models from mainstream natural philosophy were better compatible with observation and experiments. Gassendi assumed a "body soul" consisting of energy as the functional principle of the nervous system, and Willis accommodated a series of anticipations of 19th century discoveries within this model. No comparable progress resulted from Descartes' own medieval model. Cartesian dualism has become untenable in view of recent neuropsychology but it still obstructs our management of functional patients. Instead of reinforcing the delusion of separation of psyche and soma, we ought to encourage patients to understand that their malfunctioning organs are on-line with their emotions, and with their mind. PMID:2420000
NASA Astrophysics Data System (ADS)
Liao, Fei; Ye, Zhengyin
2015-12-01
Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al. [8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al. [9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM) [12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al. [11] presented new asymmetric and symmetric conservative forms of time metrics and
Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle
Li, Tingwen; Dietiker, Jean-Francois; Zhang, Yongmin; Shahnam, Mehrdad
2011-12-01
In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.
NASA Technical Reports Server (NTRS)
Coirier, William John
1994-01-01
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a
Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow
NASA Technical Reports Server (NTRS)
Berger, Marsha; Aftosmis, Michael J.
2011-01-01
The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data
The Overgrid Interface for Computational Simulations on Overset Grids
NASA Technical Reports Server (NTRS)
Chan, William M.; Kwak, Dochan (Technical Monitor)
2002-01-01
Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2007-01-01
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are
Verification and validation of the Spalart-Allmaras turbulence model for strand grids
NASA Astrophysics Data System (ADS)
Tong, Oisin
The strand-Cartesian grid approach provides many advantages for complex moving- body flow simulations, including fully-automatic volume grid generation, highly scalable domain connectivity, and high-order accuracy. In this work the Spalart-Allmaras model is implemented, verified, and validated for high Reynolds number turbulent flows in a strand- Cartesian solver. Second-order convergence is achieved using the Method of Manufactured Solutions implying correct implementation of the turbulence model. By using the NASA- Langley online resource, specific flow cases are validated with two independent compressible codes: FUN3D and CFL3D. The strand solver is validated with zero-pressure gradient flat plate and bump-in-channel cases, and shows excellent agreement with FUN3D and CFL3D for various aspects of turbulent flow, including: velocity profiles, turbulent viscosity profile, coefficient of surface pressure, and drag. Methods of handling sharp corners with strand grids through combinations of strand vector smoothing, multiple strands emanating from a single surface node, and telescoping Cartesian refinement into corner regions of the near- body grid are investigated for a NACA 0012 case. For standard viscous high-aspect ratio grids, smoothed strands with telescoping Cartesian refinement provide the most accurate results with the least complexity. Mesh discontinuities associated with use of multiple strands at sharp corners produce more error than with smoothed strands. With both strand approaches -- vector smoothing and multiple strands -- targeted Cartesian refinement is critical to capture features near sharp corners where strand grids alone are too coarse to capture. Other results show agreement with FUN3D and CFL3D. By using strand vector smoothing and telescoping Cartesian refinement, a NACA 4412 trailing edge separation case is validated with comparison against CFL3D and FUN3D. Velocity profiles show reasonable agreement with CFL3D; however implementing
Internal Coordinate Molecular Dynamics: A Foundation for Multiscale Dynamics
2015-01-01
Internal coordinates such as bond lengths, bond angles, and torsion angles (BAT) are natural coordinates for describing a bonded molecular system. However, the molecular dynamics (MD) simulation methods that are widely used for proteins, DNA, and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed with Cartesian MD simulations to enhance the conformational sampling. This makes the equations of motion in the Cartesian coordinates differential-algebraic, which adversely impacts the complexity and the robustness of the simulations. On the other hand, constraints can be easily placed in BAT coordinates by removing the degrees of freedom that need to be constrained. Thus, the internal coordinate MD (ICMD) offers an attractive alternative to Cartesian coordinate MD for developing multiscale MD method. The torsional MD method is a special adaptation of the ICMD method, where all the bond lengths and bond angles are kept rigid. The advantages of ICMD simulation methods are the longer time step size afforded by freezing high frequency degrees of freedom and performing a conformational search in the more important low frequency torsional degrees of freedom. However, the advancements in the ICMD simulations have been slow and stifled by long-standing mathematical bottlenecks. In this review, we summarize the recent mathematical advancements we have made based on spatial operator algebra, in developing a robust long time scale ICMD simulation toolkit useful for various applications. We also present the applications of ICMD simulations to study conformational changes in proteins and protein structure refinement. We review the advantages of the ICMD simulations over the Cartesian simulations when used with enhanced sampling methods and project the future use of ICMD simulations in protein dynamics. PMID:25517406
Nonlinear Accelerator with Transverse Motion Integrable in Normalized Polar Coordinates
Nagaitsev, S.; Kharkov, Y.; Morozov, I.A.; Zolkin, T.V.; /Chicago U.
2012-05-01
Several families of nonlinear accelerator lattices with integrable transverse motion were suggested recently. One of the requirements for the existence of two analytic invariants is a special longitudinal coordinate dependence of fields. This paper presents the particle motion analysis when a problem becomes integrable in the normalized polar coordinates. This case is distinguished from the others: it yields an exact analytical solution and has a uniform longitudinal coordinate dependence of the fields (since the corresponding nonlinear potential is invariant under the transformation from the Cartesian to the normalized coordinates). A number of interesting features are revealed: while the frequency of radial oscillations is independent of the amplitude, the spread of angular frequencies in a beam is absolute. A corresponding spread of frequencies of oscillations in the Cartesian coordinates is evaluated via the simulation of transverse Schottky noise.
Direct adaptive control of manipulators in Cartesian space
NASA Technical Reports Server (NTRS)
Seraji, H.
1987-01-01
A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.
Multi-fault Tolerance for Cartesian Data Distributions
Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.
2013-06-01
Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale sys- tems. Algorithm-based fault tolerance (ABFT) is a promising approach that involves modications to the algorithm to recover from faults with lower over- heads than replicated storage and a signicant reduction in lost work compared to checkpoint-restart techniques. Fault-tolerant linear algebra (FTLA) algo- rithms employ additional processors that store parities along the dimensions of a matrix to tolerate multiple, simultaneous faults. Existing approaches as- sume regular data distributions (blocked or block-cyclic) with the failures of each data block being independent. To match the characteristics of failures on parallel computers, we extend these approaches to mapping parity blocks in several important ways. First, we handle parity computation for generalized Cartesian data distributions with each processor holding arbitrary subsets of blocks in a Cartesian-distributed array. Second, techniques to handle corre- lated failures, i.e., multiple processors that can be expected to fail together, are presented. Third, we handle the colocation of parity blocks with the data blocks and do not require them to be on additional processors. Several al- ternative approaches, based on graph matching, are presented that attempt to balance the memory overhead on processors while guaranteeing the same fault tolerance properties as existing approaches that assume independent fail- ures on regular blocked data distributions. The evaluation of these algorithms demonstrates that the additional desirable properties are provided by the pro- posed approach with minimal overhead.
76 FR 46279 - Smart Grid Advisory Committee
Federal Register 2010, 2011, 2012, 2013, 2014
2011-08-02
... National Institute of Standards and Technology Smart Grid Advisory Committee AGENCY: Department of Commerce, National Institute of Standards and Technology ACTION: Notice of open meeting. SUMMARY: The Smart Grid... should be sent to Office of the National Coordinator for Smart Grid Interoperability, National...
TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide
NASA Technical Reports Server (NTRS)
Miller, David P.
1994-01-01
A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.
Finite element method formulation in polar coordinates for transient heat conduction problems
NASA Astrophysics Data System (ADS)
Duda, Piotr
2016-04-01
The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.
An Efficient Means of Adaptive Refinement Within Systems of Overset Grids
NASA Technical Reports Server (NTRS)
Meakin, Robert L.
1996-01-01
An efficient means of adaptive refinement within systems of overset grids is presented. Problem domains are segregated into near-body and off-body fields. Near-body fields are discretized via overlapping body-fitted grids that extend only a short distance from body surfaces. Off-body fields are discretized via systems of overlapping uniform Cartesian grids of varying levels of refinement. a novel off-body grid generation and management scheme provides the mechanism for carrying out adaptive refinement of off-body flow dynamics and solid body motion. The scheme allows for very efficient use of memory resources, and flow solvers and domain connectivity routines that can exploit the structure inherent to uniform Cartesian grids.
NASA Astrophysics Data System (ADS)
Ebrahimi, F.; Blackman, E. G.
2016-06-01
For cylindrical differentially rotating plasmas, we study large-scale magnetic field generation from finite amplitude non-axisymmetric perturbations by comparing numerical simulations with quasi-linear analytic theory. When initiated with a vertical magnetic field of either zero or finite net flux, our global cylindrical simulations exhibit the magnetorotational instability (MRI) and large-scale dynamo growth of radially alternating mean fields, averaged over height and azimuth. This dynamo growth is explained by our analytic calculations of a non-axisymmetric fluctuation-induced electromotive force that is sustained by azimuthal shear of the fluctuating fields. The standard `Ω effect' (shear of the mean field by differential rotation) is unimportant. For the MRI case, we express the large-scale dynamo field as a function of differential rotation. The resulting radially alternating large-scale fields may have implications for angular momentum transport in discs and corona. To connect with previous work on large-scale dynamos with local linear shear and identify the minimum conditions needed for large-scale field growth, we also solve our equations in local Cartesian coordinates. We find that large-scale dynamo growth in a linear shear flow without rotation can be sustained by shear plus non-axisymmetric fluctuations - even if not helical, a seemingly previously unidentified distinction. The linear shear flow dynamo emerges as a more restricted version of our more general new global cylindrical calculations.
Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method
Cantrell, J Nathan; Inclan, Eric J; Joshi, Abhijit S; Popov, Emilian L; Jain, Prashant K
2012-01-01
This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specific preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.
Some studies on generalized coordinate sets for polyatomic molecules
NASA Astrophysics Data System (ADS)
Li, Wenjin; Ma, Ao
2015-12-01
Generalized coordinates are widely used in various analyses of the trajectories of polyatomic molecules from molecular dynamics simulations, such as normal mode analysis and force distribution analysis. Here, we presented detailed discussions on the properties of some specific sets of generalized coordinates, which separate translational, rotational, and vibrational motions of a molecule from one another once the trajectories of dynamical systems are known. Efficient methods were suggested for estimating the transformation matrix between generalized and Cartesian coordinates. Some properties of the well-known BAT coordinates (bond length, angle, and torsional coordinates) were discussed as well.
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1997-01-01
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
NASA Technical Reports Server (NTRS)
Seki, Rycichi
1989-01-01
Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.
A HYBRID SOLAR WIND MODEL OF THE CESE+HLL METHOD WITH A YIN-YANG OVERSET GRID AND AN AMR GRID
Feng Xueshang; Zhang Shaohua; Xiang Changqing; Yang Liping; Jiang Chaowei; Wu, S. T.
2011-06-10
A hybrid three-dimensional (3D) MHD model for solar wind study is proposed in the present paper with combined grid systems and solvers. The computational domain from the Sun to Earth space is decomposed into the near-Sun and off-Sun domains, which are respectively constructed with a Yin-Yang overset grid system and a Cartesian adaptive mesh refinement (AMR) grid system and coupled with a domain connection interface in the overlapping region between the near-Sun and off-Sun domains. The space-time conservation element and solution element method is used in the near-Sun domain, while the Harten-Lax-Leer method is employed in the off-Sun domain. The Yin-Yang overset grid can avoid well-known singularity and polar grid convergence problems and its body-fitting property helps achieve high-quality resolution near the solar surface. The block structured AMR Cartesian grid can automatically capture far-field plasma flow features, such as heliospheric current sheets and shock waves, and at the same time, it can save significant computational resources compared to the uniformly structured Cartesian grid. A numerical study of the solar wind structure for Carrington rotation 2069 shows that the newly developed hybrid MHD solar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by comparisons with multiple solar and interplanetary observations.
A flux-coordinate independent field-aligned approach to plasma turbulence simulations
NASA Astrophysics Data System (ADS)
Hariri, F.; Ottaviani, M.
2013-11-01
This work illustrates a new approach to field-aligned coordinates for plasma turbulence simulations which is not based on flux variables. The method employs standard Cartesian or polar coordinates to discretize the fields. Parallel derivatives are computed directly along a coordinate that follows the local field, and poloidal derivatives are computed in the original Cartesian frame. Several advantages of this approach are presented. The tests on a drift-wave model demonstrate that the method is well suited to exploit the flute property of small parallel gradients by minimizing the number of degrees of freedom needed to treat a given problem in an accurate and efficient manner.
NASA Technical Reports Server (NTRS)
1998-01-01
Pointwise Inc.'s, Gridgen Software is a system for the generation of 3D (three dimensional) multiple block, structured grids. Gridgen is a visually-oriented, graphics-based interactive code used to decompose a 3D domain into blocks, distribute grid points on curves, initialize and refine grid points on surfaces and initialize volume grid points. Gridgen is available to U.S. citizens and American-owned companies by license.
Iterative reconstruction method for three-dimensional non-cartesian parallel MRI
NASA Astrophysics Data System (ADS)
Jiang, Xuguang
Parallel magnetic resonance imaging (MRI) with non-Cartesian sampling pattern is a promising technique that increases the scan speed using multiple receiver coils with reduced samples. However, reconstruction is challenging due to the increased complexity. Three reconstruction methods were evaluated: gridding, blocked uniform resampling (BURS) and non-uniform FFT (NUFFT). Computer simulations of parallel reconstruction were performed. Root mean square error (RMSE) of the reconstructed images to the simulated phantom were used as image quality criterion. Gridding method showed best RMSE performance. Two type of a priori constraints to reduce noise and artifacts were evaluated: edge preserving penalty, which suppresses noise and aliasing artifact in image while preventing over-smoothness, and object support penalty, which reduces background noise amplification. A trust region based step-ratio method that iteratively calculates the penalty coefficient was proposed for the penalty functions. Two methods to alleviate computation burden were evaluated: smaller over sampling ratio, and interpolation coefficient matrix compression. The performance were individually tested using computer simulations. Edge preserving penalty and object support penalty were shown to have consistent improvement on RMSE. The performance of calculated penalty coefficients on the two penalties were close to the best RMSE. Oversampling ratio as low as 1.125 was shown to have impact of less than one percent on RMSE for the radial sampling pattern reconstruction. The value reduced the three dimensional data requirement to less than 1/5 of what the conventional 2x grid needed. Interpolation matrix compression with compression ratio up to 50 percent showed small impact on RMSE. The proposed method was validated on 25MR data set from a GEMR scanner. Six image quality metrics were used to evaluate the performance. RMSE, normalized mutual information (NMI) and joint entropy (JE) relative to a reference
NASA Astrophysics Data System (ADS)
Sidler, Rolf; Carcione, José M.; Holliger, Klaus
2013-02-01
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.
Sidler, Rolf; Carcione, José M.; Holliger, Klaus
2013-02-15
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.
Stromyer, Michael L; Lilly, Cassandra P; Dillner, Adam J; Knaust, Jacqueline M
2016-01-01
Three isostructural coordination networks of Ce, Pr, and Nd nitrate with 4,4'-bi-pyridine N,N'-dioxide (bpydo) are reported, namely poly[[tris-(nitrato-κ(2) O,O')cerium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N')], [Ce(NO3)3(C10H8N2O2)2], poly[[tris-(nitrato-κ(2) O,O')praeseodymium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N')], [Pr(NO3)3(C10H8N2O2)2], and poly[[tris(nitrato-κ(2) O,O')neodymium(III)]-bis-(μ2-4,4'-bi-pyridine N,N'-dioxide-κ(2) N:N'], [Nd(NO3)3(C10H8N2O2)2]. All three compounds are isostructural to the previously reported La analogue. The asymmetric unit of [Ln(NO3)3(μ2-bpydo)2] contains one lanthanide cation, two bpydo ligands, and three nitrate anions. Both bpydo ligands act as end-to-end μ2-bridges and display nearly ideal cis and gauche conformations, respectively. The bpydo ligands link the ten-coordinate Ln (III) cations, forming inter-digitating 4(4) grid-like layers extending parallel to (-101), where inter-digitation of layers is promoted by C-H⋯O inter-actions between nitrate anions and bpydo ligands. The inter-digitated layers are linked to sets of neighboring layers via further C-H⋯O and π-π inter-actions. PMID:26870578
Stromyer, Michael L.; Lilly, Cassandra P.; Dillner, Adam J.; Knaust, Jacqueline M.
2016-01-01
Three isostructural coordination networks of Ce, Pr, and Nd nitrate with 4,4′-bipyridine N,N′-dioxide (bpydo) are reported, namely poly[[tris(nitrato-κ2 O,O′)cerium(III)]-bis(μ2-4,4′-bipyridine N,N′-dioxide-κ2 N:N′)], [Ce(NO3)3(C10H8N2O2)2], poly[[tris(nitrato-κ2 O,O′)praeseodymium(III)]-bis(μ2-4,4′-bipyridine N,N′-dioxide-κ2 N:N′)], [Pr(NO3)3(C10H8N2O2)2], and poly[[tris(nitrato-κ2 O,O′)neodymium(III)]-bis(μ2-4,4′-bipyridine N,N′-dioxide-κ2 N:N′], [Nd(NO3)3(C10H8N2O2)2]. All three compounds are isostructural to the previously reported La analogue. The asymmetric unit of [Ln(NO3)3(μ2-bpydo)2] contains one lanthanide cation, two bpydo ligands, and three nitrate anions. Both bpydo ligands act as end-to-end μ2-bridges and display nearly ideal cis and gauche conformations, respectively. The bpydo ligands link the ten-coordinate Ln III cations, forming interdigitating 44 grid-like layers extending parallel to (-101), where interdigitation of layers is promoted by C—H⋯O interactions between nitrate anions and bpydo ligands. The interdigitated layers are linked to sets of neighboring layers via further C—H⋯O and π–π interactions. PMID:26870578
General formulation of vibronic spectroscopy in internal coordinates
NASA Astrophysics Data System (ADS)
Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo
2016-02-01
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.
General formulation of vibronic spectroscopy in internal coordinates.
Baiardi, Alberto; Bloino, Julien; Barone, Vincenzo
2016-02-28
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions. PMID:26931688
Energy Science and Technology Software Center (ESTSC)
2014-07-15
Matlab Toolbox for simulating the impact of solar energy on the distribution grid. The majority of the functions are useful for interfacing OpenDSS and MATLAB, and they are of generic use for commanding OpenDSS from MATLAB and retrieving GridPV Toolbox information from simulations. A set of functions is also included for modeling PV plant output and setting up the PV plant in the OpenDSS simulation. The toolbox contains functions for modeling the OpenDSS distribution feedermore » on satellite images with GPS coordinates. Finally, example simulations functions are included to show potential uses of the toolbox functions.« less
Broderick, Robert; Quiroz, Jimmy; Grijalva, Santiago; Reno, Matthew; Coogan, Kyle
2014-07-15
Matlab Toolbox for simulating the impact of solar energy on the distribution grid. The majority of the functions are useful for interfacing OpenDSS and MATLAB, and they are of generic use for commanding OpenDSS from MATLAB and retrieving GridPV Toolbox information from simulations. A set of functions is also included for modeling PV plant output and setting up the PV plant in the OpenDSS simulation. The toolbox contains functions for modeling the OpenDSS distribution feeder on satellite images with GPS coordinates. Finally, example simulations functions are included to show potential uses of the toolbox functions.
Post, R.F.
1960-08-01
An electronic grid is designed employing magnetic forces for controlling the passage of charged particles. The grid is particularly applicable to use in gas-filled tubes such as ignitrons. thyratrons, etc., since the magnetic grid action is impartial to the polarity of the charged particles and, accordingly. the sheath effects encountered with electrostatic grids are not present. The grid comprises a conductor having sections spaced apart and extending in substantially opposite directions in the same plane, the ends of the conductor being adapted for connection to a current source.
Visual analytics for power grid contingency analysis.
Pak Chung Wong; Zhenyu Huang; Yousu Chen; Mackey, Patrick; Shuangshuang Jin
2014-01-01
Contingency analysis employs different measures to model scenarios, analyze them, and then derive the best response to any threats. A proposed visual-analytics pipeline for power grid management can transform approximately 100 million contingency scenarios to a manageable size and form. Grid operators can examine individual scenarios and devise preventive or mitigation strategies in a timely manner. Power grid engineers have applied the pipeline to a Western Electricity Coordinating Council power grid model. PMID:24808167
NASA Astrophysics Data System (ADS)
Hoeft, B.; Epting, U.; Koenig, T.
2008-07-01
While many fields relevant to Grid security are already covered by existing working groups, their remit rarely goes beyond the scope of the Grid infrastructure itself. However, security issues pertaining to the internal set-up of compute centres have at least as much impact on Grid security. Thus, this talk will present briefly the EU ISSeG project (Integrated Site Security for Grids). In contrast to groups such as OSCT (Operational Security Coordination Team) and JSPG (Joint Security Policy Group), the purpose of ISSeG is to provide a holistic approach to security for Grid computer centres, from strategic considerations to an implementation plan and its deployment. The generalised methodology of Integrated Site Security (ISS) is based on the knowledge gained during its implementation at several sites as well as through security audits, and this will be briefly discussed. Several examples of ISS implementation tasks at the Forschungszentrum Karlsruhe will be presented, including segregation of the network for administration and maintenance and the implementation of Application Gateways. Furthermore, the web-based ISSeG training material will be introduced. This aims to offer ISS implementation guidance to other Grid installations in order to help avoid common pitfalls.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
NASA Technical Reports Server (NTRS)
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary Cartesian-mesh flow solver is coupled with a three degree-offreedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves the complete system of aero-structural equations using a modular, loosely-coupled strategy which allows the lower-fidelity structural model to deform the highfidelity CFD model. The approach uses an open-source, 3-D discrete-geometry engine to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. This extended abstract includes a brief description of the architecture, along with some preliminary validation of underlying assumptions and early results on a generic 3D transport model. The final paper will present more concrete cases and validation of the approach. Preliminary results demonstrate convergence of the complete aero-structural system and investigate the accuracy of the approximations used in the formulation of the structural model.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
NASA Technical Reports Server (NTRS)
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids
Burton, D.E.
1994-10-17
We consider the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH). Hydrodynamics algorithms are often formulated in a relatively ad hoc manner in which independent discretizations are proposed for mass, momentum, energy, and so forth. We show that, once discretizations for mass and momentum are stated, the remaining discretizations are very nearly uniquely determined, so there is very little latitude for variation. As has been known for some time, the kinetic energy discretization must follow directly from the momentum equation; and the internal energy must follow directly from the energy currents affecting the kinetic energy. A fundamental requirement (termed isentropicity) for numerical hydrodynamics algorithms is the ability to remain on an isentrope in the absence of heating or viscous forces and in the limit of small timesteps. We show that the requirements of energy conservation and isentropicity lead to the replacement of the usual volume calculation with a conservation integral. They further forbid the use of higher order functional representations for either velocity or stress within zones or control volumes, forcing the use of a constant stress element and a constant velocity control volume. This, in turn, causes the point and zone coordinates to formally disappear from the Cartesian formulation. The form of the work equations and the requirement for dissipation by viscous forces strongly limits the possible algebraic forms for artificial viscosity. The momentum equation and a center-of-mass definition lead directly to an angular momentum conservation law that is satisfied by the system. With a few straightforward substitutions, the Cartesian formulation can be converted to a multidimensional curvilinear one. The formulation in 2D symmetric geometry preserves rotational symmetry.
Continuous parallel coordinates.
Heinrich, Julian; Weiskopf, Daniel
2009-01-01
Typical scientific data is represented on a grid with appropriate interpolation or approximation schemes,defined on a continuous domain. The visualization of such data in parallel coordinates may reveal patterns latently contained in the data and thus can improve the understanding of multidimensional relations. In this paper, we adopt the concept of continuous scatterplots for the visualization of spatially continuous input data to derive a density model for parallel coordinates. Based on the point-line duality between scatterplots and parallel coordinates, we propose a mathematical model that maps density from a continuous scatterplot to parallel coordinates and present different algorithms for both numerical and analytical computation of the resulting density field. In addition, we show how the 2-D model can be used to successively construct continuous parallel coordinates with an arbitrary number of dimensions. Since continuous parallel coordinates interpolate data values within grid cells, a scalable and dense visualization is achieved, which will be demonstrated for typical multi-variate scientific data. PMID:19834230
White, Vicky
2003-05-21
By now almost everyone has heard of 'The Grid', or 'Grid Computing' as it should more properly be described. There are frequent articles in both the popular and scientific press talking about 'The Grid' or about some specific Grid project. Run II Experiments, US-CMS, BTeV, the Sloane Digital Sky Survey and the Lattice QCD folks are all incorporating aspects of Grid Computing in their plans, and the Fermilab Computing Division is supporting and encouraging these efforts. Why are we doing this and what does it have to do with running a physics experiment or getting scientific results? I will explore some of these questions and try to give an overview, not so much of the technical aspects of Grid Computing, rather of what the phenomenon means for our field.
Simulation of disk-disk encounters with co-moving polar grids
NASA Technical Reports Server (NTRS)
Salo, Heikki
1990-01-01
The two-grid simulation method combining advantages of both polar and Cartesian mesh-codes is described. In addition to the stellar component reacting solely to gravitational forces, the gas component is included with dissipatively colliding particles. This allows fairly realistic simulation of planar encounters where both systems contain star plus gas disks.
Tracking algorithms using log-polar mapped image coordinates
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.; Juday, Richard D.
1990-01-01
The use of log-polar image sampling coordinates rather than conventional Cartesian coordinates offers a number of advantages for visual tracking and docking of space vehicles. Pixel count is reduced without decreasing the field of view, with commensurate reduction in peripheral resolution. Smaller memory requirements and reduced processing loads are the benefits in working environments where bulk and energy are at a premium. Rotational and zoom symmetries of log-polar coordinates accommodate range and orientation extremes without computational penalties. Separation of radial and rotational coordinates reduces the complexity of several target centering algorithms, described below.
Multiscale geometric modeling of macromolecules I: Cartesian representation
NASA Astrophysics Data System (ADS)
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-15
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei
2013-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation.
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Towards Hybrid Overset Grid Simulations of the Launch Environment
NASA Astrophysics Data System (ADS)
Moini-Yekta, Shayan
A hybrid overset grid approach has been developed for the design and analysis of launch vehicles and facilities in the launch environment. The motivation for the hybrid grid methodology is to reduce the turn-around time of computational fluid dynamic simulations and improve the ability to handle complex geometry and flow physics. The LAVA (Launch Ascent and Vehicle Aerodynamics) hybrid overset grid scheme consists of two components: an off-body immersed-boundary Cartesian solver with block-structured adaptive mesh refinement and a near-body unstructured body-fitted solver. Two-way coupling is achieved through overset connectivity between the off-body and near-body grids. This work highlights verification using code-to-code comparisons and validation using experimental data for the individual and hybrid solver. The hybrid overset grid methodology is applied to representative unsteady 2D trench and 3D generic rocket test cases.
Analysis of Crustal Magnetisation in Cartesian Vector Harmonics
NASA Astrophysics Data System (ADS)
Gubbins, D.; Ivers, D.; Williams, S.
2015-12-01
We present a new set of functions, Vector Cartesian Harmonics (VCH), analogous to the Vector Spherical Harmonics that we have applied recently to global models of crustal and lithospheric magnetisation. Like their spherical counterpart, the VCH form a complete, orthogonal set: planar models of magnetisation can be expanded in them. There are 3 distinct types of VCH, one representing that part of the magnetisation which generates the potential magnetic field above the surface, another the potential magnetic field below the surface, and a toroidal function that generates only a non-potential field. One function therefore describes the magnetisation detected by observations of the magnetic anomaly while the other two describe the null space of an inversion of magnetic observations for magnetisation. The formalism is therefore ideal for analysing the results of inversions for magnetic structures in plane layers such as local or regional surveys where Earth's curvature can be ignored. The null space is in general very large, being an arbitrary combination of a doubly-infinite set of vector functions. However, in the absence of remanence and when the inducing field is uniform the null space reduces to only 2 types of structure, uniform susceptibility (Runcorn's Theorem) and a pattern of susceptibility induced by a uniform field, the null space is restricted to uniform magnetisation and 1D patterns of susceptibility aligned with a horizontal inducing field. Both these cases are already well known, but this analysis shows them to be the ONLY members of the null space. We also give results for familiar text-book structures to show the nature of the null space in each case. Curiously, inversion of the magnetic field from a buried dipole returns exactly half the correct magnitude plus a spurious distributed magnetisation. A more complex application is the topographic structure based on the Bishop formation in California (Fairhead and Williams, SEG exp. abstr. 25, 845, 2006
The National Grid Project: A system overview
NASA Technical Reports Server (NTRS)
Gaither, Adam; Gaither, Kelly; Jean, Brian; Remotigue, Michael; Whitmire, John; Soni, Bharat; Thompson, Joe; Dannenhoffer,, John; Weatherill, Nigel
1995-01-01
The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.
NASA Technical Reports Server (NTRS)
Popovic, Zorana B.; Kim, Moonil; Rutledge, David B.
1988-01-01
Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequency-locking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.
Freitas, Andreia C; Wylezinska, Marzena; Birch, Malcolm J; Petersen, Steffen E; Miquel, Marc E
2016-01-01
Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image quality and temporal resolution trade-off, for dynamic speech imaging. Five subjects were imaged at 1.5T, while performing normal phonation, in order to assess velar motion and velopharyngeal closure. Data was acquired using both Cartesian and non-Cartesian (spiral and radial) real-time sequences at five different spatial-temporal resolution sets, between 10 fps (1.7×1.7×10 mm3) and 25 fps (1.5×1.5×10 mm3). Only standard scanning resources provided by the MRI scanner manufacturer were used to ensure easy applicability to clinical evaluation and reproducibility. Data sets were evaluated by comparing measurements of the velar structure, dynamic contrast-to-noise ratio and image quality visual scoring. Results showed that for all proposed sequences, FLASH spiral acquisitions provided higher contrast-to-noise ratio, up to a 170.34% increase at 20 fps, than equivalent bSSFP Cartesian acquisitions for the same spatial-temporal resolution. At higher frame rates (22 and 25 fps), spiral protocols were optimal and provided higher CNR and visual scoring than equivalent radial protocols. Comparison of dynamic imaging at 10 and 22 fps for radial and spiral acquisitions revealed no significant difference in CNR performance, thus indicating that temporal resolution can be doubled without compromising spatial resolution (1.9×1.9 mm2) or CNR. In summary, this study suggests that the use of FLASH spiral protocols should be preferred over bSSFP Cartesian for the dynamic imaging of velopharyngeal
Freitas, Andreia C.; Wylezinska, Marzena; Birch, Malcolm J.; Petersen, Steffen E.; Miquel, Marc E.
2016-01-01
Dynamic imaging of the vocal tract using real-time MRI has been an active and growing area of research, having demonstrated great potential to become routinely performed in the clinical evaluation of speech and swallowing disorders. Although many technical advances have been made in regards to acquisition and reconstruction methodologies, there is still no consensus in best practice protocols. This study aims to compare Cartesian and non-Cartesian real-time MRI sequences, regarding image quality and temporal resolution trade-off, for dynamic speech imaging. Five subjects were imaged at 1.5T, while performing normal phonation, in order to assess velar motion and velopharyngeal closure. Data was acquired using both Cartesian and non-Cartesian (spiral and radial) real-time sequences at five different spatial-temporal resolution sets, between 10 fps (1.7×1.7×10 mm3) and 25 fps (1.5×1.5×10 mm3). Only standard scanning resources provided by the MRI scanner manufacturer were used to ensure easy applicability to clinical evaluation and reproducibility. Data sets were evaluated by comparing measurements of the velar structure, dynamic contrast-to-noise ratio and image quality visual scoring. Results showed that for all proposed sequences, FLASH spiral acquisitions provided higher contrast-to-noise ratio, up to a 170.34% increase at 20 fps, than equivalent bSSFP Cartesian acquisitions for the same spatial-temporal resolution. At higher frame rates (22 and 25 fps), spiral protocols were optimal and provided higher CNR and visual scoring than equivalent radial protocols. Comparison of dynamic imaging at 10 and 22 fps for radial and spiral acquisitions revealed no significant difference in CNR performance, thus indicating that temporal resolution can be doubled without compromising spatial resolution (1.9×1.9 mm2) or CNR. In summary, this study suggests that the use of FLASH spiral protocols should be preferred over bSSFP Cartesian for the dynamic imaging of velopharyngeal
NASA Astrophysics Data System (ADS)
Foster, Ian
2001-08-01
The term "Grid Computing" refers to the use, for computational purposes, of emerging distributed Grid infrastructures: that is, network and middleware services designed to provide on-demand and high-performance access to all important computational resources within an organization or community. Grid computing promises to enable both evolutionary and revolutionary changes in the practice of computational science and engineering based on new application modalities such as high-speed distributed analysis of large datasets, collaborative engineering and visualization, desktop access to computation via "science portals," rapid parameter studies and Monte Carlo simulations that use all available resources within an organization, and online analysis of data from scientific instruments. In this article, I examine the status of Grid computing circa 2000, briefly reviewing some relevant history, outlining major current Grid research and development activities, and pointing out likely directions for future work. I also present a number of case studies, selected to illustrate the potential of Grid computing in various areas of science.
Unstructured Grid Generation Techniques and Software
NASA Technical Reports Server (NTRS)
Posenau, Mary-Anne K. (Editor)
1993-01-01
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop.
Advances in Distance-Based Hole Cuts on Overset Grids
NASA Technical Reports Server (NTRS)
Chan, William M.; Pandya, Shishir A.
2015-01-01
An automatic and efficient method to determine appropriate hole cuts based on distances to the wall and donor stencil maps for overset grids is presented. A new robust procedure is developed to create a closed surface triangulation representation of each geometric component for accurate determination of the minimum hole. Hole boundaries are then displaced away from the tight grid-spacing regions near solid walls to allow grid overlap to occur away from the walls where cell sizes from neighboring grids are more comparable. The placement of hole boundaries is efficiently determined using a mid-distance rule and Cartesian maps of potential valid donor stencils with minimal user input. Application of this procedure typically results in a spatially-variable offset of the hole boundaries from the minimum hole with only a small number of orphan points remaining. Test cases on complex configurations are presented to demonstrate the new scheme.