Optimization and validation of accelerated golden-angle radial sparse MRI reconstruction with self-calibrating GRAPPA operator gridding.

PubMed

Benkert, Thomas; Tian, Ye; Huang, Chenchan; DiBella, Edward V R; Chandarana, Hersh; Feng, Li

2018-07-01

Golden-angle radial sparse parallel (GRASP) MRI reconstruction requires gridding and regridding to transform data between radial and Cartesian k-space. These operations are repeatedly performed in each iteration, which makes the reconstruction computationally demanding. This work aimed to accelerate GRASP reconstruction using self-calibrating GRAPPA operator gridding (GROG) and to validate its performance in clinical imaging. GROG is an alternative gridding approach based on parallel imaging, in which k-space data acquired on a non-Cartesian grid are shifted onto a Cartesian k-space grid using information from multicoil arrays. For iterative non-Cartesian image reconstruction, GROG is performed only once as a preprocessing step. Therefore, the subsequent iterative reconstruction can be performed directly in Cartesian space, which significantly reduces computational burden. Here, a framework combining GROG with GRASP (GROG-GRASP) is first optimized and then compared with standard GRASP reconstruction in 22 prostate patients. GROG-GRASP achieved approximately 4.2-fold reduction in reconstruction time compared with GRASP (∼333 min versus ∼78 min) while maintaining image quality (structural similarity index ≈ 0.97 and root mean square error ≈ 0.007). Visual image quality assessment by two experienced radiologists did not show significant differences between the two reconstruction schemes. With a graphics processing unit implementation, image reconstruction time can be further reduced to approximately 14 min. The GRASP reconstruction can be substantially accelerated using GROG. This framework is promising toward broader clinical application of GRASP and other iterative non-Cartesian reconstruction methods. Magn Reson Med 80:286-293, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Efficient parallel seismic simulations including topography and 3-D material heterogeneities on locally refined composite grids

NASA Astrophysics Data System (ADS)

Petersson, Anders; Rodgers, Arthur

2010-05-01

The finite difference method on a uniform Cartesian grid is a highly efficient and easy to implement technique for solving the elastic wave equation in seismic applications. However, the spacing in a uniform Cartesian grid is fixed throughout the computational domain, whereas the resolution requirements in realistic seismic simulations usually are higher near the surface than at depth. This can be seen from the well-known formula h ≤ L-P which relates the grid spacing h to the wave length L, and the required number of grid points per wavelength P for obtaining an accurate solution. The compressional and shear wave lengths in the earth generally increase with depth and are often a factor of ten larger below the Moho discontinuity (at about 30 km depth), than in sedimentary basins near the surface. A uniform grid must have a grid spacing based on the small wave lengths near the surface, which results in over-resolving the solution at depth. As a result, the number of points in a uniform grid is unnecessarily large. In the wave propagation project (WPP) code, we address the over-resolution-at-depth issue by generalizing our previously developed single grid finite difference scheme to work on a composite grid consisting of a set of structured rectangular grids of different spacings, with hanging nodes on the grid refinement interfaces. The computational domain in a regional seismic simulation often extends to depth 40-50 km. Hence, using a refinement ratio of two, we need about three grid refinements from the bottom of the computational domain to the surface, to keep the local grid size in approximate parity with the local wave lengths. The challenge of the composite grid approach is to find a stable and accurate method for coupling the solution across the grid refinement interface. Of particular importance is the treatment of the solution at the hanging nodes, i.e., the fine grid points which are located in between coarse grid points. WPP implements a new, energy conserving, coupling procedure for the elastic wave equation at grid refinement interfaces. When used together with our single grid finite difference scheme, it results in a method which is provably stable, without artificial dissipation, for arbitrary heterogeneous isotropic elastic materials. The new coupling procedure is based on satisfying the summation-by-parts principle across refinement interfaces. From a practical standpoint, an important advantage of the proposed method is the absence of tunable numerical parameters, which seldom are appreciated by application experts. In WPP, the composite grid discretization is combined with a curvilinear grid approach that enables accurate modeling of free surfaces on realistic (non-planar) topography. The overall method satisfies the summation-by-parts principle and is stable under a CFL time step restriction. A feature of great practical importance is that WPP automatically generates the composite grid based on the user provided topography and the depths of the grid refinement interfaces. The WPP code has been verified extensively, for example using the method of manufactured solutions, by solving Lamb's problem, by solving various layer over half- space problems and comparing to semi-analytic (FK) results, and by simulating scenario earthquakes where results from other seismic simulation codes are available. WPP has also been validated against seismographic recordings of moderate earthquakes. WPP performs well on large parallel computers and has been run on up to 32,768 processors using about 26 Billion grid points (78 Billion DOF) and 41,000 time steps. WPP is an open source code that is available under the Gnu general public license.

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.

Euler Technology Assessment for Preliminary Aircraft Design: Compressibility Predictions by Employing the Cartesian Unstructured Grid SPLITFLOW Code

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.

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.

Efficient Unstructured Cartesian/Immersed-Boundary Method with Local Mesh Refinement to Simulate Flows in Complex 3D Geometries

NASA Astrophysics Data System (ADS)

de Zelicourt, Diane; Ge, Liang; Sotiropoulos, Fotis; Yoganathan, Ajit

2008-11-01

Image-guided computational fluid dynamics has recently gained attention as a tool for predicting the outcome of different surgical scenarios. Cartesian Immersed-Boundary methods constitute an attractive option to tackle the complexity of real-life anatomies. However, when such methods are applied to the branching, multi-vessel configurations typically encountered in cardiovascular anatomies the majority of the grid nodes of the background Cartesian mesh end up lying outside the computational domain, increasing the memory and computational overhead without enhancing the numerical resolution in the region of interest. To remedy this situation, the method presented here superimposes local mesh refinement onto an unstructured Cartesian grid formulation. A baseline unstructured Cartesian mesh is generated by eliminating all nodes that reside in the exterior of the flow domain from the grid structure, and is locally refined in the vicinity of the immersed-boundary. The potential of the method is demonstrated by carrying out systematic mesh refinement studies for internal flow problems ranging in complexity from a 90 deg pipe bend to an actual, patient-specific anatomy reconstructed from magnetic resonance.

An efficient gridding reconstruction method for multishot non-Cartesian imaging with correction of off-resonance artifacts.

PubMed

Meng, Yuguang; Lei, Hao

2010-06-01

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. (c) 2010 Wiley-Liss, Inc.

Regularization techniques on least squares non-uniform fast Fourier transform.

PubMed

Gibiino, Fabio; Positano, Vincenzo; Landini, Luigi; Santarelli, Maria Filomena

2013-05-01

Non-Cartesian acquisition strategies are widely used in MRI to dramatically reduce the acquisition time while at the same time preserving the image quality. Among non-Cartesian reconstruction methods, the least squares non-uniform fast Fourier transform (LS_NUFFT) is a gridding method based on a local data interpolation kernel that minimizes the worst-case approximation error. The interpolator is chosen using a pseudoinverse matrix. As the size of the interpolation kernel increases, the inversion problem may become ill-conditioned. Regularization methods can be adopted to solve this issue. In this study, we compared three regularization methods applied to LS_NUFFT. We used truncated singular value decomposition (TSVD), Tikhonov regularization and L₁-regularization. Reconstruction performance was evaluated using the direct summation method as reference on both simulated and experimental data. We also evaluated the processing time required to calculate the interpolator. First, we defined the value of the interpolator size after which regularization is needed. Above this value, TSVD obtained the best reconstruction. However, for large interpolator size, the processing time becomes an important constraint, so an appropriate compromise between processing time and reconstruction quality should be adopted. Copyright © 2013 John Wiley & Sons, Ltd.

PCTDSE: A parallel Cartesian-grid-based TDSE solver for modeling laser-atom interactions

NASA Astrophysics Data System (ADS)

Fu, Yongsheng; Zeng, Jiaolong; Yuan, Jianmin

2017-01-01

We present a parallel Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for modeling laser-atom interactions. It can simulate the single-electron dynamics of atoms in arbitrary time-dependent vector potentials. We use a split-operator method combined with fast Fourier transforms (FFT), on a three-dimensional (3D) Cartesian grid. Parallelization is realized using a 2D decomposition strategy based on the Message Passing Interface (MPI) library, which results in a good parallel scaling on modern supercomputers. We give simple applications for the hydrogen atom using the benchmark problems coming from the references and obtain repeatable results. The extensions to other laser-atom systems are straightforward with minimal modifications of the source code.

SACR ADVance 3-D Cartesian Cloud Cover (SACR-ADV-3D3C) product

DOE Data Explorer

Meng Wang, Tami Toto, Eugene Clothiaux, Katia Lamer, Mariko Oue

2017-03-08

SACR-ADV-3D3C remaps the outputs of SACRCORR for cross-wind range-height indicator (CW-RHI) scans to a Cartesian grid and reports reflectivity CFAD and best estimate domain averaged cloud fraction. The final output is a single NetCDF file containing all aforementioned corrected radar moments remapped on a 3-D Cartesian grid, the SACR reflectivity CFAD, a profile of best estimate cloud fraction, a profile of maximum observable x-domain size (xmax), a profile time to horizontal distance estimate and a profile of minimum observable reflectivity (dBZmin).

Euler Technology Assessment program for preliminary aircraft design employing SPLITFLOW code with Cartesian unstructured grid method

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.

A 2.5D Computational Method to Simulate Cylindrical Fluidized Beds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tingwen; Benyahia, Sofiane; Dietiker, Jeff

2015-02-17

In this paper, the limitations of axisymmetric and Cartesian two-dimensional (2D) simulations of cylindrical gas-solid fluidized beds are discussed. A new method has been proposed to carry out pseudo-two-dimensional (2.5D) simulations of a cylindrical fluidized bed by appropriately combining computational domains of Cartesian 2D and axisymmetric simulations. The proposed method was implemented in the open-source code MFIX and applied to the simulation of a lab-scale bubbling fluidized bed with necessary sensitivity study. After a careful grid study to ensure the numerical results are grid independent, detailed comparisons of the flow hydrodynamics were presented against axisymmetric and Cartesian 2D simulations. Furthermore,more » the 2.5D simulation results have been compared to the three-dimensional (3D) simulation for evaluation. This new approach yields better agreement with the 3D simulation results than with axisymmetric and Cartesian 2D simulations.« less

Parallel Cartesian grid refinement for 3D complex flow simulations

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2013-11-01

A second order accurate method for discretizing the Navier-Stokes equations on 3D unstructured Cartesian grids is presented. Although the grid generator is based on the oct-tree hierarchical method, fully unstructured data-structure is adopted enabling robust calculations for incompressible flows, avoiding both the need of synchronization of the solution between different levels of refinement and usage of prolongation/restriction operators. The current solver implements a hybrid staggered/non-staggered grid layout, employing the implicit fractional step method to satisfy the continuity equation. The pressure-Poisson equation is discretized by using a novel second order fully implicit scheme for unstructured Cartesian grids and solved using an efficient Krylov subspace solver. The momentum equation is also discretized with second order accuracy and the high performance Newton-Krylov method is used for integrating them in time. Neumann and Dirichlet conditions are used to validate the Poisson solver against analytical functions and grid refinement results to a significant reduction of the solution error. The effectiveness of the fractional step method results in the stability of the overall algorithm and enables the performance of accurate multi-resolution real life simulations. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

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.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

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.

A weakly-compressible Cartesian grid approach for hydrodynamic flows

NASA Astrophysics Data System (ADS)

Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D.

2017-11-01

The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (> 3) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article.

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.

A projection method for coupling two-phase VOF and fluid structure interaction simulations

NASA Astrophysics Data System (ADS)

Cerroni, Daniele; Da Vià, Roberto; Manservisi, Sandro

2018-02-01

The study of Multiphase Fluid Structure Interaction (MFSI) is becoming of great interest in many engineering applications. In this work we propose a new algorithm for coupling a FSI problem to a multiphase interface advection problem. An unstructured computational grid and a Cartesian mesh are used for the FSI and the VOF problem, respectively. The coupling between these two different grids is obtained by interpolating the velocity field into the Cartesian grid through a projection operator that can take into account the natural movement of the FSI domain. The piecewise color function is interpolated back on the unstructured grid with a Galerkin interpolation to obtain a point-wise function which allows the direct computation of the surface tension forces.

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.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

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.

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

Large-eddy simulation of wind turbine wake interactions on locally refined Cartesian grids

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2014-11-01

Performing high-fidelity numerical simulations of turbulent flow in wind farms remains a challenging issue mainly because of the large computational resources required to accurately simulate the turbine wakes and turbine/turbine interactions. The discretization of the governing equations on structured grids for mesoscale calculations may not be the most efficient approach for resolving the large disparity of spatial scales. A 3D Cartesian grid refinement method enabling the efficient coupling of the Actuator Line Model (ALM) with locally refined unstructured Cartesian grids adapted to accurately resolve tip vortices and multi-turbine interactions, is presented. Second order schemes are employed for the discretization of the incompressible Navier-Stokes equations in a hybrid staggered/non-staggered formulation coupled with a fractional step method that ensures the satisfaction of local mass conservation to machine zero. The current approach enables multi-resolution LES of turbulent flow in multi-turbine wind farms. The numerical simulations are in good agreement with experimental measurements and are able to resolve the rich dynamics of turbine wakes on grids containing only a small fraction of the grid nodes that would be required in simulations without local mesh refinement. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the National Science Foundation under Award number NSF PFI:BIC 1318201.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne E.

2013-01-01

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

NASA Technical Reports Server (NTRS)

Kim, Hyoungin; Liou, Meng-Sing

2011-01-01

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles.

PubMed

Yang, Ping; Kattawar, George W; Liou, Kuo-Nan; Lu, Jun Q

2004-08-10

Two grid configurations can be employed to implement the finite-difference time-domain (FDTD) technique in a Cartesian system. One configuration defines the electric and magnetic field components at the cell edges and cell-face centers, respectively, whereas the other reverses these definitions. These two grid configurations differ in terms of implication on the electromagnetic boundary conditions if the scatterer in the FDTD computation is a dielectric particle. The permittivity has an abrupt transition at the cell interface if the dielectric properties of two adjacent cells are not identical. Similarly, the discontinuity of permittivity is also observed at the edges of neighboring cells that are different in terms of their dielectric constants. We present two FDTD schemes for light scattering by dielectric particles to overcome the above-mentioned discontinuity on the basis of the electromagnetic boundary conditions for the two Cartesian grid configurations. We also present an empirical approach to accelerate the convergence of the discrete Fourier transform to obtain the field values in the frequency domain. As a new application of the FDTD method, we investigate the scattering properties of multibranched bullet-rosette ice crystals at both visible and thermal infrared wavelengths.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

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 discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

DOE PAGES

Devendran, Dharshi; Graves, Daniel; Johansen, Hans; ...

2017-05-08

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devendran, Dharshi; Graves, Daniel; Johansen, Hans

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

LAVA Applications to Open Rotors

NASA Technical Reports Server (NTRS)

Kiris, Cetin C.; Housman, Jeff; Barad, Mike; Brehm, Christoph

2015-01-01

Outline: LAVA (Launch Ascent Vehicle Aerodynamics); Introduction; Acoustics Related Applications; LAVA Applications to Open Rotor; Structured Overset Grids; Cartesian Grid with Immersed Boundary; High Speed Case; High Speed Case with Plate Low Speed Case.

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.

An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies

NASA Technical Reports Server (NTRS)

Quirk, James J.

1992-01-01

In this paper we describe an approach for dealing with arbitrary complex, two dimensional geometries, the so-called cartesian boundary method. Conceptually, the cartesian boundary method is quite simple. Solid bodies blank out areas of a background, cartesian mesh, and the resultant cut cells are singled out for special attention. However, there are several obstacles that must be overcome in order to achieve a practical scheme. We present a general strategy that overcomes these obstacles, together with some details of our successful conversion of an adaptive mesh algorithm from a body-fitted code to a cartesian boundary code.

Research in Parallel Algorithms and Software for Computational Aerosciences

DOT National Transportation Integrated Search

1996-04-01

Phase I is complete for the development of a Computational Fluid Dynamics : with automatic grid generation and adaptation for the Euler : analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian : grid code developed at Lockheed...

A mixed volume grid approach for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Jorgenson, Philip C. E.

1996-01-01

An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.

A VERSATILE SHARP INTERFACE IMMERSED BOUNDARY METHOD FOR INCOMPRESSIBLE FLOWS WITH COMPLEX BOUNDARIES

PubMed Central

Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F.M.; Vargas, A.; von Loebbecke, A.

2010-01-01

A sharp interface immersed boundary method for simulating incompressible viscous flow past three-dimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two- and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method. PMID:20216919

Lattice Boltzmann and Navier-Stokes Cartesian CFD Approaches for Airframe Noise Predictions

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Kocheemoolayil, Joseph G.; Kiris, Cetin C.

2017-01-01

Lattice Boltzmann (LB) and compressible Navier-Stokes (NS) equations based computational fluid dynamics (CFD) approaches are compared for simulating airframe noise. Both LB and NS CFD approaches are implemented within the Launch Ascent and Vehicle Aerodynamics (LAVA) framework. Both schemes utilize the same underlying Cartesian structured mesh paradigm with provision for local adaptive grid refinement and sub-cycling in time. We choose a prototypical massively separated, wake-dominated flow ideally suited for Cartesian-grid based approaches in this study - The partially-dressed, cavity-closed nose landing gear (PDCC-NLG) noise problem from AIAA's Benchmark problems for Airframe Noise Computations (BANC) series of workshops. The relative accuracy and computational efficiency of the two approaches are systematically compared. Detailed comments are made on the potential held by LB to significantly reduce time-to-solution for a desired level of accuracy within the context of modeling airframes noise from first principles.

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.

Summary and Statistical Analysis of the First AIAA Sonic Boom Prediction Workshop

NASA Technical Reports Server (NTRS)

Park, Michael A.; Morgenstern, John M.

2014-01-01

A summary is provided for the First AIAA Sonic Boom Workshop held 11 January 2014 in conjunction with AIAA SciTech 2014. Near-field pressure signatures extracted from computational fluid dynamics solutions are gathered from nineteen participants representing three countries for the two required cases, an axisymmetric body and simple delta wing body. Structured multiblock, unstructured mixed-element, unstructured tetrahedral, overset, and Cartesian cut-cell methods are used by the participants. Participants provided signatures computed on participant generated and solution adapted grids. Signatures are also provided for a series of uniformly refined workshop provided grids. These submissions are propagated to the ground and loudness measures are computed. This allows the grid convergence of a loudness measure and a validation metric (dfference norm between computed and wind tunnel measured near-field signatures) to be studied for the first time. Statistical analysis is also presented for these measures. An optional configuration includes fuselage, wing, tail, flow-through nacelles, and blade sting. This full configuration exhibits more variation in eleven submissions than the sixty submissions provided for each required case. Recommendations are provided for potential improvements to the analysis methods and a possible subsequent workshop.

VAC: Versatile Advection Code

NASA Astrophysics Data System (ADS)

Tóth, Gábor; Keppens, Rony

2012-07-01

The Versatile Advection Code (VAC) is a freely available general hydrodynamic and magnetohydrodynamic simulation software that works in 1, 2 or 3 dimensions on Cartesian and logically Cartesian grids. VAC runs on any Unix/Linux system with a Fortran 90 (or 77) compiler and Perl interpreter. VAC can run on parallel machines using either the Message Passing Interface (MPI) library or a High Performance Fortran (HPF) compiler.

Parallel Adaptive Mesh Refinement Library

NASA Technical Reports Server (NTRS)

Mac-Neice, Peter; Olson, Kevin

2005-01-01

Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.

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.

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.

Grid-based Molecular Footprint Comparison Method for Docking and De Novo Design: Application to HIVgp41

PubMed Central

Mukherjee, Sudipto; Rizzo, Robert C.

2014-01-01

Scoring functions are a critically important component of computer-aided screening methods for the identification of lead compounds during early stages of drug discovery. Here, we present a new multi-grid implementation of the footprint similarity (FPS) scoring function that was recently developed in our laboratory which has proven useful for identification of compounds which bind to a protein on a per-residue basis in a way that resembles a known reference. The grid-based FPS method is much faster than its Cartesian-space counterpart which makes it computationally tractable for on-the-fly docking, virtual screening, or de novo design. In this work, we establish that: (i) relatively few grids can be used to accurately approximate Cartesian space footprint similarity, (ii) the method yields improved success over the standard DOCK energy function for pose identification across a large test set of experimental co-crystal structures, for crossdocking, and for database enrichment, and (iii) grid-based FPS scoring can be used to tailor construction of new molecules to have specific properties, as demonstrated in a series of test cases targeting the viral protein HIVgp41. The method will be made available in the program DOCK6. PMID:23436713

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.

Dip and anisotropy effects on flow using a vertically skewed model grid.

PubMed

Hoaglund, John R; Pollard, David

2003-01-01

Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.

Numerical computation of complex multi-body Navier-Stokes flows with applications for the integrated Space Shuttle launch vehicle

NASA Technical Reports Server (NTRS)

Chan, William M.

1993-01-01

An enhanced grid system for the Space Shuttle Orbiter was built by integrating CAD definitions from several sources and then generating the surface and volume grids. The new grid system contains geometric components not modeled previously plus significant enhancements on geometry that has been modeled in the old grid system. The new orbiter grids were then integrated with new grids for the rest of the launch vehicle. Enhancements were made to the hyperbolic grid generator HYPGEN and new tools for grid projection, manipulation, and modification, Cartesian box grid and far field grid generation and post-processing of flow solver data were developed.

A Cartesian cut cell method for rarefied flow simulations around moving obstacles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dechristé, G., E-mail: Guillaume.Dechriste@math.u-bordeaux1.fr; CNRS, IMB, UMR 5251, F-33400 Talence; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux1.fr

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 amore » 3D unsteady simulation of the Crookes radiometer.« less

Calculation of radiation therapy dose using all particle Monte Carlo transport

DOEpatents

Chandler, William P.; Hartmann-Siantar, Christine L.; Rathkopf, James A.

1999-01-01

The actual radiation dose absorbed in the body is calculated using three-dimensional Monte Carlo transport. Neutrons, protons, deuterons, tritons, helium-3, alpha particles, photons, electrons, and positrons are transported in a completely coupled manner, using this Monte Carlo All-Particle Method (MCAPM). The major elements of the invention include: computer hardware, user description of the patient, description of the radiation source, physical databases, Monte Carlo transport, and output of dose distributions. This facilitated the estimation of dose distributions on a Cartesian grid for neutrons, photons, electrons, positrons, and heavy charged-particles incident on any biological target, with resolutions ranging from microns to centimeters. Calculations can be extended to estimate dose distributions on general-geometry (non-Cartesian) grids for biological and/or non-biological media.

Calculation of radiation therapy dose using all particle Monte Carlo transport

DOEpatents

Chandler, W.P.; Hartmann-Siantar, C.L.; Rathkopf, J.A.

1999-02-09

The actual radiation dose absorbed in the body is calculated using three-dimensional Monte Carlo transport. Neutrons, protons, deuterons, tritons, helium-3, alpha particles, photons, electrons, and positrons are transported in a completely coupled manner, using this Monte Carlo All-Particle Method (MCAPM). The major elements of the invention include: computer hardware, user description of the patient, description of the radiation source, physical databases, Monte Carlo transport, and output of dose distributions. This facilitated the estimation of dose distributions on a Cartesian grid for neutrons, photons, electrons, positrons, and heavy charged-particles incident on any biological target, with resolutions ranging from microns to centimeters. Calculations can be extended to estimate dose distributions on general-geometry (non-Cartesian) grids for biological and/or non-biological media. 57 figs.

Test problems for inviscid transonic flow

NASA Technical Reports Server (NTRS)

Carlson, L. A.

1979-01-01

Solving of test problems with the TRANDES program is discussed. This method utilizes the full, inviscid, perturbation potential flow equation in a Cartesian grid system that is stretched to infinity. This equation is represented by a nonconservative system of finite difference equations that includes at supersonic points a rotated difference scheme and is solved by column relaxation. The solution usually starts from a zero perturbation potential on a very coarse grid (typically 13 by 7) followed by several grid halvings until a final solution is obtained on a fine grid (97 by 49).

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.

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

NASA Astrophysics Data System (ADS)

Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander

2012-02-01

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.

Magnetohydrodynamic Simulations of Black Hole Accretion Flows Using PATCHWORK, a Multi-Patch, multi-code approach

NASA Astrophysics Data System (ADS)

Avara, Mark J.; Noble, Scott; Shiokawa, Hotaka; Cheng, Roseanne; Campanelli, Manuela; Krolik, Julian H.

2017-08-01

A multi-patch approach to numerical simulations of black hole accretion flows allows one to robustly match numerical grid shape and equations solved to the natural structure of the physical system. For instance, a cartesian gridded patch can be used to cover coordinate singularities on a spherical-polar grid, increasing computational efficiency and better capturing the physical system through natural symmetries. We will present early tests, initial applications, and first results from the new MHD implementation of the PATCHWORK framework.

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.

Thermocapillary motion of deformable drops

NASA Technical Reports Server (NTRS)

Haj-Hariri, Hossein; Shi, Qingping; Borhan, Ali

1994-01-01

The thermocapillary motion of initially spherical drops/bubbles driven by a constant temperature gradient in an unbounded liquid medium is simulated numerically. Effects of convection of momentum and energy, as well as shape deformations, are addressed. The method used is based on interface tracking on a base cartesian grid, and uses a smeared color or indicator function for the determination of the surface topology. Quad-tree adaptive refinement of the cartesian grid is implemented to enhance the fidelity of the surface tracking. It is shown that convection of energy results in a slowing of the drop, as the isotherms get wrapped around the front of the drop. Shape deformation resulting from inertial effects affect the migration velocity. The physical results obtained are in agreement with the existing literature. Furthermore, remarks are made on the sensitivity of the calculated solutions to the smearing of the fluid properties. Analysis and simulations show that the migration velocity depends very strongly on the smearing of the interfacial force whereas it is rather insensitive to the smearing of other properties, hence the adaptive grid.

Globally Optimal Path Planning with Anisotropic Running Costs

DTIC Science & Technology

2013-03-01

contours were generated on a 3852 Cartesian grid. . . . . . . . . . . . . . . . 33 A1 The N(i, j ) set shown mapped onto Ωh as large dots for the case...function NF(x) near front set as a function of x ∈ Ωh NF(i, j ) near front set as a function of (i, j ) ∈ ΩZh Υ(x) anisotropy function at x δ Cartesian...discriminant of the polynomial p, see Equation (26) argmin argument of the minimum of a function V yz(x, ζ) see Equation (28) T (i, j ) the triplet {(i, j ), V

An optimal FFT-based anisotropic power spectrum estimator

NASA Astrophysics Data System (ADS)

Hand, Nick; Li, Yin; Slepian, Zachary; Seljak, Uroš

2017-07-01

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order l requires only 2l+1 FFTs rather than the (l+1)(l+2)/2 FFTs of the Cartesian approach. For the hexadecapole (l = 4), this translates to 40% fewer FFTs, with increased savings for higher l. The reduction in wall-clock time enables the calculation of finely-binned wedges in P(k,μ), obtained by computing multipoles up to a large lmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ simeq while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of lmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using lmax=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with lmax=4.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hand, Nick; Seljak, Uroš; Li, Yin

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTsmore » of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k ,μ), obtained by computing multipoles up to a large ℓ{sub max} and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≅ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓ{sub max}, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓ{sub max}=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ{sub 8}, as compared to a 54% increase with ℓ{sub max}=4.« less

Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform

NASA Astrophysics Data System (ADS)

Zhao, Liang; Healy, John J.; Muniraj, Inbarasan; Cui, Xiao-Guang; Malallah, Ra'ed; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

Software Design Strategies for Multidisciplinary Computational Fluid Dynamics

DTIC Science & Technology

2012-07-01

on the left-hand-side of Figure 3. The resulting unstructured grid system does a good job of representing the flowfield locally around the solid... Laboratory [16–19]. It uses Cartesian block structured grids, which lead to a substantially more efficient computational execution compared to the...including blade sectional lift and pitching moment. These Helios-computed airloads show good agreement with the experimental data. Many of the

UNIFORM ESTIMATES FOR SOLUTIONS OF THE \\overline{\\partial}-EQUATION IN PSEUDOCONVEX POLYHEDRA

NASA Astrophysics Data System (ADS)

Sergeev, A. G.; Henkin, G. M.

1981-04-01

It is proved that the nonhomogeneous Cauchy-Riemann equation on an analytic submanifold "in general position" in a Cartesian product of strictly convex domains admits a solution with a uniform estimate. The possibility of weakening the requirement of general position in this result is investigated. Bibliography: 46 titles.

Numerical relativity in spherical coordinates with the Einstein Toolkit

NASA Astrophysics Data System (ADS)

Mewes, Vassilios; Zlochower, Yosef; Campanelli, Manuela; Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

2018-04-01

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.

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.

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.

Ancestral Genres of Mathematical Graphs

ERIC Educational Resources Information Center

Gerofsky, Susan

2011-01-01

Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…

A New Dynamical Core Based on the Prediction of the Curl of the Horizontal Vorticity

NASA Astrophysics Data System (ADS)

Konor, C. S.; Randall, D. A.; Heikes, R. P.

2015-12-01

The Vector-Vorticity Dynamical core (VVM) developed by Jung and Arakawa (2008) has important advantages for the use with the anelastic and unified systems of equations. The VVM predicts the horizontal vorticity vector (HVV) at each interface and the vertical vorticity at the top layer of the model. To guarantee that the three-dimensional vorticity is nondivergent, the vertical vorticity at the interior layers is diagnosed from the horizontal divergence of the HVV through a vertical integral from the top to down. To our knowledge, this is the only dynamical core that guarantees the nondivergence of the three-dimensional vorticity. The VVM uses a C-type horizontal grid, which allows a computational mode. While the computational mode does not seem to be serious in the Cartesian grid applications, it may be serious in the icosahedral grid applications because of the extra degree of freedom in such grids. Although there are special filters to minimize the effects of this computational mode, we prefer to eliminate it altogether. We have developed a new dynamical core, which uses a Z-grid to avoid the computational mode mentioned above. The dynamical core predicts the curl of the HVV and diagnoses the horizontal divergence of the HVV from the predicted vertical vorticity. The three-dimensional vorticity is guaranteed to be nondivergent as in the VVM. In this presentation, we will introduce the new dynamical core and show results obtained by using Cartesian and hexagonal grids. We will also compare the solutions to that obtained by the VVM.

Calculation of steady and unsteady transonic flow using a Cartesian mesh and gridless boundary conditions with application to aeroelasticity

NASA Astrophysics Data System (ADS)

Kirshman, David

A numerical method for the solution of inviscid compressible flow using an array of embedded Cartesian meshes in conjunction with gridless surface boundary conditions is developed. The gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the surface geometry. The method allows for accurate treatment of the surface boundary conditions using a grid resolution an order of magnitude coarser than required of typical Cartesian approaches. Additionally, the method does not suffer from issues associated with thin body geometry or extremely fine cut cells near the body. Unlike some methods that consider a gridless (or "meshless") treatment throughout the entire domain, multi-grid acceleration can be effectively incorporated and issues associated with global conservation are alleviated. The "gridless" surface boundary condition provides for efficient and simple problem set up since definition of the body geometry is generated independently from the field mesh, and automatically incorporated into the field discretization of the domain. The applicability of the method is first demonstrated for steady flow of single and multi-element airfoil configurations. Using this method, comparisons with traditional body-fitted grid simulations reveal that steady flow solutions can be obtained accurately with minimal effort associated with grid generation. The method is then extended to unsteady flow predictions. In this application, flow field simulations for the prescribed oscillation of an airfoil indicate excellent agreement with experimental data. Furthermore, it is shown that the phase lag associated with shock oscillation is accurately predicted without the need for a deformable mesh. Lastly, the method is applied to the prediction of transonic flutter using a two-dimensional wing model, in which comparisons with moving mesh simulations yield nearly identical results. As a result, applicability of the method to transient and vibrating fluid-structure interaction problems is established in which the requirement for a deformable mesh is eliminated.

A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

NASA Astrophysics Data System (ADS)

Huang, Wen-Feng; Ren, Yu-Xin; Jiang, Xiong

2018-02-01

This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifth-order WENO-JS (WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202-228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable. The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On non-uniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime, the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

Wall-layer model for LES with massive separation

NASA Astrophysics Data System (ADS)

Fakhari, Ahmad; Armenio, Vincenzo; Roman, Federico

2016-11-01

Currently, Wall Functions (WF) work well under specific conditions, mostly exhibit drawbacks specially in flows with separation beyond curvatures. In this work, we propose a more general WF which works well in attached and detached flows, in presence and absence of Immersed Boundaries (IB). First we modified an equilibrium stress WF for boundary-fitted geometry making dynamic the computation of the k (von Karman constant) of the log-law; the model was first applied to a periodic open channel flow, and then to the flow over a 2D single hill using uniform coarse grids; the model captured separation with reasonable accuracy. Thereafter IB Method by Roman et al. was improved to avoid momentum loss at the interface between the fluid-solid regions. This required calibration of interfacial eddy viscosity; also a random stochastic forcing was used in wall-normal direction to increase Reynolds stresses and improve mean velocity profile. Finally, to reproduce flow separation, a simplified boundary layer equation was applied to construct velocity at near wall computational nodes. The new scheme was tested on the 2D single hill and periodic hills applying Cartesian and curvilinear grids; good agreement with references was obtained with reduction in cost and complexity. Financial support from project COSMO "CFD open source per opera morta" PAR FSC 2007-2013, Friuli Venezia Giulia.

Fully-coupled analysis of jet mixing problems. Three-dimensional PNS model, SCIP3D

NASA Technical Reports Server (NTRS)

Wolf, D. E.; Sinha, N.; Dash, S. M.

1988-01-01

Numerical procedures formulated for the analysis of 3D jet mixing problems, as incorporated in the computer model, SCIP3D, are described. The overall methodology closely parallels that developed in the earlier 2D axisymmetric jet mixing model, SCIPVIS. SCIP3D integrates the 3D parabolized Navier-Stokes (PNS) jet mixing equations, cast in mapped cartesian or cylindrical coordinates, employing the explicit MacCormack Algorithm. A pressure split variant of this algorithm is employed in subsonic regions with a sublayer approximation utilized for treating the streamwise pressure component. SCIP3D contains both the ks and kW turbulence models, and employs a two component mixture approach to treat jet exhausts of arbitrary composition. Specialized grid procedures are used to adjust the grid growth in accordance with the growth of the jet, including a hybrid cartesian/cylindrical grid procedure for rectangular jets which moves the hybrid coordinate origin towards the flow origin as the jet transitions from a rectangular to circular shape. Numerous calculations are presented for rectangular mixing problems, as well as for a variety of basic unit problems exhibiting overall capabilities of SCIP3D.

Generation and Radiation of Acoustic Waves from a 2-D Shear Layer

NASA Technical Reports Server (NTRS)

Agarwal, Anurag; Morris, Philip J.

2000-01-01

A parallel numerical simulation of the radiation of sound from an acoustic source inside a 2-D jet is presented in this paper. This basic benchmark problem is used as a test case for scattering problems that are presently being solved by using the Impedance Mismatch Method (IMM). In this technique, a solid body in the domain is represented by setting the acoustic impedance of each medium, encountered by a wave, to a different value. This impedance discrepancy results in reflected and scattered waves with appropriate amplitudes. The great advantage of the use of this method is that no modifications to a simple Cartesian grid need to be made for complicated geometry bodies. Thus, high order finite difference schemes may be applied simply to all parts of the domain. In the IMM, the total perturbation field is split into incident and scattered fields. The incident pressure is assumed to be known and the equivalent sources for the scattered field are associated with the presence of the scattering body (through the impedance mismatch) and the propagation of the incident field through a non-uniform flow. An earlier version of the technique could only handle uniform flow in the vicinity of the source and at the outflow boundary. Scattering problems in non-uniform mean flow are of great practical importance (for example, scattering from a high lift device in a non-uniform mean flow or the effects of a fuselage boundary layer). The solution to this benchmark problem, which has an acoustic wave propagating through a non-uniform mean flow, serves as a test case for the extensions of the IMM technique.

Topography Modeling in Atmospheric Flows Using the Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Ackerman, A. S.; Senocak, I.; Mansour, N. N.; Stevens, D. E.

2004-01-01

Numerical simulation of flow over complex geometry needs accurate and efficient computational methods. Different techniques are available to handle complex geometry. The unstructured grid and multi-block body-fitted grid techniques have been widely adopted for complex geometry in engineering applications. In atmospheric applications, terrain fitted single grid techniques have found common use. Although these are very effective techniques, their implementation, coupling with the flow algorithm, and efficient parallelization of the complete method are more involved than a Cartesian grid method. The grid generation can be tedious and one needs to pay special attention in numerics to handle skewed cells for conservation purposes. Researchers have long sought for alternative methods to ease the effort involved in simulating flow over complex geometry.

Surface Modeling, Grid Generation, and Related Issues in Computational Fluid Dynamic (CFD) Solutions

NASA Technical Reports Server (NTRS)

Choo, Yung K. (Compiler)

1995-01-01

The NASA Steering Committee for Surface Modeling and Grid Generation (SMAGG) sponsored a workshop on surface modeling, grid generation, and related issues in Computational Fluid Dynamics (CFD) solutions at Lewis Research Center, Cleveland, Ohio, May 9-11, 1995. The workshop provided a forum to identify industry needs, strengths, and weaknesses of the five grid technologies (patched structured, overset structured, Cartesian, unstructured, and hybrid), and to exchange thoughts about where each technology will be in 2 to 5 years. The workshop also provided opportunities for engineers and scientists to present new methods, approaches, and applications in SMAGG for CFD. This Conference Publication (CP) consists of papers on industry overview, NASA overview, five grid technologies, new methods/ approaches/applications, and software systems.

Linear scaling computation of the Fock matrix. VI. Data parallel computation of the exchange-correlation matrix

NASA Astrophysics Data System (ADS)

Gan, Chee Kwan; Challacombe, Matt

2003-05-01

Recently, early onset linear scaling computation of the exchange-correlation matrix has been achieved using hierarchical cubature [J. Chem. Phys. 113, 10037 (2000)]. Hierarchical cubature differs from other methods in that the integration grid is adaptive and purely Cartesian, which allows for a straightforward domain decomposition in parallel computations; the volume enclosing the entire grid may be simply divided into a number of nonoverlapping boxes. In our data parallel approach, each box requires only a fraction of the total density to perform the necessary numerical integrations due to the finite extent of Gaussian-orbital basis sets. This inherent data locality may be exploited to reduce communications between processors as well as to avoid memory and copy overheads associated with data replication. Although the hierarchical cubature grid is Cartesian, naive boxing leads to irregular work loads due to strong spatial variations of the grid and the electron density. In this paper we describe equal time partitioning, which employs time measurement of the smallest sub-volumes (corresponding to the primitive cubature rule) to load balance grid-work for the next self-consistent-field iteration. After start-up from a heuristic center of mass partitioning, equal time partitioning exploits smooth variation of the density and grid between iterations to achieve load balance. With the 3-21G basis set and a medium quality grid, equal time partitioning applied to taxol (62 heavy atoms) attained a speedup of 61 out of 64 processors, while for a 110 molecule water cluster at standard density it achieved a speedup of 113 out of 128. The efficiency of equal time partitioning applied to hierarchical cubature improves as the grid work per processor increases. With a fine grid and the 6-311G(df,p) basis set, calculations on the 26 atom molecule α-pinene achieved a parallel efficiency better than 99% with 64 processors. For more coarse grained calculations, superlinear speedups are found to result from reduced computational complexity associated with data parallelism.

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

2016-11-01

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved.

Numerical solution of the full potential equation using a chimera grid approach

NASA Technical Reports Server (NTRS)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

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.

Direct numerical simulation of incompressible multiphase flow with phase change

NASA Astrophysics Data System (ADS)

Lee, Moon Soo; Riaz, Amir; Aute, Vikrant

2017-09-01

Simulation of multiphase flow with phase change is challenging because of the potential for unphysical pressure oscillations, spurious velocity fields and mass flux errors across the interface. The resulting numerical errors may become critical when large density contrasts are present. To address these issues, we present a new approach for multiphase flow with phase change that features, (i) a smooth distribution of sharp velocity jumps and mass flux within a narrow region surrounding the interface, (ii) improved mass flux projection from the implicit interface onto the uniform Cartesian grid and (iii) post-advection velocity correction step to ensure accurate velocity divergence in interfacial cells. These new features are implemented in combination with a sharp treatment of the jumps in pressure and temperature gradient. A series of 1-D, 2-D, axisymmetric and 3-D problems are solved to verify the improvements afforded by the new approach. Axisymmetric film boiling results are also presented, which show good qualitative agreement with heat transfer correlations as well as experimental observations of bubble shapes.

The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ku, Hwar-Ching; Popel, Aleksander S.

1996-01-01

A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.

An Application of Cartesian-Grid and Volume-of-Fluid Methods to Numerical Ship Hydrodynamics

DTIC Science & Technology

2007-10-01

water-particle ve- locity is discontinuous across the air-water interface, and where CiEA is the Levi - Civita function. rj is the moment the vertical...methods and volume-of- immersed- body and volume-of-fluid (VOF) methods. fluid methods is used to simulate breaking waves around The governing equations are...of a ship hull is used as input to automat- body -fitted grids. The sole geometric input into NFA ically generate an immersed-boundary representation of

Parallel Unsteady Overset Mesh Methodology for a Multi-Solver Paradigm with Adaptive Cartesian Grids

DTIC Science & Technology

2008-08-21

Engineer, U.S. Army Research Laboratory ., Matthew.W.Floros@nasa.gov, AIAA Member ‡Senior Research Scientist, Scaled Numerical Physics LLC., awissink...IV.E and IV.D). Good linear scalability was observed for all three cases up to 12 processors. Beyond that the scalability drops off depending on grid...Research Laboratory for the usage of SUGGAR module and Yikloon Lee at NAVAIR for the usage of the NAVAIR-IHC code. 13 of 22 American Institute of

Stability Analysis of Algebraic Reconstruction for Immersed Boundary Methods with Application in Flow and Transport in Porous Media

NASA Astrophysics Data System (ADS)

Yousefzadeh, M.; Battiato, I.

2017-12-01

Flow and reactive transport problems in porous media often involve complex geometries with stationary or evolving boundaries due to absorption and dissolution processes. Grid based methods (e.g. finite volume, finite element, etc.) are a vital tool for studying these problems. Yet, implementing these methods requires one to answer a very first question of what type of grid is to be used. Among different possible answers, Cartesian grids are one of the most attractive options as they possess simple discretization stencil and are usually straightforward to generate at roughly no computational cost. The Immersed Boundary Method, a Cartesian based methodology, maintains most of the useful features of the structured grids while exhibiting a high-level resilience in dealing with complex geometries. These features make it increasingly more attractive to model transport in evolving porous media as the cost of grid generation reduces greatly. Yet, stability issues and severe time-step restriction due to explicit-time implementation combined with limited studies on the implementation of Neumann (constant flux) and linear and non-linear Robin (e.g. reaction) boundary conditions (BCs) have significantly limited the applicability of IBMs to transport in porous media. We have developed an implicit IBM capable of handling all types of BCs and addressed some numerical issues, including unconditional stability criteria, compactness and reduction of spurious oscillations near the immersed boundary. We tested the method for several transport and flow scenarios, including dissolution processes in porous media, and demonstrate its capabilities. Successful validation against both experimental and numerical data has been carried out.

New high order schemes in BATS-R-US

NASA Astrophysics Data System (ADS)

Toth, G.; van der Holst, B.; Daldorff, L.; Chen, Y.; Gombosi, T. I.

2013-12-01

The University of Michigan global magnetohydrodynamics code BATS-R-US has long relied on the block-adaptive mesh refinement (AMR) to increase accuracy in regions of interest, and we used a second order accurate TVD scheme. While AMR can in principle produce arbitrarily accurate results, there are still practical limitations due to computational resources. To further improve the accuracy of the BATS-R-US code, recently, we have implemented a 4th order accurate finite volume scheme (McCorquodale and Colella, 2011}), the 5th order accurate Monotonicity Preserving scheme (MP5, Suresh and Huynh, 1997) and the 5th order accurate CWENO5 scheme (Capdeville, 2008). In the first implementation the high order accuracy is achieved in the uniform parts of the Cartesian grids, and we still use the second order TVD scheme at resolution changes. For spherical grids the new schemes are only second order accurate so far, but still much less diffusive than the TVD scheme. We show a few verification tests that demonstrate the order of accuracy as well as challenging space physics applications. The high order schemes are less robust than the TVD scheme, and it requires some tricks and effort to make the code work. When the high order scheme works, however, we find that in most cases it can obtain similar or better results than the TVD scheme on twice finer grids. For three dimensional time dependent simulations this means that the high order scheme is almost 10 times faster requires 8 times less storage than the second order method.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

An assessment of unstructured grid technology for timely CFD analysis

NASA Technical Reports Server (NTRS)

Kinard, Tom A.; Schabowski, Deanne M.

1995-01-01

An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.

Development of a Finite-Difference Time Domain (FDTD) Model for Propagation of Transient Sounds in Very Shallow Water.

PubMed

Sprague, Mark W; Luczkovich, Joseph J

2016-01-01

This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

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.

Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

NASA Astrophysics Data System (ADS)

Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team

2017-11-01

We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).

Numerical grid generation in computational field simulations. Volume 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soni, B.K.; Thompson, J.F.; Haeuser, J.

1996-12-31

To enhance the CFS technology to its next level of applicability (i.e., to create acceptance of CFS in an integrated product and process development involving multidisciplinary optimization) the basic requirements are: rapid turn-around time, reliable and accurate simulation, affordability and appropriate linkage to other engineering disciplines. In response to this demand, there has been a considerable growth in the grid generation related research activities involving automization, parallel processing, linkage with the CAD-CAM systems, CFS with dynamic motion and moving boundaries, strategies and algorithms associated with multi-block structured, unstructured, hybrid, hexahedral, and Cartesian grids, along with its applicability to various disciplinesmore » including biomedical, semiconductor, geophysical, ocean modeling, and multidisciplinary optimization.« less

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

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.

Investigation of Multiphase Flow in a Packed Bed Reactor Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Lian, Yongsheng; Motil, Brian; Rame, Enrique

2016-01-01

In this paper we study the two-phase flow phenomena in a packed bed reactor using an integrated experimental and numerical method. The cylindrical bed is filled with uniformly sized spheres. In the experiment water and air are injected into the bed simultaneously. The pressure distribution along the bed will be measured. The numerical simulation is based on a two-phase flow solver which solves the Navier-Stokes equations on Cartesian grids. A novel coupled level set and moment of fluid method is used to construct the interface. A sequential method is used to position spheres in the cylinder. Preliminary experimental results showed that the tested flow rates resulted in pulse flow. The numerical simulation revealed that air bubbles could merge into larger bubbles and also could break up into smaller bubbles to pass through the pores in the bed. Preliminary results showed that flow passed through regions where the porosity is high. Comparison between the experimental and numerical results in terms of pressure distributions at different flow injection rates will be conducted. Comparison of flow phenomena under terrestrial gravity and microgravity will be made.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

NASA Astrophysics Data System (ADS)

Gjennestad, Magnus Aa.; Gruber, Andrea; Lervåg, Karl Yngve; Johansen, Øyvind; Ervik, Åsmund; Hammer, Morten; Munkejord, Svend Tollak

2017-11-01

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose thermodynamic properties are calculated using the Span-Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge-Kutta method. We demonstrate close to fifth-order convergence for advection-diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.

A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids

PubMed Central

Boschitsch, Alexander H.; Fenley, Marcia O.

2011-01-01

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 assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities – obtained with both linear and nonlinear Poisson-Boltzmann equation – for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers. PMID:21984876

MAGNETO-FRICTIONAL MODELING OF CORONAL NONLINEAR FORCE-FREE FIELDS. I. TESTING WITH ANALYTIC SOLUTIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Y.; Keppens, R.; Xia, C.

2016-09-10

We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov–Démoulin model. We compare different combinations of spatial and temporal discretizations, and find thatmore » the fourth-order central difference with a local Lax–Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.« less

Numerical Simulations of STOVL Hot Gas Ingestion in Ground Proximity Using a Multigrid Solution Procedure

NASA Technical Reports Server (NTRS)

Wang, Gang

2003-01-01

A multi grid solution procedure for the numerical simulation of turbulent flows in complex geometries has been developed. A Full Multigrid-Full Approximation Scheme (FMG-FAS) is incorporated into the continuity and momentum equations, while the scalars are decoupled from the multi grid V-cycle. A standard kappa-Epsilon turbulence model with wall functions has been used to close the governing equations. The numerical solution is accomplished by solving for the Cartesian velocity components either with a traditional grid staggering arrangement or with a multiple velocity grid staggering arrangement. The two solution methodologies are evaluated for relative computational efficiency. The solution procedure with traditional staggering arrangement is subsequently applied to calculate the flow and temperature fields around a model Short Take-off and Vertical Landing (STOVL) aircraft hovering in ground proximity.

RIACS

NASA Technical Reports Server (NTRS)

Oliger, Joseph

1997-01-01

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

NASA Technical Reports Server (NTRS)

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

1991-01-01

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere

NASA Technical Reports Server (NTRS)

Engwirda, Darren

2015-01-01

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

A review of level-set methods and some recent applications

NASA Astrophysics Data System (ADS)

Gibou, Frederic; Fedkiw, Ronald; Osher, Stanley

2018-01-01

We review some of the recent advances in level-set methods and their applications. In particular, we discuss how to impose boundary conditions at irregular domains and free boundaries, as well as the extension of level-set methods to adaptive Cartesian grids and parallel architectures. Illustrative applications are taken from the physical and life sciences. Fast sweeping methods are briefly discussed.

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

NASA Astrophysics Data System (ADS)

Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.

2017-09-01

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid-fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid-fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.

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.

Vessel Segmentation and Blood Flow Simulation Using Level-Sets and Embedded Boundary Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deschamps, T; Schwartz, P; Trebotich, D

In this article we address the problem of blood flow simulation in realistic vascular objects. The anatomical surfaces are extracted by means of Level-Sets methods that accurately model the complex and varying surfaces of pathological objects such as aneurysms and stenoses. The surfaces obtained are defined at the sub-pixel level where they intersect the Cartesian grid of the image domain. It is therefore straightforward to construct embedded boundary representations of these objects on the same grid, for which recent work has enabled discretization of the Navier-Stokes equations for incompressible fluids. While most classical techniques require construction of a structured meshmore » that approximates the surface in order to extrapolate a 3D finite-element gridding of the whole volume, our method directly simulates the blood-flow inside the extracted surface without losing any complicated details and without building additional grids.« less

Automated Approach to Very High-Order Aeroacoustic Computations. Revision

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Goodrich, John W.

2001-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Online dynamical downscaling of temperature and precipitation within the iLOVECLIM model (version 1.1)

NASA Astrophysics Data System (ADS)

Quiquet, Aurélien; Roche, Didier M.; Dumas, Christophe; Paillard, Didier

2018-02-01

This paper presents the inclusion of an online dynamical downscaling of temperature and precipitation within the model of intermediate complexity iLOVECLIM v1.1. We describe the following methodology to generate temperature and precipitation fields on a 40 km × 40 km Cartesian grid of the Northern Hemisphere from the T21 native atmospheric model grid. Our scheme is not grid specific and conserves energy and moisture in the same way as the original climate model. We show that we are able to generate a high-resolution field which presents a spatial variability in better agreement with the observations compared to the standard model. Although the large-scale model biases are not corrected, for selected model parameters, the downscaling can induce a better overall performance compared to the standard version on both the high-resolution grid and on the native grid. Foreseen applications of this new model feature include the improvement of ice sheet model coupling and high-resolution land surface models.

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Goodrich, John W.

2000-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Streamline integration as a method for two-dimensional elliptic grid generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at; Held, M.; Einkemmer, L.

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metricsmore » we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.« less

Trajectory Calculations for Spherical Geodesic Grids in Cartesian Space

DTIC Science & Technology

1999-07-01

2 Dtu , t). By applying a rotation transformation as in McDonald and Bates (1989), we get the arrival points in the rotated space l9 5 arctan[cosu sin...see Ritchie (1987)] are required to converge to the solution at which point, the departure point is calcu- lated by Dt x 5 x 2 Dtu x , t 1 .D A M1 22

Design of Rail Instrumentation for Wind Tunnel Sonic Boom Measurements and Computational-Experimental Comparisons

NASA Technical Reports Server (NTRS)

Cliff, Susan E.; Elmiligui, A.; Aftosmis, M.; Morgenstern, J.; Durston, D.; Thomas, S.

2012-01-01

An innovative pressure rail concept for wind tunnel sonic boom testing of modern aircraft configurations with very low overpressures was designed with an adjoint-based solution-adapted Cartesian grid method. The computational method requires accurate free-air calculations of a test article as well as solutions modeling the influence of rail and tunnel walls. Specialized grids for accurate Euler and Navier-Stokes sonic boom computations were used on several test articles including complete aircraft models with flow-through nacelles. The computed pressure signatures are compared with recent results from the NASA 9- x 7-foot Supersonic Wind Tunnel using the advanced rail design.

A geometricla error in some Computer Programs based on the Aki-Christofferson-Husebye (ACH) Method of Teleseismic Tomography

USGS Publications Warehouse

Julian, B.R.; Evans, J.R.; Pritchard, M.J.; Foulger, G.R.

2000-01-01

Some computer programs based on the Aki-Christofferson-Husebye (ACH) method of teleseismic tomography contain an error caused by identifying local grid directions with azimuths on the spherical Earth. This error, which is most severe in high latitudes, introduces systematic errors into computed ray paths and distorts inferred Earth models. It is best dealt with by explicity correcting for the difference between true and grid directions. Methods for computing these directions are presented in this article and are likely to be useful in many other kinds of regional geophysical studies that use Cartesian coordinates and flat-earth approximations.

Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cantrell, J Nathan; Inclan, Eric J; Joshi, Abhijit S

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 specificmore » 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.« less

Velocity field calculation for non-orthogonal numerical grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flach, G. P.

2015-03-01

Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation,more » and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non-orthogonal grid, Darcy velocity components are rigorously derived in this study from normal fluxes to cell faces, which are assumed to be provided by or readily computed from porous-medium simulation code output. The normal fluxes are presumed to satisfy mass balances for every computational cell, and if so, the derived velocity fields are consistent with these mass balances. Derivations are provided for general two-dimensional quadrilateral and three-dimensional hexagonal systems, and for the commonly encountered special cases of perfectly vertical side faces in 2D and 3D and a rectangular footprint in 3D.« less

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

NASA Astrophysics Data System (ADS)

Ge, Yongbin; Cao, Fujun

2011-05-01

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.

Strongly Coupled Fluid-Body Dynamics in the Immersed Boundary Projection Method

NASA Astrophysics Data System (ADS)

Wang, Chengjie; Eldredge, Jeff D.

2014-11-01

A computational algorithm is developed to simulate dynamically coupled interaction between fluid and rigid bodies. The basic computational framework is built upon a multi-domain immersed boundary method library, whirl, developed in previous work. In this library, the Navier-Stokes equations for incompressible flow are solved on a uniform Cartesian grid by the vorticity-based immersed boundary projection method of Colonius and Taira. A solver for the dynamics of rigid-body systems is also included. The fluid and rigid-body solvers are strongly coupled with an iterative approach based on the block Gauss-Seidel method. Interfacial force, with its intimate connection with the Lagrange multipliers used in the fluid solver, is used as the primary iteration variable. Relaxation, developed from a stability analysis of the iterative scheme, is used to achieve convergence in only 2-4 iterations per time step. Several two- and three-dimensional numerical tests are conducted to validate and demonstrate the method, including flapping of flexible wings, self-excited oscillations of a system of linked plates and three-dimensional propulsion of flexible fluked tail. This work has been supported by AFOSR, under Award FA9550-11-1-0098.

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

NASA Technical Reports Server (NTRS)

Engwirda, Darren

2017-01-01

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

NASA Astrophysics Data System (ADS)

Engwirda, Darren

2017-06-01

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi-Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

Development of Intelligent Unmanned Systems

DTIC Science & Technology

2011-05-01

statistical analysis on the terrain map. The data points are stored in the corresponding cells of the Traversability Grid as a linked list of 3-D Cartesian...allowed for multiple configurations of specified data to be as flexible as possible. For example, when an object is being created the knowledge store ...library was also used for querying and storing spatial data . It provided many geometric abstractions necessary such as overlap and intersects

Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

NASA Astrophysics Data System (ADS)

Wu, Leyuan

2018-01-01

We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.

pySeismicFMM: Python based Travel Time Calculation in Regular 2D and 3D Grids in Cartesian and Geographic Coordinates using Fast Marching Method

NASA Astrophysics Data System (ADS)

Wilde-Piorko, M.; Polkowski, M.

2016-12-01

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 final release of 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. Source code of pySeismicFMM will be published before Fall Meeting. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.

Code and Solution Verification of 3D Numerical Modeling of Flow in the Gust Erosion Chamber

NASA Astrophysics Data System (ADS)

Yuen, A.; Bombardelli, F. A.

2014-12-01

Erosion microcosms are devices commonly used to investigate the erosion and transport characteristics of sediments at the bed of rivers, lakes, or estuaries. In order to understand the results these devices provide, the bed shear stress and flow field need to be accurately described. In this research, the UMCES Gust Erosion Microcosm System (U-GEMS) is numerically modeled using Finite Volume Method. The primary aims are to simulate the bed shear stress distribution at the surface of the sediment core/bottom of the microcosm, and to validate the U-GEMS produces uniform bed shear stress at the bottom of the microcosm. The mathematical model equations are solved by on a Cartesian non-uniform grid. Multiple numerical runs were developed with different input conditions and configurations. Prior to developing the U-GEMS model, the General Moving Objects (GMO) model and different momentum algorithms in the code were verified. Code verification of these solvers was done via simulating the flow inside the top wall driven square cavity on different mesh sizes to obtain order of convergence. The GMO model was used to simulate the top wall in the top wall driven square cavity as well as the rotating disk in the U-GEMS. Components simulated with the GMO model were rigid bodies that could have any type of motion. In addition cross-verification was conducted as results were compared with numerical results by Ghia et al. (1982), and good agreement was found. Next, CFD results were validated by simulating the flow within the conventional microcosm system without suction and injection. Good agreement was found when the experimental results by Khalili et al. (2008) were compared. After the ability of the CFD solver was proved through the above code verification steps. The model was utilized to simulate the U-GEMS. The solution was verified via classic mesh convergence study on four consecutive mesh sizes, in addition to that Grid Convergence Index (GCI) was calculated and based on that the computation uncertainty was quantified. The numerical results reveal that the bed shear stress distribution for the U-GEMS model was not uniform. The mean and standard deviation of the bed shear stress for the U-GEMS model was 0.04 and 0.019 Pa respectively.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Transonic analysis of canted winglets

NASA Technical Reports Server (NTRS)

Rosen, B. S.

1984-01-01

A computational method developed to provide a transonic analysis for upper/lower surface wing-tip mounted winglets is described. Winglets with arbitrary planform, cant and toe angle, and airfoil section can be modeled. The embedded grid approach provides high flow field resolution and the required geometric flexibility. In particular, coupled Cartesian/cylindrical grid systems are used to model the complex geometry presented by canted upper/lower surface winglets. A new rotated difference scheme is introduced in order to maintain the stability of the small-disturbance formulation in the presence of large spanwise velocities. Wing and winglet viscous effects are modeled using a two-dimensional 'strip' boundary layer analysis. Correlations with wind tunnel and flight test data for three transport configurations are included.

Method of constructing dished ion thruster grids to provide hole array spacing compensation

NASA Technical Reports Server (NTRS)

Banks, B. A. (Inventor)

1976-01-01

The center-to-center spacings of a photoresist pattern for an array of holes applied to a thin metal sheet are increased by uniformly stretching the thin metal sheet in all directions along the plane of the sheet. The uniform stretching is provided by securely clamping the periphery of the sheet and applying an annular force against the face of the sheet, within the periphery of the sheet and around the photoresist pattern. The technique is used in the construction of ion thruster grid units where the outer or downstream grid is subjected to uniform stretching prior to convex molding. The technique provides alignment of the holes of grid pairs so as to direct the ion beamlets in a direction parallel to the axis of the grid unit and thereby provide optimization of the available thrust.

Numerical Simulations Using the Immersed Boundary Technique

NASA Technical Reports Server (NTRS)

Piomelli, Ugo; Balaras, Elias

1997-01-01

The immersed-boundary method can be used to simulate flows around complex geometries within a Cartesian grid. This method has been used quite extensively in low Reynolds-number flows, and is now being applied to turbulent flows more frequently. The technique will be discussed, and three applications of the method will be presented, with increasing complexity. to illustrate the potential and limitations of the method, and some of the directions for future work.

PDEs on moving surfaces via the closest point method and a modified grid based particle method

NASA Astrophysics Data System (ADS)

Petras, A.; Ruuth, S. J.

2016-05-01

Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman (2008) [20]) is a recent embedding method that has been used to solve a variety of PDEs on smooth surfaces using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. The original closest point method (CPM) was designed for problems posed on static surfaces, however the solution of PDEs on moving surfaces is of considerable interest as well. Here we propose solving PDEs on moving surfaces using a combination of the CPM and a modification of the grid based particle method (Leung and Zhao (2009) [12]). The grid based particle method (GBPM) represents and tracks surfaces using meshless particles and an Eulerian reference grid. Our modification of the GBPM introduces a reconstruction step into the original method to ensure that all the grid points within a computational tube surrounding the surface are active. We present a number of examples to illustrate the numerical convergence properties of our combined method. Experiments for advection-diffusion equations that are strongly coupled to the velocity of the surface are also presented.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Stable and efficient retrospective 4D-MRI using non-uniformly distributed quasi-random numbers

NASA Astrophysics Data System (ADS)

Breuer, Kathrin; Meyer, Cord B.; Breuer, Felix A.; Richter, Anne; Exner, Florian; Weng, Andreas M.; Ströhle, Serge; Polat, Bülent; Jakob, Peter M.; Sauer, Otto A.; Flentje, Michael; Weick, Stefan

2018-04-01

The purpose of this work is the development of a robust and reliable three-dimensional (3D) Cartesian imaging technique for fast and flexible retrospective 4D abdominal MRI during free breathing. To this end, a non-uniform quasi random (NU-QR) reordering of the phase encoding (k y –k z ) lines was incorporated into 3D Cartesian acquisition. The proposed sampling scheme allocates more phase encoding points near the k-space origin while reducing the sampling density in the outer part of the k-space. Respiratory self-gating in combination with SPIRiT-reconstruction is used for the reconstruction of abdominal data sets in different respiratory phases (4D-MRI). Six volunteers and three patients were examined at 1.5 T during free breathing. Additionally, data sets with conventional two-dimensional (2D) linear and 2D quasi random phase encoding order were acquired for the volunteers for comparison. A quantitative evaluation of image quality versus scan times (from 70 s to 626 s) for the given sampling schemes was obtained by calculating the normalized mutual information (NMI) for all volunteers. Motion estimation was accomplished by calculating the maximum derivative of a signal intensity profile of a transition (e.g. tumor or diaphragm). The 2D non-uniform quasi-random distribution of phase encoding lines in Cartesian 3D MRI yields more efficient undersampling patterns for parallel imaging compared to conventional uniform quasi-random and linear sampling. Median NMI values of NU-QR sampling are the highest for all scan times. Therefore, within the same scan time 4D imaging could be performed with improved image quality. The proposed method allows for the reconstruction of motion artifact reduced 4D data sets with isotropic spatial resolution of 2.1  ×  2.1  ×  2.1 mm3 in a short scan time, e.g. 10 respiratory phases in only 3 min. Cranio-caudal tumor displacements between 23 and 46 mm could be observed. NU-QR sampling enables for stable 4D-MRI with high temporal and spatial resolution within short scan time for visualization of organ or tumor motion during free breathing. Further studies, e.g. the application of the method for radiotherapy planning are needed to investigate the clinical applicability and diagnostic value of the approach.

More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs

PubMed Central

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

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

NASA Astrophysics Data System (ADS)

Medl'a, Matej; Mikula, Karol; Čunderlík, Róbert; Macák, Marek

2018-01-01

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth's topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth's surface. It is based on an evolution of a surface, which approximates the Earth's topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth's surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth's topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.

Aerodynamic analysis of three advanced configurations using the TranAir full-potential code

NASA Technical Reports Server (NTRS)

Madson, M. D.; Carmichael, R. L.; Mendoza, J. P.

1989-01-01

Computational results are presented for three advanced configurations: the F-16A with wing tip missiles and under wing fuel tanks, the Oblique Wing Research Aircraft, and an Advanced Turboprop research model. These results were generated by the latest version of the TranAir full potential code, which solves for transonic flow over complex configurations. TranAir embeds a surface paneled geometry definition in a uniform rectangular flow field grid, thus avoiding the use of surface conforming grids, and decoupling the grid generation process from the definition of the configuration. The new version of the code locally refines the uniform grid near the surface of the geometry, based on local panel size and/or user input. This method distributes the flow field grid points much more efficiently than the previous version of the code, which solved for a grid that was uniform everywhere in the flow field. TranAir results are presented for the three configurations and are compared with wind tunnel data.

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.

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.

Grid Transmission Expansion Planning Model Based on Grid Vulnerability

NASA Astrophysics Data System (ADS)

Tang, Quan; Wang, Xi; Li, Ting; Zhang, Quanming; Zhang, Hongli; Li, Huaqiang

2018-03-01

Based on grid vulnerability and uniformity theory, proposed global network structure and state vulnerability factor model used to measure different grid models. established a multi-objective power grid planning model which considering the global power network vulnerability, economy and grid security constraint. Using improved chaos crossover and mutation genetic algorithm to optimize the optimal plan. For the problem of multi-objective optimization, dimension is not uniform, the weight is not easy given. Using principal component analysis (PCA) method to comprehensive assessment of the population every generation, make the results more objective and credible assessment. the feasibility and effectiveness of the proposed model are validated by simulation results of Garver-6 bus system and Garver-18 bus.

Galerkin finite difference Laplacian operators on isolated unstructured triangular meshes by linear combinations

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1990-01-01

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formulae in Cartesian coordinates for the Laplacian operator on isolated unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator along with linear combinations of the residual equations are used to develop the algorithm. The algorithm was tested for a wide variety of unstructured meshes and found to give satisfactory results.

Analysis of lightning field changes produced by Florida thunderstorms

NASA Technical Reports Server (NTRS)

Koshak, William John

1991-01-01

A new method is introduced for inferring the charges deposited in a lightning flash. Lightning-caused field changes (delta E's) are described by a more general volume charge distribution than is defined on a large cartesian grid system centered above the measuring networks. It is shown that a linear system of equations can be used to relate delta E's at the ground to the values of charge on this grid. It is possible to apply more general physical constraints to the charge solutions, and it is possible to access the information content of the delta E data. Computer-simulated delta E inversions show that the location and symmetry of the charge retrievals are usually consistent with the known test sources.

PARAMESH: A Parallel Adaptive Mesh Refinement Community Toolkit

NASA Technical Reports Server (NTRS)

MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; deFainchtein, Rosalinda; Packer, Charles

1999-01-01

In this paper, we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes. The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement. Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.

Scenario Based Approach for Multiple Source Tsunami Hazard Assessment for Sines, Portugal

NASA Astrophysics Data System (ADS)

Wronna, Martin; Omira, Rachid; Baptista, Maria Ana

2015-04-01

In this paper, we present a scenario-based approach for tsunami hazard assessment for the city and harbour of Sines, Portugal one the test-sites of project ASTARTE. Sines holds one of the most important deep-water ports which contains oil-bearing, petrochemical, liquid bulk, coal and container terminals. The port and its industrial infrastructures are facing the ocean to the southwest facing the main seismogenic sources. This work considers two different seismic zones: the Southwest Iberian Margin and the Gloria Fault. Within these two regions, a total of five scenarios were selected to assess tsunami impact at the test site. These scenarios correspond to the worst-case credible scenario approach based upon the largest events of the historical and paleo tsunami catalogues. The tsunami simulations from the source area towards the coast is carried out using NSWING a Non-linear Shallow Water Model With Nested Grids. The code solves the non-linear shallow water equations using the discretization and explicit leap-frog finite difference scheme, in a Cartesian or Spherical frame. The initial sea surface displacement is assumed to be equal to the sea bottom deformation that is computed by Okada equations. Both uniform and non-uniform slip conditions are used. The presented results correspond to the models using non-uniform slip conditions. In this study, the static effect of tides is analysed for three different tidal stages MLLW (mean lower low water) MSL (mean sea level) and MHHW (mean higher high water). For each scenario, inundation is described by maximum values of wave height, flow depth, drawdown, run-up and inundation distance. Synthetic waveforms are computed at virtual tide gages at specific locations outside and inside the harbour. The final results consist of Aggregate Scenario Maps presented for the different inundation parameters. This work is funded by ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

A unified momentum equation approach for computing thermal residual stresses during melting and solidification

NASA Astrophysics Data System (ADS)

Yeo, Haram; Ki, Hyungson

2018-03-01

In this article, we present a novel numerical method for computing thermal residual stresses from a viewpoint of fluid-structure interaction (FSI). In a thermal processing of a material, residual stresses are developed as the material undergoes melting and solidification, and liquid, solid, and a mixture of liquid and solid (or mushy state) coexist and interact with each other during the process. In order to accurately account for the stress development during phase changes, we derived a unified momentum equation from the momentum equations of incompressible fluids and elastoplastic solids. In this approach, the whole fluid-structure system is treated as a single continuum, and the interaction between fluid and solid phases across the mushy zone is naturally taken into account in a monolithic way. For thermal analysis, an enthalpy-based method was employed. As a numerical example, a two-dimensional laser heating problem was considered, where a carbon steel sheet was heated by a Gaussian laser beam. Momentum and energy equations were discretized on a uniform Cartesian grid in a finite volume framework, and temperature-dependent material properties were used. The austenite-martensite phase transformation of carbon steel was also considered. In this study, the effects of solid strains, fluid flow, mushy zone size, and laser heating time on residual stress formation were investigated.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Global Dynamic Modeling of Space-Geodetic Data

NASA Technical Reports Server (NTRS)

Bird, Peter

1995-01-01

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

A Robust Solver for Incompressible Flow on Cartesian Grids with Colocated Variables

DTIC Science & Technology

2005-07-13

three-dimensional calculations for a channel micromixer including a herringbone-patterned surface geometry. 13 Figure 2 shows the flowfield in a two...1973) 38-69. [121 C.R. Kaplan, D.R. Mott, E.S. Oran, Towards the Design of Efficient Micromixers , AIAA paper 2004-0931, 42nd AIAA Aerospace Sciences...Meeting and Exhibit, Reno, Nevada, 2004. [13] C.R. Kaplan, D.R. Mott, E.S. Oran, J. Liu. "Towards the Design of Efficient Micromixers ," in preparation

Large deformation frictional contact analysis with immersed boundary method

NASA Astrophysics Data System (ADS)

Navarro-Jiménez, José Manuel; Tur, Manuel; Albelda, José; Ródenas, Juan José

2018-01-01

This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.

Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow

NASA Astrophysics Data System (ADS)

Henshaw, William D.; Schwendeman, Donald W.

2006-08-01

We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows that demonstrate the use and accuracy of the numerical approach.

SU-F-J-158: Respiratory Motion Resolved, Self-Gated 4D-MRI Using Rotating Cartesian K-Space Sampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, F; Zhou, Z; Yang, Y

Purpose: Dynamic MRI has been used to quantify respiratory motion of abdominal organs in radiation treatment planning. Many existing 4D-MRI methods based on 2D acquisitions suffer from limited slice resolution and additional stitching artifacts when evaluated in 3D{sup 1}. To address these issues, we developed a 4D-MRI (3D dynamic) technique with true 3D k-space encoding and respiratory motion self-gating. Methods: The 3D k-space was acquired using a Rotating Cartesian K-space (ROCK) pattern, where the Cartesian grid was reordered in a quasi-spiral fashion with each spiral arm rotated using golden angle{sup 2}. Each quasi-spiral arm started with the k-space center-line, whichmore » were used as self-gating{sup 3} signal for respiratory motion estimation. The acquired k-space data was then binned into 8 respiratory phases and the golden angle ensures a near-uniform k-space sampling in each phase. Finally, dynamic 3D images were reconstructed using the ESPIRiT technique{sup 4}. 4D-MRI was performed on 6 healthy volunteers, using the following parameters (bSSFP, Fat-Sat, TE/TR=2ms/4ms, matrix size=500×350×120, resolution=1×1×1.2mm, TA=5min, 8 respiratory phases). Supplemental 2D real-time images were acquired in 9 different planes. Dynamic locations of the diaphragm dome and left kidney were measured from both 4D and 2D images. The same protocol was also performed on a MRI-compatible motion phantom where the motion was programmed with different amplitude (10–30mm) and frequency (3–10/min). Results: High resolution 4D-MRI were obtained successfully in 5 minutes. Quantitative motion measurements from 4D-MRI agree with the ones from 2D CINE (<5% error). The 4D images are free of the stitching artifacts and their near-isotropic resolution facilitates 3D visualization and segmentation of abdominal organs such as the liver, kidney and pancreas. Conclusion: Our preliminary studies demonstrated a novel ROCK 4D-MRI technique with true 3D k-space encoding and respiratory motion self-gating. The technique leads to high-resolution and artifacts-free 4D images for improved abdominal organ motion studies. K.S acknowledges funding support from NIH R01CA188300.« less

Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates.

PubMed

Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

2017-09-01

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.

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.

Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

NASA Technical Reports Server (NTRS)

Yang, Jiann-Cherng; Soni, B. K.

1992-01-01

An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.

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 an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems.

PubMed

Liu, Ping; Li, Guodong; Liu, Xinggao; Xiao, Long; Wang, Yalin; Yang, Chunhua; Gui, Weihua

2018-02-01

High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost; meanwhile, the control quality is efficiently improved. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

DOE PAGES

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

2018-06-07

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

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.

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

Dynamic MRI of Grid-Tagged Hyperpolarized Helium-3 for the Assessment of Lung Motion During Breathing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai Jing; Sheng Ke; Benedict, Stanley H.

2009-09-01

Purpose: To develop a dynamic magnetic resonance imaging (MRI) tagging technique using hyperpolarized helium-3 (HP He-3) to track lung motion. Methods and Materials: An accelerated non-Cartesian k-space trajectory was used to gain acquisition speed, at the cost of introducing image artifacts, providing a viable strategy for obtaining whole-lung coverage with adequate temporal resolution. Multiple-slice two-dimensional dynamic images of the lung were obtained in three healthy subjects after inhaling He-3 gas polarized to 35%-40%. Displacement, strain, and ventilation maps were computed from the observed motion of the grid peaks. Results: Both temporal and spatial variations of pulmonary mechanics were observed inmore » normal subjects, including shear motion between different lobes of the same lung. Conclusion: These initial results suggest that dynamic imaging of grid-tagged hyperpolarized magnetization may potentially be a powerful tool for observing and quantifying pulmonary biomechanics on a regional basis and for assessing, validating, and improving lung deformable image registration algorithms.« less

Clinical characterization of 2D pressure field in human left ventricles

NASA Astrophysics Data System (ADS)

Borja, Maria; Rossini, Lorenzo; Martinez-Legazpi, Pablo; Benito, Yolanda; Alhama, Marta; Yotti, Raquel; Perez Del Villar, Candelas; Gonzalez-Mansilla, Ana; Barrio, Alicia; Fernandez-Aviles, Francisco; Bermejo, Javier; Khan, Andrew; Del Alamo, Juan Carlos

2014-11-01

The evaluation of left ventricle (LV) function in the clinical setting remains a challenge. Pressure gradient is a reliable and reproducible indicator of the LV function. We obtain 2D relative pressure field in the LV using in-vivo measurements obtained by processing Doppler-echocardiography images of healthy and dilated hearts. Exploiting mass conservation, we solve the Poisson pressure equation (PPE) dropping the time derivatives and viscous terms. The flow acceleration appears only in the boundary conditions, making our method weakly sensible to the time resolution of in-vivo acquisitions. To ensure continuity with respect to the discrete operator and grid used, a potential flow correction is applied beforehand, which gives another Poisson equation. The new incompressible velocity field ensures that the compatibility equation for the PPE is satisfied. Both Poisson equations are efficiently solved on a Cartesian grid using a multi-grid method and immersed boundary for the LV wall. The whole process is computationally inexpensive and could play a diagnostic role in the clinical assessment of LV function.

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.

Linearity-Preserving Limiters on Irregular Grids

NASA Technical Reports Server (NTRS)

Berger, Marsha; Aftosmis, Michael; Murman, Scott

2004-01-01

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. We note that on non-uniform grids the scalar formulation in standard use today sacrifices k-exactness, even for linear solutions, impacting both accuracy and convergence. We rewrite some well-known limiters in a n way to highlight their underlying symmetry, and use this to examine both traditional and novel limiter formulations. A consistent method of handling stretched meshes is developed, as is a new directional formulation in multiple dimensions for irregular grids. Results are presented demonstrating improved accuracy and convergence using a combination of model problems and complex three-dimensional examples.

User Manual for the PROTEUS Mesh Tools

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Micheal A.; Shemon, Emily R

2016-09-19

PROTEUS is built around a finite element representation of the geometry for visualization. In addition, the PROTEUS-SN solver was built to solve the even-parity transport equation on a finite element mesh provided as input. Similarly, PROTEUS-MOC and PROTEUS-NEMO were built to apply the method of characteristics on unstructured finite element meshes. Given the complexity of real world problems, experience has shown that using commercial mesh generator to create rather simple input geometries is overly complex and slow. As a consequence, significant effort has been put into place to create multiple codes that help assist in the mesh generation and manipulation.more » There are three input means to create a mesh in PROTEUS: UFMESH, GRID, and NEMESH. At present, the UFMESH is a simple way to generate two-dimensional Cartesian and hexagonal fuel assembly geometries. The UFmesh input allows for simple assembly mesh generation while the GRID input allows the generation of Cartesian, hexagonal, and regular triangular structured grid geometry options. The NEMESH is a way for the user to create their own mesh or convert another mesh file format into a PROTEUS input format. Given that one has an input mesh format acceptable for PROTEUS, we have constructed several tools which allow further mesh and geometry construction (i.e. mesh extrusion and merging). This report describes the various mesh tools that are provided with the PROTEUS code giving both descriptions of the input and output. In many cases the examples are provided with a regression test of the mesh tools. The most important mesh tools for any user to consider using are the MT_MeshToMesh.x and the MT_RadialLattice.x codes. The former allows the conversion between most mesh types handled by PROTEUS while the second allows the merging of multiple (assembly) meshes into a radial structured grid. Note that the mesh generation process is recursive in nature and that each input specific for a given mesh tool (such as .axial or .merge) can be used as “mesh” input for any of the mesh tools discussed in this manual.« less

Parallel grid library for rapid and flexible simulation development

NASA Astrophysics Data System (ADS)

Honkonen, I.; von Alfthan, S.; Sandroos, A.; Janhunen, P.; Palmroth, M.

2013-04-01

We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as cell data. The amount of data in grid cells can vary both in space and time allowing dccrg to be used in very different types of simulations, for example in fluid and particle codes. Dccrg transfers the data between neighboring cells on different processes transparently and asynchronously allowing one to overlap computation and communication. This enables excellent scalability at least up to 32 k cores in magnetohydrodynamic tests depending on the problem and hardware. In the version of dccrg presented here part of the mesh metadata is replicated between MPI processes reducing the scalability of adaptive mesh refinement (AMR) to between 200 and 600 processes. Dccrg is free software that anyone can use, study and modify and is available at https://gitorious.org/dccrg. Users are also kindly requested to cite this work when publishing results obtained with dccrg. Catalogue identifier: AEOM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License version 3 No. of lines in distributed program, including test data, etc.: 54975 No. of bytes in distributed program, including test data, etc.: 974015 Distribution format: tar.gz Programming language: C++. Computer: PC, cluster, supercomputer. Operating system: POSIX. The code has been parallelized using MPI and tested with 1-32768 processes RAM: 10 MB-10 GB per process Classification: 4.12, 4.14, 6.5, 19.3, 19.10, 20. External routines: MPI-2 [1], boost [2], Zoltan [3], sfc++ [4] Nature of problem: Grid library supporting arbitrary data in grid cells, parallel adaptive mesh refinement, transparent remote neighbor data updates and load balancing. Solution method: The simulation grid is represented by an adjacency list (graph) with vertices stored into a hash table and edges into contiguous arrays. Message Passing Interface standard is used for parallelization. Cell data is given as a template parameter when instantiating the grid. Restrictions: Logically cartesian grid. Running time: Running time depends on the hardware, problem and the solution method. Small problems can be solved in under a minute and very large problems can take weeks. The examples and tests provided with the package take less than about one minute using default options. In the version of dccrg presented here the speed of adaptive mesh refinement is at most of the order of 106 total created cells per second. http://www.mpi-forum.org/. http://www.boost.org/. K. Devine, E. Boman, R. Heaphy, B. Hendrickson, C. Vaughan, Zoltan data management services for parallel dynamic applications, Comput. Sci. Eng. 4 (2002) 90-97. http://dx.doi.org/10.1109/5992.988653. https://gitorious.org/sfc++.

Constrained CVT meshes and a comparison of triangular mesh generators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Hoa; Burkardt, John; Gunzburger, Max

2009-01-01

Mesh generation in regions in Euclidean space is a central task in computational science, and especially for commonly used numerical methods for the solution of partial differential equations, e.g., finite element and finite volume methods. We focus on the uniform Delaunay triangulation of planar regions and, in particular, on how one selects the positions of the vertices of the triangulation. We discuss a recently developed method, based on the centroidal Voronoi tessellation (CVT) concept, for effecting such triangulations and present two algorithms, including one new one, for CVT-based grid generation. We also compare several methods, including CVT-based methods, for triangulatingmore » planar domains. To this end, we define several quantitative measures of the quality of uniform grids. We then generate triangulations of several planar regions, including some having complexities that are representative of what one may encounter in practice. We subject the resulting grids to visual and quantitative comparisons and conclude that all the methods considered produce high-quality uniform grids and that the CVT-based grids are at least as good as any of the others.« less

Impeller tandem blade study with grid embedding for local grid refinement

NASA Technical Reports Server (NTRS)

Bache, George

1992-01-01

Flow non-uniformity at the discharge of high power density impellers can result in significant unsteady interactions between impeller blades and downstream diffuser vanes. These interactions result in degradation of both performance and pump reliability. The MSFC Pump Technology Team has recognized the importance of resolving this problem and has thus initiated the development and testing of a high head coefficient impeller. One of the primary goals of this program is to improve impeller performance and discharge flow uniformity. The objective of the present work is complimentary. Flow uniformity and performance gains were sought through the application of a tandem blade arrangement. The approach adopted was to numerically establish flow characteristics at the impeller discharge for the baseline MSFC impeller and then parametrically evaluate tandem blade configurations. A tandem design was sought that improves both impeller performance and discharge uniformity. The Navier-Stokes solver AEROVISC was used to conduct the study. Grid embedding is used to resolve local gradients while attempting to minimize model size. Initial results indicate that significant gains in flow uniformity can be achieved through the tandem blade concept and that blade clocking rather than slot location is the primary driver for flow uniformity.

Fast and accurate 3D tensor calculation of the Fock operator in a general basis

NASA Astrophysics Data System (ADS)

Khoromskaia, V.; Andrae, D.; Khoromskij, B. N.

2012-11-01

The present paper contributes to the construction of a “black-box” 3D solver for the Hartree-Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank, discretized on a fine N×N×N Cartesian grid. We prove the Ch2 error estimate in terms of mesh parameter, h=O(1/N), that allows to gain a guaranteed accuracy of the core Hamiltonian part in the Fock operator as h→0. However, the commonly used problem adapted basis functions have low regularity yielding a considerable increase of the constant C, hence, demanding a rather large grid-size N of about several tens of thousands to ensure the high resolution. Modern tensor-formatted arithmetics of complexity O(N), or even O(logN), practically relaxes the limitations on the grid-size. Our tensor-based approach allows to improve significantly the standard basis sets in quantum chemistry by including simple combinations of Slater-type, local finite element and other basis functions. Numerical experiments for moderate size organic molecules show efficiency and accuracy of grid-based calculations to the core Hamiltonian in the range of grid parameter N3˜1015.

Finite-volume scheme for anisotropic diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

B-spline Method in Fluid Dynamics

NASA Technical Reports Server (NTRS)

Botella, Olivier; Shariff, Karim; Mansour, Nagi N. (Technical Monitor)

2001-01-01

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

CFD Approaches for Simulation of Wing-Body Stage Separation

NASA Technical Reports Server (NTRS)

Buning, Pieter G.; Gomez, Reynaldo J.; Scallion, William I.

2004-01-01

A collection of computational fluid dynamics tools and techniques are being developed and tested for application to stage separation and abort simulation for next-generation launch vehicles. In this work, an overset grid Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of a belly-to-belly wing-body configuration. Steady cases show excellent agreement between Navier-Stokes results, Cartesian grid Euler solutions, and wind tunnel data at Mach 3. Good agreement has been obtained between Navier-Stokes, Euler, and wind tunnel results at Mach 6. An analysis of a dynamic separation at Mach 3 demonstrates that unsteady aerodynamic effects are not important for this scenario. Results provide an illustration of the relative applicability of Euler and Navier-Stokes methods to these types of problems.

Tempest - Efficient Computation of Atmospheric Flows Using High-Order Local Discretization Methods

NASA Astrophysics Data System (ADS)

Ullrich, P. A.; Guerra, J. E.

2014-12-01

The Tempest Framework composes several compact numerical methods to easily facilitate intercomparison of atmospheric flow calculations on the sphere and in rectangular domains. This framework includes the implementations of Spectral Elements, Discontinuous Galerkin, Flux Reconstruction, and Hybrid Finite Element methods with the goal of achieving optimal accuracy in the solution of atmospheric problems. Several advantages of this approach are discussed such as: improved pressure gradient calculation, numerical stability by vertical/horizontal splitting, arbitrary order of accuracy, etc. The local numerical discretization allows for high performance parallel computation and efficient inclusion of parameterizations. These techniques are used in conjunction with a non-conformal, locally refined, cubed-sphere grid for global simulations and standard Cartesian grids for simulations at the mesoscale. A complete implementation of the methods described is demonstrated in a non-hydrostatic setting.

A multi-resolution approach to electromagnetic modelling

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Egbert, G. D.; Smirnov, M. Yu

2018-07-01

We present a multi-resolution approach for 3-D magnetotelluric forward modelling. Our approach is motivated by the fact that fine-grid resolution is typically required at shallow levels to adequately represent near surface inhomogeneities, topography and bathymetry, while a much coarser grid may be adequate at depth where the diffusively propagating electromagnetic fields are much smoother. With a conventional structured finite difference grid, the fine discretization required to adequately represent rapid variations near the surface is continued to all depths, resulting in higher computational costs. Increasing the computational efficiency of the forward modelling is especially important for solving regularized inversion problems. We implement a multi-resolution finite difference scheme that allows us to decrease the horizontal grid resolution with depth, as is done with vertical discretization. In our implementation, the multi-resolution grid is represented as a vertical stack of subgrids, with each subgrid being a standard Cartesian tensor product staggered grid. Thus, our approach is similar to the octree discretization previously used for electromagnetic modelling, but simpler in that we allow refinement only with depth. The major difficulty arose in deriving the forward modelling operators on interfaces between adjacent subgrids. We considered three ways of handling the interface layers and suggest a preferable one, which results in similar accuracy as the staggered grid solution, while retaining the symmetry of coefficient matrix. A comparison between multi-resolution and staggered solvers for various models shows that multi-resolution approach improves on computational efficiency without compromising the accuracy of the solution.

Recent Progress on the Parallel Implementation of Moving-Body Overset Grid Schemes

NASA Technical Reports Server (NTRS)

Wissink, Andrew; Allen, Edwin (Technical Monitor)

1998-01-01

Viscous calculations about geometrically complex bodies in which there is relative motion between component parts is one of the most computationally demanding problems facing CFD researchers today. This presentation documents results from the first two years of a CHSSI-funded effort within the U.S. Army AFDD to develop scalable dynamic overset grid methods for unsteady viscous calculations with moving-body problems. The first pan of the presentation will focus on results from OVERFLOW-D1, a parallelized moving-body overset grid scheme that employs traditional Chimera methodology. The two processes that dominate the cost of such problems are the flow solution on each component and the intergrid connectivity solution. Parallel implementations of the OVERFLOW flow solver and DCF3D connectivity software are coupled with a proposed two-part static-dynamic load balancing scheme and tested on the IBM SP and Cray T3E multi-processors. The second part of the presentation will cover some recent results from OVERFLOW-D2, a new flow solver that employs Cartesian grids with various levels of refinement, facilitating solution adaption. A study of the parallel performance of the scheme on large distributed- memory multiprocessor computer architectures will be reported.

An efficient basis set representation for calculating electrons in molecules

DOE PAGES

Jones, Jeremiah R.; Rouet, Francois -Henry; Lawler, Keith V.; ...

2016-04-27

The method of McCurdy, Baertschy, and Rescigno, is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. Themore » calculation of contracted two-electron matrix elements among orbitals requires only O( Nlog (N)) multiplication operations, not O( N 4), where N is the number of basis functions; N = n 3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionisation potentials are reported for 1- (He +, H + 2), 2- (H 2, He), 10- (CH 4), and 56-electron (C 8H 8) systems.« less

The island dynamics model on parallel quadtree grids

NASA Astrophysics Data System (ADS)

Mistani, Pouria; Guittet, Arthur; Bochkov, Daniil; Schneider, Joshua; Margetis, Dionisios; Ratsch, Christian; Gibou, Frederic

2018-05-01

We introduce an approach for simulating epitaxial growth by use of an island dynamics model on a forest of quadtree grids, and in a parallel environment. To this end, we use a parallel framework introduced in the context of the level-set method. This framework utilizes: discretizations that achieve a second-order accurate level-set method on non-graded adaptive Cartesian grids for solving the associated free boundary value problem for surface diffusion; and an established library for the partitioning of the grid. We consider the cases with: irreversible aggregation, which amounts to applying Dirichlet boundary conditions at the island boundary; and an asymmetric (Ehrlich-Schwoebel) energy barrier for attachment/detachment of atoms at the island boundary, which entails the use of a Robin boundary condition. We provide the scaling analyses performed on the Stampede supercomputer and numerical examples that illustrate the capability of our methodology to efficiently simulate different aspects of epitaxial growth. The combination of adaptivity and parallelism in our approach enables simulations that are several orders of magnitude faster than those reported in the recent literature and, thus, provides a viable framework for the systematic study of mound formation on crystal surfaces.

Analysis of Slope Limiters on Irregular Grids

NASA Technical Reports Server (NTRS)

Berger, Marsha; Aftosmis, Michael J.

2005-01-01

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

A multi-resolution approach to electromagnetic modeling.

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Egbert, G. D.; Smirnov, M. Yu

2018-04-01

We present a multi-resolution approach for three-dimensional magnetotelluric forward modeling. Our approach is motivated by the fact that fine grid resolution is typically required at shallow levels to adequately represent near surface inhomogeneities, topography, and bathymetry, while a much coarser grid may be adequate at depth where the diffusively propagating electromagnetic fields are much smoother. This is especially true for forward modeling required in regularized inversion, where conductivity variations at depth are generally very smooth. With a conventional structured finite-difference grid the fine discretization required to adequately represent rapid variations near the surface are continued to all depths, resulting in higher computational costs. Increasing the computational efficiency of the forward modeling is especially important for solving regularized inversion problems. We implement a multi-resolution finite-difference scheme that allows us to decrease the horizontal grid resolution with depth, as is done with vertical discretization. In our implementation, the multi-resolution grid is represented as a vertical stack of sub-grids, with each sub-grid being a standard Cartesian tensor product staggered grid. Thus, our approach is similar to the octree discretization previously used for electromagnetic modeling, but simpler in that we allow refinement only with depth. The major difficulty arose in deriving the forward modeling operators on interfaces between adjacent sub-grids. We considered three ways of handling the interface layers and suggest a preferable one, which results in similar accuracy as the staggered grid solution, while retaining the symmetry of coefficient matrix. A comparison between multi-resolution and staggered solvers for various models show that multi-resolution approach improves on computational efficiency without compromising the accuracy of the solution.

Random noise attenuation of non-uniformly sampled 3D seismic data along two spatial coordinates using non-equispaced curvelet transform

NASA Astrophysics Data System (ADS)

Zhang, Hua; Yang, Hui; Li, Hongxing; Huang, Guangnan; Ding, Zheyi

2018-04-01

The attenuation of random noise is important for improving the signal to noise ratio (SNR). However, the precondition for most conventional denoising methods is that the noisy data must be sampled on a uniform grid, making the conventional methods unsuitable for non-uniformly sampled data. In this paper, a denoising method capable of regularizing the noisy data from a non-uniform grid to a specified uniform grid is proposed. Firstly, the denoising method is performed for every time slice extracted from the 3D noisy data along the source and receiver directions, then the 2D non-equispaced fast Fourier transform (NFFT) is introduced in the conventional fast discrete curvelet transform (FDCT). The non-equispaced fast discrete curvelet transform (NFDCT) can be achieved based on the regularized inversion of an operator that links the uniformly sampled curvelet coefficients to the non-uniformly sampled noisy data. The uniform curvelet coefficients can be calculated by using the inversion algorithm of the spectral projected-gradient for ℓ1-norm problems. Then local threshold factors are chosen for the uniform curvelet coefficients for each decomposition scale, and effective curvelet coefficients are obtained respectively for each scale. Finally, the conventional inverse FDCT is applied to the effective curvelet coefficients. This completes the proposed 3D denoising method using the non-equispaced curvelet transform in the source-receiver domain. The examples for synthetic data and real data reveal the effectiveness of the proposed approach in applications to noise attenuation for non-uniformly sampled data compared with the conventional FDCT method and wavelet transformation.

A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

NASA Astrophysics Data System (ADS)

Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John

2016-07-01

In this paper, we present a method for performing uniformly high-order direct numerical simulations of high-speed flows over arbitrary geometries. The method was developed with the goal of simulating and studying the effects of complex isolated roughness elements on the stability of hypersonic boundary layers. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-stencil method. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries and a third-order Runge-Kutta method is used for time advancement. A multi-zone refinement method was also utilized to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme in space and third order in time. Results confirming the method's high order of convergence are shown. Two-dimensional and three-dimensional test cases are presented and show good agreement with previous results. A simulation of Mach 3 flow over the logo of the Ubuntu Linux distribution is shown to demonstrate the method's capabilities for handling complex geometries. Results for Mach 6 wall-bounded flow over a three-dimensional cylindrical roughness element are also presented. The results demonstrate that the method is a promising tool for the study of hypersonic roughness-induced transition.

Uniformity on the grid via a configuration framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Igor V Terekhov et al.

2003-03-11

As Grid permeates modern computing, Grid solutions continue to emerge and take shape. The actual Grid development projects continue to provide higher-level services that evolve in functionality and operate with application-level concepts which are often specific to the virtual organizations that use them. Physically, however, grids are comprised of sites whose resources are diverse and seldom project readily onto a grid's set of concepts. In practice, this also creates problems for site administrators who actually instantiate grid services. In this paper, we present a flexible, uniform framework to configure a grid site and its facilities, and otherwise describe the resourcesmore » and services it offers. We start from a site configuration and instantiate services for resource advertisement, monitoring and data handling; we also apply our framework to hosting environment creation. We use our ideas in the Information Management part of the SAM-Grid project, a grid system which will deliver petabyte-scale data to the hundreds of users. Our users are High Energy Physics experimenters who are scattered worldwide across dozens of institutions and always use facilities that are shared with other experiments as well as other grids. Our implementation represents information in the XML format and includes tools written in XQuery and XSLT.« less

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

Turbofan forced mixer lobe flow modeling. 2: Three-dimensional inviscid mixer analysis (FLOMIX)

NASA Technical Reports Server (NTRS)

Barber, T.

1988-01-01

A three-dimensional potential analysis (FLOMIX) was formulated and applied to the inviscid flow over a turbofan foced mixer. The method uses a small disturbance formulation to analytically uncouple the circumferential flow from the radial and axial flow problem, thereby reducing the analysis to the solution of a series of axisymmetric problems. These equations are discretized using a flux volume formulation along a Cartesian grid. The method extends earlier applications of the Cartesian method to complex cambered geometries. The effects of power addition are also included within the potential formulation. Good agreement is obtained with an alternate small disturbance analysis for a high penetration symmetric mixer in a planar duct. In addition, calculations showing pressure distributions and induced secondary vorticity fields are presented for practical trubofan mixer configurations, and where possible, comparison was made with available experimental data. A detailed description of the required data input and coordinate definition is presented along with a sample data set for a practical forced mixer configuration. A brief description of the program structure and subroutines is also provided.

Grid refinement in Cartesian coordinates for groundwater flow models using the divergence theorem and Taylor's series.

PubMed

Mansour, M M; Spink, A E F

2013-01-01

Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non-reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes. © 2012, British Geological Survey © NERC 2012. Ground Water © 2012, National GroundWater Association.

An immersed-boundary method for flow–structure interaction in biological systems with application to phonation

PubMed Central

Luo, Haoxiang; Mittal, Rajat; Zheng, Xudong; Bielamowicz, Steven A.; Walsh, Raymond J.; Hahn, James K.

2008-01-01

A new numerical approach for modeling a class of flow–structure interaction problems typically encountered in biological systems is presented. In this approach, a previously developed, sharp-interface, immersed-boundary method for incompressible flows is used to model the fluid flow and a new, sharp-interface Cartesian grid, immersed boundary method is devised to solve the equations of linear viscoelasticity that governs the solid. The two solvers are coupled to model flow–structure interaction. This coupled solver has the advantage of simple grid generation and efficient computation on simple, single-block structured grids. The accuracy of the solid-mechanics solver is examined by applying it to a canonical problem. The solution methodology is then applied to the problem of laryngeal aerodynamics and vocal fold vibration during human phonation. This includes a three-dimensional eigen analysis for a multi-layered vocal fold prototype as well as two-dimensional, flow-induced vocal fold vibration in a modeled larynx. Several salient features of the aerodynamics as well as vocal-fold dynamics are presented. PMID:19936017

Numerical Simulation of Bow Waves and Transom-Stern Flows

NASA Astrophysics Data System (ADS)

Dommermuth, Douglas G.; Schlageter, Eric A.; Talcott, John C.; Wyatt, Donald C.; Novikov, Evgeny A.

1997-11-01

A stratified-flow formulation is used to model the breaking bow wave and the separated transom-stern flow that are generated by a ship moving with forward speed. The interface of the air with the water is identified as the zero level-set of a three-dimensional function. The ship is modeled using a body-force technique on a cartesian grid. The three-dimensional body-force is generated using a surface panelization of the entire ship, including the above-water geometry up to and including the deck. The effects of surface tension are modeled as a source term that is concentrated at the air-water interface. The effects of gravity are modeled as a volumetric force. The three-dimensional, unsteady, Navier-Stokes equations are expressed in primitive-variable form. A LES formulation with a Smagorinsky sub-grid-scale model is used to model turbulence. Numerical convergence is demonstrated using 128x64x65, 256x128x129, and 512x256x257 grid points. The numerical results compare well to whisker-probe measurements of the free-surface elevation generated by a naval combatant.

A Very Fast and Angular Momentum Conserving Tree Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marcello, Dominic C., E-mail: dmarce504@gmail.com

There are many methods used to compute the classical gravitational field in astrophysical simulation codes. With the exception of the typically impractical method of direct computation, none ensure conservation of angular momentum to machine precision. Under uniform time-stepping, the Cartesian fast multipole method of Dehnen (also known as the very fast tree code) conserves linear momentum to machine precision. We show that it is possible to modify this method in a way that conserves both angular and linear momenta.

Coherent states on horospheric three-dimensional Lobachevsky space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by; Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by; Rybak, I., E-mail: Ivan.Rybak@astro.up.pt

2016-08-15

In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules.

PubMed

Mosheiff, Noga; Agmon, Haggai; Moriel, Avraham; Burak, Yoram

2017-06-01

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

PubMed Central

Mosheiff, Noga; Agmon, Haggai; Moriel, Avraham

2017-01-01

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal’s motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing. PMID:28628647

Seismic Waves, 4th order accurate

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-08-16

SW4 is a program for simulating seismic wave propagation on parallel computers. SW4 colves the seismic wave equations in Cartesian corrdinates. It is therefore appropriate for regional simulations, where the curvature of the earth can be neglected. SW4 implements a free surface boundary condition on a realistic topography, absorbing super-grid conditions on the far-field boundaries, and a kinematic source model consisting of point force and/or point moment tensor source terms. SW4 supports a fully 3-D heterogeneous material model that can be specified in several formats. SW4 can output synthetic seismograms in an ASCII test format, or in the SAC finarymore » format. It can also present simulation information as GMT scripts, whixh can be used to create annotated maps. Furthermore, SW4 can output the solution as well as the material model along 2-D grid planes.« less

Development of a Hybrid RANS/LES Method for Compressible Mixing Layer Simulations

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Alexander, J. Iwan D.; Reshotko, Eli

2001-01-01

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modem day aircraft and also those of hypersonic vehicles currently under development. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS/LES method on stretched, non-Cartesian grids. The hybrid RANS/LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two-dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Actual LES calculations, performed in three spatial directions, indicated an initial vortex shedding followed by rapid transition to turbulence, which is in agreement with experimental observations.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

Correlation of ion and beam current densities in Kaufman thrusters.

NASA Technical Reports Server (NTRS)

Wilbur, P. J.

1973-01-01

In the absence of direct impingement erosion, electrostatic thruster accelerator grid lifetime is defined by the charge exchange erosion that occurs at peak values of the ion beam current density. In order to maximize the thrust from an engine with a specified grid lifetime, the ion beam current density profile should therefore be as flat as possible. Knauer (1970) has suggested this can be achieved by establishing a radial plasma uniformity within the thruster discharge chamber; his tests with the radial field thruster provide an example of uniform plasma properties within the chamber and a flat ion beam profile occurring together. It is shown that, in particular, the ion density profile within the chamber determines the beam current density profile, and that a uniform ion density profile at the screen grid end of the discharge chamber should lead to a flat beam current density profile.

Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air

NASA Technical Reports Server (NTRS)

Rupesh, K-A. B.; Ravi, B. R.; Mittal, R.; Raju, R.; Gallas, Q.; Cattafesta, L.

2007-01-01

The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 8: Cooling Flow/heat Transfer Analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Topp, David A.; Heidegger, Nathan J.; Delaney, Robert A.

1994-01-01

The focus of this task was to validate the ADPAC code for heat transfer calculations. To accomplish this goal, the ADPAC code was modified to allow for a Cartesian coordinate system capability and to add boundary conditions to handle spanwise periodicity and transpiration boundaries. The primary validation case was the film cooled C3X vane. The cooling hole modeling included both a porous region and grid in each discrete hold. Predictions for these models as well as smooth wall compared well with the experimental data.

Numerical computation of diffusion on a surface.

PubMed

Schwartz, Peter; Adalsteinsson, David; Colella, Phillip; Arkin, Adam Paul; Onsum, Matthew

2005-08-09

We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based on level set methods for solving the Hamilton-Jacobi and eikonal equations. We demonstrate that the method is second-order accurate in space and time and is capable of computing solutions on complex surface geometries obtained from image data of cells.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

A combined direct/inverse three-dimensional transonic wing design method for vector computers

NASA Technical Reports Server (NTRS)

Weed, R. A.; Carlson, L. A.; Anderson, W. K.

1984-01-01

A three-dimensional transonic-wing design algorithm for vector computers is developed, and the results of sample computations are presented graphically. The method incorporates the direct/inverse scheme of Carlson (1975), a Cartesian grid system with boundary conditions applied at a mean plane, and a potential-flow solver based on the conservative form of the full potential equation and using the ZEBRA II vectorizable solution algorithm of South et al. (1980). The accuracy and consistency of the method with regard to direct and inverse analysis and trailing-edge closure are verified in the test computations.

Numerical Simulation of Floating Bodies in Extreme Free Surface Waves

NASA Astrophysics Data System (ADS)

Hu, Zheng Zheng; Causon, Derek; Mingham, Clive; Qiang, Ling

2010-05-01

A task of the EPSRC funded research project 'Extreme Wave loading on Offshore Wave Energy Devices: a Hierarchical Team Approach' is to investigate the survivability of two wave energy converter (WEC) devices Pelamis and the Manchester Bobber using different CFD approaches. Both devices float on the water surface, generating the electricity from the motion of the waves. In this paper, we describe developments of the AMAZON-SC 3D numerical wave tank (NWT) to study extreme wave loading of a fixed or floating (in Heave motion) structure. The extreme wave formulation as an inlet condition is due to Dalzell (1999) and Ning et. al. (2009) in which a first or second-order Stokes focused wave can be prescribed. The AMAZON-SC 3D code (see e.g. Hu et al. (2009)) uses a cell centred finite volume method of the Godunov-type for the space discretization of the Euler and Navier Stokes equations. The computational domain includes both air and water regions with the air/water boundary captured as a discontinuity in the density field thereby admitting the break up and recombination of the free surface. Temporal discretisation uses the artificial compressibility method and a dual time stepping strategy to maintain a divergence free velocity field. Cartesian cut cells are used to provide a fully boundary-fitted gridding capability on an regular background Cartesian grid. Solid objects are cut out of the background mesh leaving a set of irregularly shaped cells fitted to the boundary. The advantages of the cut cell approach have been outlined previously by Causon et al. (2000, 2001) including its flexibility for dealing with complex geometries whether stationary or in relative motion. The field grid does not need to be recomputed globally or even locally for moving body cases; all that is necessary is to update the local cut cell data at the body contour for as long as the motion continues. The handing of numerical wave paddles and device motion in a NWT is therefore straightforward and efficient. Firstly, extreme design wave conditions are generated in an empty NWT and compared with physical experiments as a precursor to calculations to investigate the survivability of the Bobber device operating in a challenging wave climate. Secondly, we consider a bench-mark test case involving in a first order regular wave maker acting on a fixed cylinder and Pelamis. Finally, a floating Bobber has been simulated under extreme wave conditions. These results will be reported at the meeting. Causon D.M., Ingram D.M., Mingham C.G., Yang G. Pearson R.V. (2000). Calculation of shallow water flows using a Cartesian cut cell approach. Advances in Water resources, 23: 545-562. Causon D.M., Ingram D.M., Mingham C.G. (2000). A Cartesian cut cell method for shallow water flows with moving boundaries. Advances in Water resources, 24: 899-911. Dalzell J.F. 1999 A note on finite depth second-order wave-wave interactions. Appl. Ocean Res. 21, 105-111. Ning D.Z., Zang J., Liu S.X. Eatock Taylor R. Teng B. & Taylor P.H. 2009 Free surface and wave kinematics for nonlinear focused wave groups. J. Ocean Engineering. Accepted. Hu Z.Z., Causon D.M., Mingham C.M. and Qian L.(2009). Numerical wave tank study of a wave energy converter in heave. Proceedlings 19th ISOPE conference, Osaka, Japan Qian L., Causon D.M. & Mingham C.G., Ingram D.M. 2006 A free-surface capturing method for two fluid flows with moving bodies. Proc. Roy. Soc. London, Vol. A 462 21-42.

Grid generation on trimmed Bezier and NURBS quilted surfaces

NASA Technical Reports Server (NTRS)

Woan, Chung-Jin; Clever, Willard C.; Tam, Clement K.

1995-01-01

This paper presents some recently added capabilities to RAGGS, Rockwell Automated Grid Generation System. Included are the trimmed surface handling and display capability and structures and unstructured grid generation on trimmed Bezier and NURBS (non-uniform rational B-spline surfaces) quilted surfaces. Samples are given to demonstrate the new capabilities.

Orientation domains: A mobile grid clustering algorithm with spherical corrections

NASA Astrophysics Data System (ADS)

Mencos, Joana; Gratacós, Oscar; Farré, Mercè; Escalante, Joan; Arbués, Pau; Muñoz, Josep Anton

2012-12-01

An algorithm has been designed and tested which was devised as a tool assisting the analysis of geological structures solely from orientation data. More specifically, the algorithm was intended for the analysis of geological structures that can be approached as planar and piecewise features, like many folded strata. Input orientation data is expressed as pairs of angles (azimuth and dip). The algorithm starts by considering the data in Cartesian coordinates. This is followed by a search for an initial clustering solution, which is achieved by comparing the results output from the systematic shift of a regular rigid grid over the data. This initial solution is optimal (achieves minimum square error) once the grid size and the shift increment are fixed. Finally, the algorithm corrects for the variable spread that is generally expected from the data type using a reshaped non-rigid grid. The algorithm is size-oriented, which implies the application of conditions over cluster size through all the process in contrast to density-oriented algorithms, also widely used when dealing with spatial data. Results are derived in few seconds and, when tested over synthetic examples, they were found to be consistent and reliable. This makes the algorithm a valuable alternative to the time-consuming traditional approaches available to geologists.

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback. Results indicate: (1) The new method exhibits quadratic convergence for homogeneous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. ?? 2002 Elsevier Science Ltd. All rights reserved.

UNFOLD-SENSE: a parallel MRI method with self-calibration and artifact suppression.

PubMed

Madore, Bruno

2004-08-01

This work aims at improving the performance of parallel imaging by using it with our "unaliasing by Fourier-encoding the overlaps in the temporal dimension" (UNFOLD) temporal strategy. A self-calibration method called "self, hybrid referencing with UNFOLD and GRAPPA" (SHRUG) is presented. SHRUG combines the UNFOLD-based sensitivity mapping strategy introduced in the TSENSE method by Kellman et al. (5), with the strategy introduced in the GRAPPA method by Griswold et al. (10). SHRUG merges the two approaches to alleviate their respective limitations, and provides fast self-calibration at any given acceleration factor. UNFOLD-SENSE further includes an UNFOLD artifact suppression scheme to significantly suppress artifacts and amplified noise produced by parallel imaging. This suppression scheme, which was published previously (4), is related to another method that was presented independently as part of TSENSE. While the two are equivalent at accelerations < or = 2.0, the present approach is shown here to be significantly superior at accelerations > 2.0, with up to double the artifact suppression at high accelerations. Furthermore, a slight modification of Cartesian SENSE is introduced, which allows departures from purely Cartesian sampling grids. This technique, termed variable-density SENSE (vdSENSE), allows the variable-density data required by SHRUG to be reconstructed with the simplicity and fast processing of Cartesian SENSE. UNFOLD-SENSE is given by the combination of SHRUG for sensitivity mapping, vdSENSE for reconstruction, and UNFOLD for artifact/amplified noise suppression. The method was implemented, with online reconstruction, on both an SSFP and a myocardium-perfusion sequence. The results from six patients scanned with UNFOLD-SENSE are presented.

Cut-cell method based large-eddy simulation of tip-leakage flow

NASA Astrophysics Data System (ADS)

Pogorelov, Alexej; Meinke, Matthias; Schröder, Wolfgang

2015-07-01

The turbulent low Mach number flow through an axial fan at a Reynolds number of 9.36 × 105 based on the outer casing diameter is investigated by large-eddy simulation. A finite-volume flow solver in an unstructured hierarchical Cartesian setup for the compressible Navier-Stokes equations is used. To account for sharp edges, a fully conservative cut-cell approach is applied. A newly developed rotational periodic boundary condition for Cartesian meshes is introduced such that the simulations are performed just for a 72° segment, i.e., the flow field over one out of five axial blades is resolved. The focus of this numerical analysis is on the development of the vortical flow structures in the tip-gap region. A detailed grid convergence study is performed on four computational grids with 50 × 106, 250 × 106, 1 × 109, and 1.6 × 109 cells. Results of the instantaneous and the mean fan flow field are thoroughly analyzed based on the solution with 1 × 109 cells. High levels of turbulent kinetic energy and pressure fluctuations are generated by a tip-gap vortex upstream of the blade, the separating vortices inside the tip gap, and a counter-rotating vortex on the outer casing wall. An intermittent interaction of the turbulent wake, generated by the tip-gap vortex, with the downstream blade, leads to a cyclic transition with high pressure fluctuations on the suction side of the blade and a decay of the tip-gap vortex. The disturbance of the tip-gap vortex results in an unsteady behavior of the turbulent wake causing the intermittent interaction. For this interaction and the cyclic transition, two dominant frequencies are identified which perfectly match with the characteristic frequencies in the experimental sound power level and therefore explain their physical origin.

Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity

NASA Astrophysics Data System (ADS)

Delfani, M. R.; Latifi Shahandashti, M.

2017-09-01

In this paper, within the complete form of Mindlin's second strain gradient theory, the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non-uniform distribution of eigenfields is determined. These eigenfields, in addition to eigenstrain, comprise eigen double and eigen triple strains. After the derivation of a closed-form expression for Green's function associated with the problem, two different cases of non-uniform distribution of the eigenfields are considered as follows: (i) radial distribution, i.e. the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion, and (ii) polynomial distribution, i.e. the distributions of the eigenfields are polynomial functions in the Cartesian coordinates of points. While the obtained solution for the elastic field of the latter case takes the form of an infinite series, the solution to the former case is represented in a closed form. Moreover, Eshelby's tensors associated with the two mentioned cases are obtained.

New method for solving inductive electric fields in the non-uniformly conducting ionosphere

NASA Astrophysics Data System (ADS)

Vanhamäki, H.; Amm, O.; Viljanen, A.

2006-10-01

We present a new calculation method for solving inductive electric fields in the ionosphere. The time series of the potential part of the ionospheric electric field, together with the Hall and Pedersen conductances serves as the input to this method. The output is the time series of the induced rotational part of the ionospheric electric field. The calculation method works in the time-domain and can be used with non-uniform, time-dependent conductances. In addition, no particular symmetry requirements are imposed on the input potential electric field. The presented method makes use of special non-local vector basis functions called the Cartesian Elementary Current Systems (CECS). This vector basis offers a convenient way of representing curl-free and divergence-free parts of 2-dimensional vector fields and makes it possible to solve the induction problem using simple linear algebra. The new calculation method is validated by comparing it with previously published results for Alfvén wave reflection from a uniformly conducting ionosphere.

Using Computing and Data Grids for Large-Scale Science and Engineering

NASA Technical Reports Server (NTRS)

Johnston, William E.

2001-01-01

We use the term "Grid" to refer to a software system that provides uniform and location independent access to geographically and organizationally dispersed, heterogeneous resources that are persistent and supported. These emerging data and computing Grids promise to provide a highly capable and scalable environment for addressing large-scale science problems. We describe the requirements for science Grids, the resulting services and architecture of NASA's Information Power Grid (IPG) and DOE's Science Grid, and some of the scaling issues that have come up in their implementation.

Orthogonal fast spherical Bessel transform on uniform grid

NASA Astrophysics Data System (ADS)

Serov, Vladislav V.

2017-07-01

We propose an algorithm for the orthogonal fast discrete spherical Bessel transform on a uniform grid. Our approach is based upon the spherical Bessel transform factorization into the two subsequent orthogonal transforms, namely the fast Fourier transform and the orthogonal transform founded on the derivatives of the discrete Legendre orthogonal polynomials. The method utility is illustrated by its implementation for the problem of a two-atomic molecule in a time-dependent external field simulating the one utilized in the attosecond streaking technique.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Reduction of a grid moiré pattern by integrating a carbon-interspaced high precision x-ray grid with a digital radiographic detector.

PubMed

Yoon, Jai-Woong; Park, Young-Guk; Park, Chun-Joo; Kim, Do-Il; Lee, Jin-Ho; Chung, Nag-Kun; Choe, Bo-Young; Suh, Tae-Suk; Lee, Hyoung-Koo

2007-11-01

The stationary grid commonly used with a digital x-ray detector causes a moiré interference pattern due to the inadequate sampling of the grid shadows by the detector pixels. There are limitations with the previous methods used to remove the moiré such as imperfect electromagnetic interference shielding and the loss of image information. A new method is proposed for removing the moiré pattern by integrating a carbon-interspaced high precision x-ray grid with high grid line uniformity with the detector for frequency matching. The grid was aligned to the detector by translating and rotating the x-ray grid with respect to the detector using microcontrolled alignment mechanism. The gap between the grid and the detector surface was adjusted with micrometer precision to precisely match the projected grid line pitch to the detector pixel pitch. Considering the magnification of the grid shadows on the detector plane, the grids were manufactured such that the grid line frequency was slightly higher than the detector sampling frequency. This study examined the factors that affect the moiré pattern, particularly the line frequency and displacement. The frequency of the moiré pattern was found to be sensitive to the angular displacement of the grid with respect to the detector while the horizontal translation alters the phase but not the moiré frequency. The frequency of the moiré pattern also decreased with decreasing difference in frequency between the grid and the detector, and a moiré-free image was produced after complete matching for a given source to detector distance. The image quality factors including the contrast, signal-to-noise ratio and uniformity in the images with and without the moiré pattern were investigated.

On removing interpolation and resampling artifacts in rigid image registration.

PubMed

Aganj, Iman; Yeo, Boon Thye Thomas; Sabuncu, Mert R; Fischl, Bruce

2013-02-01

We show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts. These artifacts negatively affect the accuracy of registration by producing local optima, altering the gradient, shifting the global optimum, and making rigid registration asymmetric. In this paper, after an extensive literature review, we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically. We show the sum-of-squared-differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration. We then discuss aliasing that occurs in rotation, which is due to the fact that an image represented in the Cartesian grid is sampled with different rates in different directions, and propose the use of oscillatory isotropic interpolation kernels, which allow better recovery of true global optima by overcoming this type of aliasing. Through our experiments on brain, fingerprint, and white noise images, we illustrate the superior performance of the integral registration cost function in both the Cartesian and spherical coordinates, and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration.

On Removing Interpolation and Resampling Artifacts in Rigid Image Registration

PubMed Central

Aganj, Iman; Yeo, Boon Thye Thomas; Sabuncu, Mert R.; Fischl, Bruce

2013-01-01

We show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts. These artifacts negatively affect the accuracy of registration by producing local optima, altering the gradient, shifting the global optimum, and making rigid registration asymmetric. In this paper, after an extensive literature review, we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically. We show the sum-of-squared-differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration. We then discuss aliasing that occurs in rotation, which is due to the fact that an image represented in the Cartesian grid is sampled with different rates in different directions, and propose the use of oscillatory isotropic interpolation kernels, which allow better recovery of true global optima by overcoming this type of aliasing. Through our experiments on brain, fingerprint, and white noise images, we illustrate the superior performance of the integral registration cost function in both the Cartesian and spherical coordinates, and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration. PMID:23076044

Structural and electrical properties of Ag grid/poly(3,4-ethylenedioxythiophene): poly(styrene sulfonate) coatings for diode application through advanced printing technology.

PubMed

Duraisamy, Navaneethan; Ponniah, Ganeshthangaraj; Jo, Jeongdai; Choi, Kyung-Hyun

2013-08-01

This paper is focused on printed techniques for the fabrication of hybrid structure of silver (Ag) grid/poly(3,4-ethylenedioxythiophene): Poly(styrenesulfonate) (PEDOT:PSS) on polyethylene terepthalate (PET) as a flexible substrate. Ag grid has been printed on PET substrate by using gravure offset printing process, followed by PEDOT:PSS thin film deposition on Ag grid through electrohydrodynamic atomization (EHDA) technique. The important parameters for achieving uniform hybrid structure of Ag grid/PEDOT:PSS through printed techniques have been clearly discussed. Field emission scanning electron microscope studies revealed the uniformity of printed Ag grid with homogeneous deposition of PEDOT:PSS on Ag grid. The optical properties of Ag grid/PEDOT:PSS were measured by UV-visible spectroscopy, which showed nearly 80-82% of transparency in the visible region and it was nearly same as PEDOT:PSS thin film on PET substrate. Current-voltage (I-V) analysis of fabricated hybrid device by using printed Ag grid/PEDOT:PSS as a bottom electrode showed good rectifying behavior with possible interfacial mechanisms. Capacitance-voltage (C-V) analysis was carried over different frequencies. These results suggest that fabrication of hybrid structure through printed techniques will play a significant role in mass production of printed electronic devices for commercial application by using flexible substrate.

Non-Cartesian Parallel Imaging Reconstruction

PubMed Central

Wright, Katherine L.; Hamilton, Jesse I.; Griswold, Mark A.; Gulani, Vikas; Seiberlich, Nicole

2014-01-01

Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be employed to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the non-homogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian GRAPPA, and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. PMID:24408499

Efficient high-quality volume rendering of SPH data.

PubMed

Fraedrich, Roland; Auer, Stefan; Westermann, Rüdiger

2010-01-01

High quality volume rendering of SPH data requires a complex order-dependent resampling of particle quantities along the view rays. In this paper we present an efficient approach to perform this task using a novel view-space discretization of the simulation domain. Our method draws upon recent work on GPU-based particle voxelization for the efficient resampling of particles into uniform grids. We propose a new technique that leverages a perspective grid to adaptively discretize the view-volume, giving rise to a continuous level-of-detail sampling structure and reducing memory requirements compared to a uniform grid. In combination with a level-of-detail representation of the particle set, the perspective grid allows effectively reducing the amount of primitives to be processed at run-time. We demonstrate the quality and performance of our method for the rendering of fluid and gas dynamics SPH simulations consisting of many millions of particles.

A Radiation Solver for the National Combustion Code

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

2015-01-01

A methodology is given that converts an existing finite volume radiative transfer method that requires input of local absorption coefficients to one that can treat a mixture of combustion gases and compute the coefficients on the fly from the local mixture properties. The Full-spectrum k-distribution method is used to transform the radiative transfer equation (RTE) to an alternate wave number variable, g . The coefficients in the transformed equation are calculated at discrete temperatures and participating species mole fractions that span the values of the problem for each value of g. These results are stored in a table and interpolation is used to find the coefficients at every cell in the field. Finally, the transformed RTE is solved for each g and Gaussian quadrature is used to find the radiant heat flux throughout the field. The present implementation is in an existing cartesian/cylindrical grid radiative transfer code and the local mixture properties are given by a solution of the National Combustion Code (NCC) on the same grid. Based on this work the intention is to apply this method to an existing unstructured grid radiation code which can then be coupled directly to NCC.

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

PubMed

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

Advanced CFD Methods for Hypervelocity Wind Tunnels

DTIC Science & Technology

2011-03-10

Mach 14 nozzle produces non-uniformities in the test section flow that are not desirable [1,2]. Calibration runs with Pitot pressure rakes suggest...flows is presented. The grid is based on the characteristic lines of the supersonic regions of the flow. This allows for grid alignment and clustering...novel grid generation scheme for hypersonic nozzle flows is presented. The grid is based on the characteristic lines of the supersonic regions of the

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.

CPIC: a curvilinear Particle-In-Cell code for plasma-material interaction studies

NASA Astrophysics Data System (ADS)

Delzanno, G.; Camporeale, E.; Moulton, J. D.; Borovsky, J. E.; MacDonald, E.; Thomsen, M. F.

2012-12-01

We present a recently developed Particle-In-Cell (PIC) code in curvilinear geometry called CPIC (Curvilinear PIC) [1], where the standard PIC algorithm is coupled with a grid generation/adaptation strategy. Through the grid generator, which maps the physical domain to a logical domain where the grid is uniform and Cartesian, the code can simulate domains of arbitrary complexity, including the interaction of complex objects with a plasma. At present the code is electrostatic. Poisson's equation (in logical space) can be solved with either an iterative method based on the Conjugate Gradient (CG) or the Generalized Minimal Residual (GMRES) coupled with a multigrid solver used as a preconditioner, or directly with multigrid. The multigrid strategy is critical for the solver to perform optimally or nearly optimally as the dimension of the problem increases. CPIC also features a hybrid particle mover, where the computational particles are characterized by position in logical space and velocity in physical space. The advantage of a hybrid mover, as opposed to more conventional movers that move particles directly in the physical space, is that the interpolation of the particles in logical space is straightforward and computationally inexpensive, since one does not have to track the position of the particle. We will present our latest progress on the development of the code and document the code performance on standard plasma-physics tests. Then we will present the (preliminary) application of the code to a basic dynamic-charging problem, namely the charging and shielding of a spherical spacecraft in a magnetized plasma for various level of magnetization and including the pulsed emission of an electron beam from the spacecraft. The dynamical evolution of the sheath and the time-dependent current collection will be described. This study is in support of the ConnEx mission concept to use an electron beam from a magnetospheric spacecraft to trace magnetic field lines from the magnetosphere to the ionosphere [2]. [1] G.L. Delzanno, E. Camporeale, "CPIC: a new Particle-in-Cell code for plasma-material interaction studies", in preparation (2012). [2] J.E. Borovsky, D.J. McComas, M.F. Thomsen, J.L. Burch, J. Cravens, C.J. Pollock, T.E. Moore, and S.B. Mende, "Magnetosphere-Ionosphere Observatory (MIO): A multisatellite mission designed to solve the problem of what generates auroral arcs," Eos. Trans. Amer. Geophys. Union 79 (45), F744 (2000).

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.

Modeling target normal sheath acceleration using handoffs between multiple simulations

NASA Astrophysics Data System (ADS)

McMahon, Matthew; Willis, Christopher; Mitchell, Robert; King, Frank; Schumacher, Douglass; Akli, Kramer; Freeman, Richard

2013-10-01

We present a technique to model the target normal sheath acceleration (TNSA) process using full-scale LSP PIC simulations. The technique allows for a realistic laser, full size target and pre-plasma, and sufficient propagation length for the accelerated ions and electrons. A first simulation using a 2D Cartesian grid models the laser-plasma interaction (LPI) self-consistently and includes field ionization. Electrons accelerated by the laser are imported into a second simulation using a 2D cylindrical grid optimized for the initial TNSA process and incorporating an equation of state. Finally, all of the particles are imported to a third simulation optimized for the propagation of the accelerated ions and utilizing a static field solver for initialization. We also show use of 3D LPI simulations. Simulation results are compared to recent ion acceleration experiments using SCARLET laser at The Ohio State University. This work was performed with support from ASOFR under contract # FA9550-12-1-0341, DARPA, and allocations of computing time from the Ohio Supercomputing Center.

Numerical Simulations of Close and Contact Binary Systems Having Bipolytropic Equation of State

NASA Astrophysics Data System (ADS)

Kadam, Kundan; Clayton, Geoffrey C.; Motl, Patrick M.; Marcello, Dominic; Frank, Juhan

2017-01-01

I present the results of the numerical simulations of the mass transfer in close and contact binary systems with both stars having a bipolytropic (composite polytropic) equation of state. The initial binary systems are obtained by a modifying Hachisu’s self-consistent field technique. Both the stars have fully resolved cores with a molecular weight jump at the core-envelope interface. The initial properties of these simulations are chosen such that they satisfy the mass-radius relation, composition and period of a late W-type contact binary system. The simulations are carried out using two different Eulerian hydrocodes, Flow-ER with a fixed cylindrical grid, and Octo-tiger with an AMR capable cartesian grid. The detailed comparison of the simulations suggests an agreement between the results obtained from the two codes at different resolutions. The set of simulations can be treated as a benchmark, enabling us to reliably simulate mass transfer and merger scenarios of binary systems involving bipolytropic components.

Explosive force of primacord grid forms large sheet metal parts

NASA Technical Reports Server (NTRS)

1966-01-01

Primacord which is woven through fish netting in a grid pattern is used for explosive forming of large sheet metal parts. The explosive force generated by the primacord detonation is uniformly distributed over the entire surface of the sheet metal workpiece.

Grid effects on the derived ion temperature and ram velocity from the simulated results of the retarding potential analyzer data

NASA Astrophysics Data System (ADS)

Chao, C. K.; Su, S.-Y.; Yeh, H. C.

2003-12-01

The ROCSAT-1 satellite circulating at 600 km altitude in the low- and mid-latitude topside ionosphere carries a retarding potential analyzer to measure the ion composition, temperature, and the plasma flow velocity in the ram direction. Based on an existing three-dimensional model, the particle's motion inside the instrument is simulated with the exact wire and mesh sizes but with a smaller aperture of the real sensor configuration. The simulation results indicate that the retarding grids could not provide a uniform retarding potential barrier to completely repel low energy particles. Some of low energy particles could pass through those grids and arrive at the collector. The leakage will cause the ram velocity to be over-estimated for by about 180 m/sec. Furthermore, the simulated O + temperature derived from the I-V curve is lower than the input temperature due to ion losses from colliding with the grids from the non-uniform potential field generated by the high retarding voltage.

Evaluation of tropical channel refinement using MPAS-A aquaplanet simulations

DOE PAGES

Martini, Matus N.; Gustafson, Jr., William I.; O'Brien, Travis A.; ...

2015-09-13

Climate models with variable-resolution grids offer a computationally less expensive way to provide more detailed information at regional scales and increased accuracy for processes that cannot be resolved by a coarser grid. This study uses the Model for Prediction Across Scales–Atmosphere (MPAS22A), consisting of a nonhydrostatic dynamical core and a subset of Advanced Research Weather Research and Forecasting (ARW-WRF) model atmospheric physics that have been modified to include the Community Atmosphere Model version 5 (CAM5) cloud fraction parameterization, to investigate the potential benefits of using increased resolution in an tropical channel. The simulations are performed with an idealized aquaplanet configurationmore » using two quasi-uniform grids, with 30 km and 240 km grid spacing, and two variable-resolution grids spanning the same grid spacing range; one with a narrow (20°S–20°N) and one with a wide (30°S–30°N) tropical channel refinement. Results show that increasing resolution in the tropics impacts both the tropical and extratropical circulation. Compared to the quasi-uniform coarse grid, the narrow-channel simulation exhibits stronger updrafts in the Ferrel cell as well as in the middle of the upward branch of the Hadley cell. The wider tropical channel has a closer correspondence to the 30 km quasi-uniform simulation. However, the total atmospheric poleward energy transports are similar in all simulations. The largest differences are in the low-level cloudiness. The refined channel simulations show improved tropical and extratropical precipitation relative to the global 240 km simulation when compared to the global 30 km simulation. All simulations have a single ITCZ. Furthermore, the relatively small differences in mean global and tropical precipitation rates among the simulations are a promising result, and the evidence points to the tropical channel being an effective method for avoiding the extraneous numerical artifacts seen in earlier studies that only refined portion of the tropics.« less

Optically sectioned fluorescence endomicroscopy with hybrid-illumination imaging through a flexible fiber bundle.

PubMed

Santos, Silvia; Chu, Kengyeh K; Lim, Daryl; Bozinovic, Nenad; Ford, Tim N; Hourtoule, Claire; Bartoo, Aaron C; Singh, Satish K; Mertz, Jerome

2009-01-01

We present an endomicroscope apparatus that exhibits out-of-focus background rejection based on wide-field illumination through a flexible imaging fiber bundle. Our technique, called HiLo microscopy, involves acquiring two images, one with grid-pattern illumination and another with standard uniform illumination. An evaluation of the image contrast with grid-pattern illumination provides an optically sectioned image with low resolution. This is complemented with high-resolution information from the uniform illumination image, leading to a full-resolution image that is optically sectioned. HiLo endomicroscope movies are presented of fluorescently labeled rat colonic mucosa.

Optically sectioned fluorescence endomicroscopy with hybrid-illumination imaging through a flexible fiber bundle

NASA Astrophysics Data System (ADS)

Santos, Silvia; Chu, Kengyeh K.; Lim, Daryl; Bozinovic, Nenad; Ford, Tim N.; Hourtoule, Claire; Bartoo, Aaron C.; Singh, Satish K.; Mertz, Jerome

2009-05-01

We present an endomicroscope apparatus that exhibits out-of-focus background rejection based on wide-field illumination through a flexible imaging fiber bundle. Our technique, called HiLo microscopy, involves acquiring two images, one with grid-pattern illumination and another with standard uniform illumination. An evaluation of the image contrast with grid-pattern illumination provides an optically sectioned image with low resolution. This is complemented with high-resolution information from the uniform illumination image, leading to a full-resolution image that is optically sectioned. HiLo endomicroscope movies are presented of fluorescently labeled rat colonic mucosa.

Numerical Simulation of Shock Interaction with Deformable Particles Using a Constrained Interface Reinitialization Scheme

NASA Astrophysics Data System (ADS)

Jackson, Thomas L.; Sridharan, Prashanth; Zhang, Ju; Balachandar, S.

2015-11-01

In this work we present axisymmetric numerical simulations of shock propagating in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. The numerical method is a finite-volume based solver on a Cartesian grid, which allows for multi-material interfaces and shocks. To preserve particle mass and volume, a novel constraint reinitialization scheme is introduced. We compute the unsteady drag coefficient as a function of post-shock pressure, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. Using this information, we also present a simplified point-particle force model that can be used for mesoscale simulations.

Bounded Error Schemes for the Wave Equation on Complex Domains

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir

1998-01-01

This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.

Comparison of local grid refinement methods for MODFLOW

USGS Publications Warehouse

Mehl, S.; Hill, M.C.; Leake, S.A.

2006-01-01

Many ground water modeling efforts use a finite-difference method to solve the ground water flow equation, and many of these models require a relatively fine-grid discretization to accurately represent the selected process in limited areas of interest. Use of a fine grid over the entire domain can be computationally prohibitive; using a variably spaced grid can lead to cells with a large aspect ratio and refinement in areas where detail is not needed. One solution is to use local-grid refinement (LGR) whereby the grid is only refined in the area of interest. This work reviews some LGR methods and identifies advantages and drawbacks in test cases using MODFLOW-2000. The first test case is two dimensional and heterogeneous; the second is three dimensional and includes interaction with a meandering river. Results include simulations using a uniform fine grid, a variably spaced grid, a traditional method of LGR without feedback, and a new shared node method with feedback. Discrepancies from the solution obtained with the uniform fine grid are investigated. For the models tested, the traditional one-way coupled approaches produced discrepancies in head up to 6.8% and discrepancies in cell-to-cell fluxes up to 7.1%, while the new method has head and cell-to-cell flux discrepancies of 0.089% and 0.14%, respectively. Additional results highlight the accuracy, flexibility, and CPU time trade-off of these methods and demonstrate how the new method can be successfully implemented to model surface water-ground water interactions. Copyright ?? 2006 The Author(s).

Towards a Viscous Wall Model for Immersed Boundary Methods

NASA Technical Reports Server (NTRS)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

Immersed boundary methods are frequently employed for simulating flows at low Reynolds numbers or for applications where viscous boundary layer effects can be neglected. The primary shortcoming of Cartesian mesh immersed boundary methods is the inability of efficiently resolving thin turbulent boundary layers in high-Reynolds number flow application. The inefficiency of resolving the thin boundary is associated with the use of constant aspect ratio Cartesian grid cells. Conventional CFD approaches can efficiently resolve the large wall normal gradients by utilizing large aspect ratio cells near the wall. This paper presents different approaches for immersed boundary methods to account for the viscous boundary layer interaction with the flow-field away from the walls. Different wall modeling approaches proposed in previous research studies are addressed and compared to a new integral boundary layer based approach. In contrast to common wall-modeling approaches that usually only utilize local flow information, the integral boundary layer based approach keeps the streamwise history of the boundary layer. This allows the method to remain effective at much larger y+ values than local wall modeling approaches. After a theoretical discussion of the different approaches, the method is applied to increasingly more challenging flow fields including fully attached, separated, and shock-induced separated (laminar and turbulent) flows.

Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh

NASA Astrophysics Data System (ADS)

Misaka, Takashi; Sasaki, Daisuke; Obayashi, Shigeru

2017-11-01

We developed a framework for a distributed-memory parallel computer that enables dynamic data management for adaptive mesh refinement and load balancing. We employed simple data structure of the building cube method (BCM) where a computational domain is divided into multi-level cubic domains and each cube has the same number of grid points inside, realising a multi-level block-structured Cartesian mesh. Solution adaptive mesh refinement, which works efficiently with the help of the dynamic load balancing, was implemented by dividing cubes based on mesh refinement criteria. The framework was investigated with the Laplace equation in terms of adaptive mesh refinement, load balancing and the parallel efficiency. It was then applied to the incompressible Navier-Stokes equations to simulate a turbulent flow around a sphere. We considered wall-adaptive cube refinement where a non-dimensional wall distance y+ near the sphere is used for a criterion of mesh refinement. The result showed the load imbalance due to y+ adaptive mesh refinement was corrected by the present approach. To utilise the BCM framework more effectively, we also tested a cube-wise algorithm switching where an explicit and implicit time integration schemes are switched depending on the local Courant-Friedrichs-Lewy (CFL) condition in each cube.

A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries

NASA Astrophysics Data System (ADS)

Uddin, H.; Kramer, R. M. J.; Pantano, C.

2014-04-01

An immersed boundary methodology to solve the compressible Navier-Stokes equations around complex geometries in Cartesian fluid dynamics solvers is described. The objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts. A standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended. Boundary conditions on the surface are enforced by an approach inspired by analytic continuation. Each fluid field is extended independently, constrained only by the boundary condition associated with that field. Unlike most existing methods, no jump conditions or explicit derivation of them from the boundary conditions are required in this approach. Numerical stiffness that arises when the fluid-solid interface is close to grid points of the mesh is addressed by preconditioning. In addition, the embedded geometry technique is coupled with a stable high-order adaptive discretization that is enabled around the object boundary to enhance resolution. The stencils used to transition the order of accuracy of the discretization are derived using the summation-by-parts technique that ensures stability. Applications to shock reflections, shock-ramp interactions, and supersonic and low-Mach number flows over two- and three-dimensional geometries are presented.

Impact of tip-gap size and periodicity on turbulent transition

NASA Astrophysics Data System (ADS)

Pogorelov, Alexej; Meinke, Matthias; Schroeder, Wolfgang

2015-11-01

Large-Eddy Simulations of the flow field in an axial fan are performed at a Reynolds number of 936.000 based on the diameter and the rotational speed of the casing wall. A finite-volume flow solver based on a conservative Cartesian cut-cell method is used to solve the unsteady compressible Navier-Stokes equations. Computations are performed at a flow rate coefficient of 0.165 and a tip-gap size of s/D =0.01, for a 72 degrees fan section resolving only one out of five blades and a full fan resolving all five blades to investigate the impact of the periodic boundary condition. Furthermore, a grid convergence study is performed using four computational grids. Results of the flow field are analyzed for the computational grid with 1 billion cells. An interaction of the turbulent wake, generated by the tip-gap vortex, with the downstream blade, is observed, which leads to a cyclic transition with high pressure fluctuations on the suction side of the blade. Two dominant frequencies are identified which perfectly match with the characteristic frequencies in the experimental sound power level such that their physical origin is explained. A variation of the tip-gap size alters the transition on the suction side, i.e., no cyclic transition is observed.

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation

NASA Astrophysics Data System (ADS)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation to operations involving only 1D vectors however retaining the linear complexity scaling in the number of potentials. Here, we introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D N × N × N grid with the computational requirements only weakly dependent on the number of summed potentials. It is based on the assembled low-rank canonical tensor representations of the collected potentials using pointwise sums of shifted canonical vectors representing the single generating function, say the Newton kernel. For a sum of electrostatic potentials over L × L × L lattice embedded in a box the required storage scales linearly in the 1D grid-size, O(N) , while the numerical cost is estimated by O(NL) . For periodic boundary conditions, the storage demand remains proportional to the 1D grid-size of a unit cell, n = N / L, while the numerical cost reduces to O(N) , that outperforms the FFT-based Ewald-type summation algorithms of complexity O(N3 log N) . The complexity in the grid parameter N can be reduced even to the logarithmic scale O(log N) by using data-sparse representation of canonical N-vectors via the quantics tensor approximation. For justification, we prove an upper bound on the quantics ranks for the canonical vectors in the overall lattice sum. The presented approach is beneficial in applications which require further functional calculus with the lattice potential, say, scalar product with a function, integration or differentiation, which can be performed easily in tensor arithmetics on large 3D grids with 1D cost. Numerical tests illustrate the performance of the tensor summation method and confirm the estimated bounds on the tensor ranks.

Optimization of sampling pattern and the design of Fourier ptychographic illuminator.

PubMed

Guo, Kaikai; Dong, Siyuan; Nanda, Pariksheet; Zheng, Guoan

2015-03-09

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

NASA Astrophysics Data System (ADS)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

Fully Automated Single-Zone Elliptic Grid Generation for Mars Science Laboratory (MSL) Aeroshell and Canopy Geometries

NASA Technical Reports Server (NTRS)

kaul, Upender K.

2008-01-01

A procedure for generating smooth uniformly clustered single-zone grids using enhanced elliptic grid generation has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy. The procedure obviates the need for generating multizone grids for such geometries, as reported in the literature. This has been possible because the enhanced elliptic grid generator automatically generates clustered grids without manual prescription of decay parameters needed with the conventional approach. In fact, these decay parameters are calculated as decay functions as part of the solution, and they are not constant over a given boundary. Since these decay functions vary over a given boundary, orthogonal grids near any arbitrary boundary can be clustered automatically without having to break up the boundaries and the corresponding interior domains into various zones for grid generation.

An adaptive grid to improve the efficiency and accuracy of modelling underwater noise from shipping

NASA Astrophysics Data System (ADS)

Trigg, Leah; Chen, Feng; Shapiro, Georgy; Ingram, Simon; Embling, Clare

2017-04-01

Underwater noise from shipping is becoming a significant concern and has been listed as a pollutant under Descriptor 11 of the Marine Strategy Framework Directive. Underwater noise models are an essential tool to assess and predict noise levels for regulatory procedures such as environmental impact assessments and ship noise monitoring. There are generally two approaches to noise modelling. The first is based on simplified energy flux models, assuming either spherical or cylindrical propagation of sound energy. These models are very quick but they ignore important water column and seabed properties, and produce significant errors in the areas subject to temperature stratification (Shapiro et al., 2014). The second type of model (e.g. ray-tracing and parabolic equation) is based on an advanced physical representation of sound propagation. However, these acoustic propagation models are computationally expensive to execute. Shipping noise modelling requires spatial discretization in order to group noise sources together using a grid. A uniform grid size is often selected to achieve either the greatest efficiency (i.e. speed of computations) or the greatest accuracy. In contrast, this work aims to produce efficient and accurate noise level predictions by presenting an adaptive grid where cell size varies with distance from the receiver. The spatial range over which a certain cell size is suitable was determined by calculating the distance from the receiver at which propagation loss becomes uniform across a grid cell. The computational efficiency and accuracy of the resulting adaptive grid was tested by comparing it to uniform 1 km and 5 km grids. These represent an accurate and computationally efficient grid respectively. For a case study of the Celtic Sea, an application of the adaptive grid over an area of 160×160 km reduced the number of model executions required from 25600 for a 1 km grid to 5356 in December and to between 5056 and 13132 in August, which represents a 2 to 5-fold increase in efficiency. The 5 km grid reduces the number of model executions further to 1024. However, over the first 25 km the 5 km grid produces errors of up to 13.8 dB when compared to the highly accurate but inefficient 1 km grid. The newly developed adaptive grid generates much smaller errors of less than 0.5 dB while demonstrating high computational efficiency. Our results show that the adaptive grid provides the ability to retain the accuracy of noise level predictions and improve the efficiency of the modelling process. This can help safeguard sensitive marine ecosystems from noise pollution by improving the underwater noise predictions that inform management activities. References Shapiro, G., Chen, F., Thain, R., 2014. The Effect of Ocean Fronts on Acoustic Wave Propagation in a Shallow Sea, Journal of Marine System, 139: 217 - 226. http://dx.doi.org/10.1016/j.jmarsys.2014.06.007.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burton, D.E.; Miller, D.S.; Palmer, T.

The authors describe FLAG, a 3D adaptive free-Lagrange method for unstructured grids. The grid elements were 3D polygons, which move with the flow, and are refined or reconnected as necessary to achieve uniform accuracy. The authors stressed that they were able to construct a 3D hydro version of this code in 3 months, using an object-oriented FORTRAN approach.

Dynamic grid refinement for partial differential equations on parallel computers

NASA Technical Reports Server (NTRS)

Mccormick, S.; Quinlan, D.

1989-01-01

The fast adaptive composite grid method (FAC) is an algorithm that uses various levels of uniform grids to provide adaptive resolution and fast solution of PDEs. An asynchronous version of FAC, called AFAC, that completely eliminates the bottleneck to parallelism is presented. This paper describes the advantage that this algorithm has in adaptive refinement for moving singularities on multiprocessor computers. This work is applicable to the parallel solution of two- and three-dimensional shock tracking problems.

Development and application of a volume penalization immersed boundary method for the computation of blood flow and shear stresses in cerebral vessels and aneurysms.

PubMed

Mikhal, Julia; Geurts, Bernard J

2013-12-01

A volume-penalizing immersed boundary method is presented for the simulation of laminar incompressible flow inside geometrically complex blood vessels in the human brain. We concentrate on cerebral aneurysms and compute flow in curved brain vessels with and without spherical aneurysm cavities attached. We approximate blood as an incompressible Newtonian fluid and simulate the flow with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. A key element of the immersed boundary method is the so-called masking function. This is a binary function with which we identify at any location in the domain whether it is 'solid' or 'fluid', allowing to represent objects immersed in a Cartesian grid. We compare three definitions of the masking function for geometries that are non-aligned with the grid. In each case a 'staircase' representation is used in which a grid cell is either 'solid' or 'fluid'. Reliable findings are obtained with our immersed boundary method, even at fairly coarse meshes with about 16 grid cells across a velocity profile. The validation of the immersed boundary method is provided on the basis of classical Poiseuille flow in a cylindrical pipe. We obtain first order convergence for the velocity and the shear stress, reflecting the fact that in our approach the solid-fluid interface is localized with an accuracy on the order of a grid cell. Simulations for curved vessels and aneurysms are done for different flow regimes, characterized by different values of the Reynolds number (Re). The validation is performed for laminar flow at Re = 250, while the flow in more complex geometries is studied at Re = 100 and Re = 250, as suggested by physiological conditions pertaining to flow of blood in the circle of Willis.

Crystallographic Lattice Boltzmann Method

PubMed Central

Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh

2016-01-01

Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Research in Parallel Algorithms and Software for Computational Aerosciences

NASA Technical Reports Server (NTRS)

Domel, Neal D.

1996-01-01

Phase I is complete for the development of a Computational Fluid Dynamics parallel code with automatic grid generation and adaptation for the Euler analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian grid code developed at Lockheed Martin Tactical Aircraft Systems, has been modified for a distributed memory/massively parallel computing environment. The parallel code is operational on an SGI network, Cray J90 and C90 vector machines, SGI Power Challenge, and Cray T3D and IBM SP2 massively parallel machines. Parallel Virtual Machine (PVM) is the message passing protocol for portability to various architectures. A domain decomposition technique was developed which enforces dynamic load balancing to improve solution speed and memory requirements. A host/node algorithm distributes the tasks. The solver parallelizes very well, and scales with the number of processors. Partially parallelized and non-parallelized tasks consume most of the wall clock time in a very fine grain environment. Timing comparisons on a Cray C90 demonstrate that Parallel SPLITFLOW runs 2.4 times faster on 8 processors than its non-parallel counterpart autotasked over 8 processors.

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Research in Parallel Algorithms and Software for Computational Aerosciences

NASA Technical Reports Server (NTRS)

Domel, Neal D.

1996-01-01

Phase 1 is complete for the development of a computational fluid dynamics CFD) parallel code with automatic grid generation and adaptation for the Euler analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian grid code developed at Lockheed Martin Tactical Aircraft Systems, has been modified for a distributed memory/massively parallel computing environment. The parallel code is operational on an SGI network, Cray J90 and C90 vector machines, SGI Power Challenge, and Cray T3D and IBM SP2 massively parallel machines. Parallel Virtual Machine (PVM) is the message passing protocol for portability to various architectures. A domain decomposition technique was developed which enforces dynamic load balancing to improve solution speed and memory requirements. A host/node algorithm distributes the tasks. The solver parallelizes very well, and scales with the number of processors. Partially parallelized and non-parallelized tasks consume most of the wall clock time in a very fine grain environment. Timing comparisons on a Cray C90 demonstrate that Parallel SPLITFLOW runs 2.4 times faster on 8 processors than its non-parallel counterpart autotasked over 8 processors.

Impact of earthquake source complexity and land elevation data resolution on tsunami hazard assessment and fatality estimation

NASA Astrophysics Data System (ADS)

Muhammad, Ario; Goda, Katsuichiro

2018-03-01

This study investigates the impact of model complexity in source characterization and digital elevation model (DEM) resolution on the accuracy of tsunami hazard assessment and fatality estimation through a case study in Padang, Indonesia. Two types of earthquake source models, i.e. complex and uniform slip models, are adopted by considering three resolutions of DEMs, i.e. 150 m, 50 m, and 10 m. For each of the three grid resolutions, 300 complex source models are generated using new statistical prediction models of earthquake source parameters developed from extensive finite-fault models of past subduction earthquakes, whilst 100 uniform slip models are constructed with variable fault geometry without slip heterogeneity. The results highlight that significant changes to tsunami hazard and fatality estimates are observed with regard to earthquake source complexity and grid resolution. Coarse resolution (i.e. 150 m) leads to inaccurate tsunami hazard prediction and fatality estimation, whilst 50-m and 10-m resolutions produce similar results. However, velocity and momentum flux are sensitive to the grid resolution and hence, at least 10-m grid resolution needs to be implemented when considering flow-based parameters for tsunami hazard and risk assessments. In addition, the results indicate that the tsunami hazard parameters and fatality number are more sensitive to the complexity of earthquake source characterization than the grid resolution. Thus, the uniform models are not recommended for probabilistic tsunami hazard and risk assessments. Finally, the findings confirm that uncertainties of tsunami hazard level and fatality in terms of depth, velocity and momentum flux can be captured and visualized through the complex source modeling approach. From tsunami risk management perspectives, this indeed creates big data, which are useful for making effective and robust decisions.

Summary of Data from the Sixth AIAA CFD Drag Prediction Workshop: CRM Cases 2 to 5

NASA Technical Reports Server (NTRS)

Tinoco, Edward N.; Brodersen, Olaf P.; Keye, Stefan; Laflin, Kelly R.; Feltrop, Edward; Vassberg, John C.; Mani, Mori; Rider, Ben; Wahls, Richard A.; Morrison, Joseph H.;

Optimization of electrostatic dual-grid beam-deflection system

NASA Technical Reports Server (NTRS)

Hudson, W. R.; Lathem, W. C.; Power, J. L.; Banks, B. A.

1972-01-01

Tests were performed to minimize accelerator grid erosion of a 5-cm diameter Kaufman ion thruster due to direct beam impingement. Several different screen hole diameters, pillow-shape-square screen holes, and dished screen grids were tried. The optimization was accomplished by copper plating the accelerator grid before testing each grid configuration on a thruster for a 2-hour run. The thruster beam sputtered copper and molybdenum from the accelerator grid where the beam impinged. The observed erosion patterns and measured accelerator currents were used to determine how to modify the accelerator system. The lowest erosion was obtained for a 50-percent open area pillow-shape-square-aperture screen grid, dished 0.043 centimeter convex toward the accelerator grid, which was positioned with the center of the screen grid 0.084 centimeter from the accelerator grid. During this investigation the accelerator current was reduced from 120 to 55 microamperes and was also more uniformly distributed over the area of the accelerator grid.

Stability and error estimation for Component Adaptive Grid methods

NASA Technical Reports Server (NTRS)

Oliger, Joseph; Zhu, Xiaolei

1994-01-01

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

Enhancement of a 2D front-tracking algorithm with a non-uniform distribution of Lagrangian markers

NASA Astrophysics Data System (ADS)

Febres, Mijail; Legendre, Dominique

2018-04-01

The 2D front tracking method is enhanced to control the development of spurious velocities for non-uniform distributions of markers. The hybrid formulation of Shin et al. (2005) [7] is considered. A new tangent calculation is proposed for the calculation of the tension force at markers. A new reconstruction method is also proposed to manage non-uniform distributions of markers. We show that for both the static and the translating spherical drop test case the spurious currents are reduced to the machine precision. We also show that the ratio of the Lagrangian grid size Δs over the Eulerian grid size Δx has to satisfy Δs / Δx > 0.2 for ensuring such low level of spurious velocity. The method is found to provide very good agreement with benchmark test cases from the literature.

Summary of the Tandem Cylinder Solutions from the Benchmark Problems for Airframe Noise Computations-I Workshop

NASA Technical Reports Server (NTRS)

Lockard, David P.

2011-01-01

Fifteen submissions in the tandem cylinders category of the First Workshop on Benchmark problems for Airframe Noise Computations are summarized. Although the geometry is relatively simple, the problem involves complex physics. Researchers employed various block-structured, overset, unstructured and embedded Cartesian grid techniques and considerable computational resources to simulate the flow. The solutions are compared against each other and experimental data from 2 facilities. Overall, the simulations captured the gross features of the flow, but resolving all the details which would be necessary to compute the noise remains challenging. In particular, how to best simulate the effects of the experimental transition strip, and the associated high Reynolds number effects, was unclear. Furthermore, capturing the spanwise variation proved difficult.

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Multi-Dimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2009-01-01

The quality of simulated hypersonic stagnation region heating on tetrahedral meshes is investigated by using a three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. Two test problems are investigated: hypersonic flow over a three-dimensional cylinder with special attention to the uniformity of the solution in the spanwise direction and hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problem provides a sensitive test for algorithmic effects on heating. This investigation is believed to be unique in its focus on three-dimensional, rotated upwind schemes for the simulation of hypersonic heating on tetrahedral grids. This study attempts to fill the void left by the inability of conventional (quasi-one-dimensional) approaches to accurately simulate heating in a tetrahedral grid system. Results show significant improvement in spanwise uniformity of heating with some penalty of ringing at the captured shock. Issues with accuracy near the peak shear location are identified and require further study.

Use of Emerging Grid Computing Technologies for the Analysis of LIGO Data

NASA Astrophysics Data System (ADS)

Koranda, Scott

2004-03-01

The LIGO Scientific Collaboration (LSC) today faces the challenge of enabling analysis of terabytes of LIGO data by hundreds of scientists from institutions all around the world. To meet this challenge the LSC is developing tools, infrastructure, applications, and expertise leveraging Grid Computing technologies available today, and making available to LSC scientists compute resources at sites across the United States and Europe. We use digital credentials for strong and secure authentication and authorization to compute resources and data. Building on top of products from the Globus project for high-speed data transfer and information discovery we have created the Lightweight Data Replicator (LDR) to securely and robustly replicate data to resource sites. We have deployed at our computing sites the Virtual Data Toolkit (VDT) Server and Client packages, developed in collaboration with our partners in the GriPhyN and iVDGL projects, providing uniform access to distributed resources for users and their applications. Taken together these Grid Computing technologies and infrastructure have formed the LSC DataGrid--a coherent and uniform environment across two continents for the analysis of gravitational-wave detector data. Much work, however, remains in order to scale current analyses and recent lessons learned need to be integrated into the next generation of Grid middleware.

Aerostructural Shape and Topology Optimization of Aircraft Wings

NASA Astrophysics Data System (ADS)

James, Kai

A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a three-dimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2 g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO approach. While the sequentially optimized wing exhibits a nearly-elliptical lift distribution, the MDO design seeks to push a greater portion of the load toward the root, thus reducing the structural deflection, and allowing for a lighter structure. By exploiting this trade-off, the MDO design achieves a 42% lower drag than the sequential result.

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

NASA Technical Reports Server (NTRS)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

Translation by anisotropic peeling or fracturing in elastic media

NASA Astrophysics Data System (ADS)

Zheng, Zhong; Lister, John; Neufeld, Jerome

2017-11-01

The influence of rock anisotropy on the direction of hydraulic fracturing is an important open question. Two canonical systems have been proposed to investigate the fundamental aspects of such fluid-structure interaction problems: (i) Fluid injection and fracturing into an infinite elastic matrix (e.g., solid gelatin) and (ii) Fluid invasion and peeling beneath a deforming elastic sheet (e.g., bending plate). We investigate the second system and impose a non-uniform prewetting film thickness beneath the elastic sheet. We notice that while the bulk of the elastic sheet retains the static blister shape, a non-uniform prewetting film thickness can cause a horizontal translation of the blister. In particular, for a step jump in prewetting film thickness, asymptotic analysis indicates that, under constant fluid injection, the horizontal translation follows a t 7 / 17 time dependence in cartesian coordinates, and the prefactor of power-law translation depends on the ratio of the distinct prewetting film thicknesses on either side. We also provide numerical and experimental evidence demonstrating anisotropic blister evolution. This can be thought of as a model system for fluid-driven fracturing where the non-uniform prewetting film thickness mimics heterogeneity in material toughness.

The R package 'icosa' for coarse resolution global triangular and penta-hexagonal gridding

NASA Astrophysics Data System (ADS)

Kocsis, Adam T.

2017-04-01

With the development of the internet and the computational power of personal computers, open source programming environments have become indispensable for science in the past decade. This includes the increase of the GIS capacity of the free R environment, which was originally developed for statistical analyses. The flexibility of R made it a preferred programming tool in a multitude of disciplines from the area of the biological and geological sciences. Many of these subdisciplines operate with incidence (occurrence) data that are in a large number of cases to be grained before further analyses can be conducted. This graining is executed mostly by gridding data to cells of a Gaussian grid of various resolutions to increase the density of data in a single unit of the analyses. This method has obvious shortcomings despite the ease of its application: well-known systematic biases are induced to cell sizes and shapes that can interfere with the results of statistical procedures, especially if the number of incidence points influences the metrics in question. The 'icosa' package employs a common method to overcome this obstacle by implementing grids with roughly equal cell sizes and shapes that are based on tessellated icosahedra. These grid objects are essentially polyhedra with xyz Cartesian vertex data that are linked to tables of faces and edges. At its current developmental stage, the package uses a single method of tessellation which balances grid cell size and shape distortions, but its structure allows the implementation of various other types of tessellation algorithms. The resolution of the grids can be set by the number of breakpoints inserted into a segment forming an edge of the original icosahedron. Both the triangular and their inverted penta-hexagonal grids are available for creation with the package. The package also incorporates functions to look up coordinates in the grid very effectively and data containers to link data to the grid structure. The classes defined in the package are communicating with classes of the 'sp' and 'raster' packages and functions are supplied that allow resolution change and type conversions. Three-dimensional rendering is made available with the 'rgl' package and two-dimensional projections can be calculated using 'sp' and 'rgdal'. The package was developed as part of a project funded by the Deutsche Forschungsgemeinschaft (KO - 5382/1-1).

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A.

Here, we present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid–structure interface are avoided and far-field (smooth) velo city and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torquesmore » through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13]). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.« less

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

DOE PAGES

Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A.; ...

2017-10-01

Here, we present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid–structure interface are avoided and far-field (smooth) velo city and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torquesmore » through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13]). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.« less

Parallelization of TWOPORFLOW, a Cartesian Grid based Two-phase Porous Media Code for Transient Thermo-hydraulic Simulations

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.

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

NASA Technical Reports Server (NTRS)

Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)

1995-01-01

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

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.

Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation

NASA Technical Reports Server (NTRS)

Adams, N. A.

1995-01-01

The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.

MeshVoro: A Three-Dimensional Voronoi Mesh Building Tool for the TOUGH Family of Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freeman, C. M.; Boyle, K. L.; Reagan, M.

2013-09-30

Few tools exist for creating and visualizing complex three-dimensional simulation meshes, and these have limitations that restrict their application to particular geometries and circumstances. Mesh generation needs to trend toward ever more general applications. To that end, we have developed MeshVoro, a tool that is based on the Voro (Rycroft 2009) library and is capable of generating complex threedimensional Voronoi tessellation-based (unstructured) meshes for the solution of problems of flow and transport in subsurface geologic media that are addressed by the TOUGH (Pruess et al. 1999) family of codes. MeshVoro, which includes built-in data visualization routines, is a particularly usefulmore » tool because it extends the applicability of the TOUGH family of codes by enabling the scientifically robust and relatively easy discretization of systems with challenging 3D geometries. We describe several applications of MeshVoro. We illustrate the ability of the tool to straightforwardly transform a complex geological grid into a simulation mesh that conforms to the specifications of the TOUGH family of codes. We demonstrate how MeshVoro can describe complex system geometries with a relatively small number of grid blocks, and we construct meshes for geometries that would have been practically intractable with a standard Cartesian grid approach. We also discuss the limitations and appropriate applications of this new technology.« less

The Efficiency and the Scalability of an Explicit Operator on an IBM POWER4 System

NASA Technical Reports Server (NTRS)

Frumkin, Michael; Biegel, Bryan A. (Technical Monitor)

2002-01-01

We present an evaluation of the efficiency and the scalability of an explicit CFD operator on an IBM POWER4 system. The POWER4 architecture exhibits a common trend in HPC architectures: boosting CPU processing power by increasing the number of functional units, while hiding the latency of memory access by increasing the depth of the memory hierarchy. The overall machine performance depends on the ability of the caches-buses-fabric-memory to feed the functional units with the data to be processed. In this study we evaluate the efficiency and scalability of one explicit CFD operator on an IBM POWER4. This operator performs computations at the points of a Cartesian grid and involves a few dozen floating point numbers and on the order of 100 floating point operations per grid point. The computations in all grid points are independent. Specifically, we estimate the efficiency of the RHS operator (SP of NPB) on a single processor as the observed/peak performance ratio. Then we estimate the scalability of the operator on a single chip (2 CPUs), a single MCM (8 CPUs), 16 CPUs, and the whole machine (32 CPUs). Then we perform the same measurements for a chache-optimized version of the RHS operator. For our measurements we use the HPM (Hardware Performance Monitor) counters available on the POWER4. These counters allow us to analyze the obtained performance results.

High Precision Grids for Neutron, Hard X-Ray, and Gamma-Ray Imaging Systems

NASA Technical Reports Server (NTRS)

Campbell, Jonathan W. (Inventor)

2002-01-01

Fourier telescopes permit observations over a very broad band of energy. They generally include synthetic spatial filtering structures, known as multilayer grids or grid pairs consisting of alternate layers of absorbing and transparent materials depending on whether neutrons or photons are being imaged. For hard x-rays and gamma rays high (absorbing) and low (transparent) atomic number elements, termed high-Z and low-Z materials may be used. Fabrication of these multilayer grid structures is not without its difficulties. Herein the alternate layers of the higher material and the lower material are inserted in a polyhedron, transparent to photons of interest, through an open face of the polyhedron. The inserted layers are then uniformly compressed to form a multilayer grid.

A highly efficient machine planting system for forestry research plantations—the Wright-MSU method

Treesearch

James R. McKenna; Oriana Rueda-Krauss; Brian Beheler

2011-01-01

For forestry research purposes, grid planting with uniform tree spacing is superior to planting with nonuniform spacing because it controls density across the plantation and facilitates accurate repeat measurements. The ability to cross-check tree positions in a grid-type plantation avoids problems associated with dead or missing trees and increases the efficiency and...

On Accuracy of Adaptive Grid Methods for Captured Shocks

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2002-01-01

The accuracy of two grid adaptation strategies, grid redistribution and local grid refinement, is examined by solving the 2-D Euler equations for the supersonic steady flow around a cylinder. Second- and fourth-order linear finite difference shock-capturing schemes, based on the Lax-Friedrichs flux splitting, are used to discretize the governing equations. The grid refinement study shows that for the second-order scheme, neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points. For the fourth-order scheme, the dominant first-order error component is reduced by the grid adaptation, while the design-order error component drastically increases because of the grid nonuniformity. As a result, both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved. Similar error behavior has been obtained for the pressure integral across the shock. A simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy. Based on these results, a new grid adaptation criterion for captured shocks is proposed.

Adding muscle where you need it: non-uniform hypertrophy patterns in elite sprinters.

PubMed

Handsfield, G G; Knaus, K R; Fiorentino, N M; Meyer, C H; Hart, J M; Blemker, S S

2017-10-01

Sprint runners achieve much higher gait velocities and accelerations than average humans, due in part to large forces generated by their lower limb muscles. Various factors have been explored in the past to understand sprint biomechanics, but the distribution of muscle volumes in the lower limb has not been investigated in elite sprinters. In this study, we used non-Cartesian MRI to determine muscle sizes in vivo in a group of 15 NCAA Division I sprinters. Normalizing muscle sizes by body size, we compared sprinter muscles to non-sprinter muscles, calculated Z-scores to determine non-uniformly large muscles in sprinters, assessed bilateral symmetry, and assessed gender differences in sprinters' muscles. While limb musculature per height-mass was 22% greater in sprinters than in non-sprinters, individual muscles were not all uniformly larger. Hip- and knee-crossing muscles were significantly larger among sprinters (mean difference: 30%, range: 19-54%) but only one ankle-crossing muscle was significantly larger (tibialis posterior, 28%). Population-wide asymmetry was not significant in the sprint population but individual muscle asymmetries exceeded 15%. Gender differences in normalized muscle sizes were not significant. The results of this study suggest that non-uniform hypertrophy patterns, particularly large hip and knee flexors and extensors, are advantageous for fast sprinting. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

NASA Astrophysics Data System (ADS)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.

2017-06-01

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge-Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas-liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D., E-mail: jregele@iastate.edu

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kuttamore » method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.« less

The Evolution of the "Cartesian Connection"

ERIC Educational Resources Information Center

Anderson, Gail M.

2008-01-01

Students often struggle with the connection between algebraic and graphical representations of functions. This overview of the history of the Cartesian coordinate system helps the classroom teacher consider new ways to aid students in making the "Cartesian connection." (Contains 7 figures.)

Position Papers for the First Workshop on Principles and Practice of Constraint Programming Held in Newport, Rhode Island on April 28-30, 1993

DTIC Science & Technology

1993-04-30

There are alternative methods to MBB’s, based on decomposition of space into disjoint cells. These include uniform grid method [Fr84], quadtree-based...space. The IIn grid and quadtree methods there is a trade off between the resolution of the cells (and thus quantity of the cells) and the effectiveness...Mathematics, 13, pp. 221-229, 1983. 9 IFr84] W.R. Franklin, Adaptive grids for geometric operations, Cartographica 21, 2 g 3, pp. 160-167, 1984. (Gun87

Multiresolution strategies for the numerical solution of optimal control problems

NASA Astrophysics Data System (ADS)

Jain, Sachin

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

A variable resolution nonhydrostatic global atmospheric semi-implicit semi-Lagrangian model

NASA Astrophysics Data System (ADS)

Pouliot, George Antoine

2000-10-01

The objective of this project is to develop a variable-resolution finite difference adiabatic global nonhydrostatic semi-implicit semi-Lagrangian (SISL) model based on the fully compressible nonhydrostatic atmospheric equations. To achieve this goal, a three-dimensional variable resolution dynamical core was developed and tested. The main characteristics of the dynamical core can be summarized as follows: Spherical coordinates were used in a global domain. A hydrostatic/nonhydrostatic switch was incorporated into the dynamical equations to use the fully compressible atmospheric equations. A generalized horizontal variable resolution grid was developed and incorporated into the model. For a variable resolution grid, in contrast to a uniform resolution grid, the order of accuracy of finite difference approximations is formally lost but remains close to the order of accuracy associated with the uniform resolution grid provided the grid stretching is not too significant. The SISL numerical scheme was implemented for the fully compressible set of equations. In addition, the generalized minimum residual (GMRES) method with restart and preconditioner was used to solve the three-dimensional elliptic equation derived from the discretized system of equations. The three-dimensional momentum equation was integrated in vector-form to incorporate the metric terms in the calculations of the trajectories. Using global re-analysis data for a specific test case, the model was compared to similar SISL models previously developed. Reasonable agreement between the model and the other independently developed models was obtained. The Held-Suarez test for dynamical cores was used for a long integration and the model was successfully integrated for up to 1200 days. Idealized topography was used to test the variable resolution component of the model. Nonhydrostatic effects were simulated at grid spacings of 400 meters with idealized topography and uniform flow. Using a high-resolution topographic data set and the variable resolution grid, sets of experiments with increasing resolution were performed over specific regions of interest. Using realistic initial conditions derived from re-analysis fields, nonhydrostatic effects were significant for grid spacings on the order of 0.1 degrees with orographic forcing. If the model code was adapted for use in a message passing interface (MPI) on a parallel supercomputer today, it was estimated that a global grid spacing of 0.1 degrees would be achievable for a global model. In this case, nonhydrostatic effects would be significant for most areas. A variable resolution grid in a global model provides a unified and flexible approach to many climate and numerical weather prediction problems. The ability to configure the model from very fine to very coarse resolutions allows for the simulation of atmospheric phenomena at different scales using the same code. We have developed a dynamical core illustrating the feasibility of using a variable resolution in a global model.

Linear and nonlinear properties of numerical methods for the rotating shallow water equations

NASA Astrophysics Data System (ADS)

Eldred, Chris

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal-pentagonal icosahedral grids and cubed-sphere grids are presented. Finally, some remarks and thoughts about the suitability of these two schemes as the basis for atmospheric dynamical development are given.

FUN3D and CFL3D Computations for the First High Lift Prediction Workshop

NASA Technical Reports Server (NTRS)

Park, Michael A.; Lee-Rausch, Elizabeth M.; Rumsey, Christopher L.

2011-01-01

Two Reynolds-averaged Navier-Stokes codes were used to compute flow over the NASA Trapezoidal Wing at high lift conditions for the 1st AIAA CFD High Lift Prediction Workshop, held in Chicago in June 2010. The unstructured-grid code FUN3D and the structured-grid code CFL3D were applied to several different grid systems. The effects of code, grid system, turbulence model, viscous term treatment, and brackets were studied. The SST model on this configuration predicted lower lift than the Spalart-Allmaras model at high angles of attack; the Spalart-Allmaras model agreed better with experiment. Neglecting viscous cross-derivative terms caused poorer prediction in the wing tip vortex region. Output-based grid adaptation was applied to the unstructured-grid solutions. The adapted grids better resolved wake structures and reduced flap flow separation, which was also observed in uniform grid refinement studies. Limitations of the adaptation method as well as areas for future improvement were identified.

CAGI: Computer Aided Grid Interface. A work in progress

NASA Technical Reports Server (NTRS)

Soni, Bharat K.; Yu, Tzu-Yi; Vaughn, David

1992-01-01

Progress realized in the development of a Computer Aided Grid Interface (CAGI) software system in integrating CAD/CAM geometric system output and/or Interactive Graphics Exchange Standard (IGES) files, geometry manipulations associated with grid generation, and robust grid generation methodologies is presented. CAGI is being developed in a modular fashion and will offer fast, efficient and economical response to geometry/grid preparation, allowing the ability to upgrade basic geometry in a step-by-step fashion interactively and under permanent visual control along with minimizing the differences between the actual hardware surface descriptions and corresponding numerical analog. The computer code GENIE is used as a basis. The Non-Uniform Rational B-Splines (NURBS) representation of sculptured surfaces is utilized for surface grid redistribution. The computer aided analysis system, PATRAN, is adapted as a CAD/CAM system. The progress realized in NURBS surface grid generation, the development of IGES transformer, and geometry adaption using PATRAN will be presented along with their applicability to grid generation associated with rocket propulsion applications.

FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

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.

The high performance parallel algorithm for Unified Gas-Kinetic Scheme

NASA Astrophysics Data System (ADS)

Li, Shiyi; Li, Qibing; Fu, Song; Xu, Jinxiu

2016-11-01

A high performance parallel algorithm for UGKS is developed to simulate three-dimensional flows internal and external on arbitrary grid system. The physical domain and velocity domain are divided into different blocks and distributed according to the two-dimensional Cartesian topology with intra-communicators in physical domain for data exchange and other intra-communicators in velocity domain for sum reduction to moment integrals. Numerical results of three-dimensional cavity flow and flow past a sphere agree well with the results from the existing studies and validate the applicability of the algorithm. The scalability of the algorithm is tested both on small (1-16) and large (729-5832) scale processors. The tested speed-up ratio is near linear ashind thus the efficiency is around 1, which reveals the good scalability of the present algorithm.

LES of cavitating flow inside a Diesel injector including dynamic needle movement

NASA Astrophysics Data System (ADS)

Örley, F.; Hickel, S.; Schmidt, S. J.; Adams, N. A.

2015-12-01

We perform large-eddy simulations (LES) of the turbulent, cavitating flow inside a 9-hole solenoid common-rail injector including jet injection into gas during a full injection cycle. The liquid fuel, vapor, and gas phases are modelled by a homogeneous mixture approach. The cavitation model is based on a thermodynamic equilibrium assumption. The geometry of the injector is represented on a Cartesian grid by a conservative cut-element immersed boundary method. The strategy allows for the simulation of complex, moving geometries with sub-cell resolution. We evaluate the effects of needle movement on the cavitation characteristics in the needle seat and tip region during opening and closing of the injector. Moreover, we study the effect of cavitation inside the injector nozzles on primary jet break-up.

Development of direct-inverse 3-D methods for applied transonic aerodynamic wing design and analysis

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1989-01-01

An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.

Solutions to Three-Dimensional Thin-Layer Navier-Stokes Equations in Rotating Coordinates for Flow Through Turbomachinery

NASA Technical Reports Server (NTRS)

Ghosh, Amrit Raj

1996-01-01

The viscous, Navier-Stokes solver for turbomachinery applications, MSUTC has been modified to include the rotating frame formulation. The three-dimensional thin-layer Navier-Stokes equations have been cast in a rotating Cartesian frame enabling the freezing of grid motion. This also allows the flow-field associated with an isolated rotor to be viewed as a steady-state problem. Consequently, local time stepping can be used to accelerate convergence. The formulation is validated by running NASA's Rotor 67 as the test case. results are compared between the rotating frame code and the absolute frame code. The use of the rotating frame approach greatly enhances the performance of the code with respect to savings in computing time, without degradation of the solution.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography.

PubMed

Xu, Daguang; Huang, Yong; Kang, Jin U

2014-06-16

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Improved image quality of cone beam CT scans for radiotherapy image guidance using fiber-interspaced antiscatter grid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stankovic, Uros; Herk, Marcel van; Ploeger, Lennert S.

Purpose: Medical linear accelerator mounted cone beam CT (CBCT) scanner provides useful soft tissue contrast for purposes of image guidance in radiotherapy. The presence of extensive scattered radiation has a negative effect on soft tissue visibility and uniformity of CBCT scans. Antiscatter grids (ASG) are used in the field of diagnostic radiography to mitigate the scatter. They usually do increase the contrast of the scan, but simultaneously increase the noise. Therefore, and considering other scatter mitigation mechanisms present in a CBCT scanner, the applicability of ASGs with aluminum interspacing for a wide range of imaging conditions has been inconclusive inmore » previous studies. In recent years, grids using fiber interspacers have appeared, providing grids with higher scatter rejection while maintaining reasonable transmission of primary radiation. The purpose of this study was to evaluate the impact of one such grid on CBCT image quality. Methods: The grid used (Philips Medical Systems) had ratio of 21:1, frequency 36 lp/cm, and nominal selectivity of 11.9. It was mounted on the kV flat panel detector of an Elekta Synergy linear accelerator and tested in a phantom and a clinical study. Due to the flex of the linac and presence of gridline artifacts an angle dependent gain correction algorithm was devised to mitigate resulting artifacts. Scan reconstruction was performed using XVI4.5 augmented with inhouse developed image lag correction and Hounsfield unit calibration. To determine the necessary parameters for Hounsfield unit calibration and software scatter correction parameters, the Catphan 600 (The Phantom Laboratory) phantom was used. Image quality parameters were evaluated using CIRS CBCT Image Quality and Electron Density Phantom (CIRS) in two different geometries: one modeling head and neck and other pelvic region. Phantoms were acquired with and without the grid and reconstructed with and without software correction which was adapted for the different acquisition scenarios. Parameters used in the phantom study weret{sub cup} for nonuniformity and contrast-to-noise ratio (CNR) for soft tissue visibility. Clinical scans were evaluated in an observer study in which four experienced radiotherapy technologists rated soft tissue visibility and uniformity of scans with and without the grid. Results: The proposed angle dependent gain correction algorithm suppressed the visible ring artifacts. Grid had a beneficial impact on nonuniformity, contrast to noise ratio, and Hounsfield unit accuracy for both scanning geometries. The nonuniformity reduced by 90% for head sized object and 91% for pelvic-sized object. CNR improved compared to no corrections on average by a factor 2.8 for the head sized object, and 2.2 for the pelvic sized phantom. Grid outperformed software correction alone, but adding additional software correction to the grid was overall the best strategy. In the observer study, a significant improvement was found in both soft tissue visibility and nonuniformity of scans when grid is used. Conclusions: The evaluated fiber-interspaced grid improved the image quality of the CBCT system for broad range of imaging conditions. Clinical scans show significant improvement in soft tissue visibility and uniformity without the need to increase the imaging dose.« less

Improved image quality of cone beam CT scans for radiotherapy image guidance using fiber-interspaced antiscatter grid.

PubMed

Stankovic, Uros; van Herk, Marcel; Ploeger, Lennert S; Sonke, Jan-Jakob

2014-06-01

Medical linear accelerator mounted cone beam CT (CBCT) scanner provides useful soft tissue contrast for purposes of image guidance in radiotherapy. The presence of extensive scattered radiation has a negative effect on soft tissue visibility and uniformity of CBCT scans. Antiscatter grids (ASG) are used in the field of diagnostic radiography to mitigate the scatter. They usually do increase the contrast of the scan, but simultaneously increase the noise. Therefore, and considering other scatter mitigation mechanisms present in a CBCT scanner, the applicability of ASGs with aluminum interspacing for a wide range of imaging conditions has been inconclusive in previous studies. In recent years, grids using fiber interspacers have appeared, providing grids with higher scatter rejection while maintaining reasonable transmission of primary radiation. The purpose of this study was to evaluate the impact of one such grid on CBCT image quality. The grid used (Philips Medical Systems) had ratio of 21:1, frequency 36 lp/cm, and nominal selectivity of 11.9. It was mounted on the kV flat panel detector of an Elekta Synergy linear accelerator and tested in a phantom and a clinical study. Due to the flex of the linac and presence of gridline artifacts an angle dependent gain correction algorithm was devised to mitigate resulting artifacts. Scan reconstruction was performed using XVI4.5 augmented with inhouse developed image lag correction and Hounsfield unit calibration. To determine the necessary parameters for Hounsfield unit calibration and software scatter correction parameters, the Catphan 600 (The Phantom Laboratory) phantom was used. Image quality parameters were evaluated using CIRS CBCT Image Quality and Electron Density Phantom (CIRS) in two different geometries: one modeling head and neck and other pelvic region. Phantoms were acquired with and without the grid and reconstructed with and without software correction which was adapted for the different acquisition scenarios. Parameters used in the phantom study were t(cup) for nonuniformity and contrast-to-noise ratio (CNR) for soft tissue visibility. Clinical scans were evaluated in an observer study in which four experienced radiotherapy technologists rated soft tissue visibility and uniformity of scans with and without the grid. The proposed angle dependent gain correction algorithm suppressed the visible ring artifacts. Grid had a beneficial impact on nonuniformity, contrast to noise ratio, and Hounsfield unit accuracy for both scanning geometries. The nonuniformity reduced by 90% for head sized object and 91% for pelvic-sized object. CNR improved compared to no corrections on average by a factor 2.8 for the head sized object, and 2.2 for the pelvic sized phantom. Grid outperformed software correction alone, but adding additional software correction to the grid was overall the best strategy. In the observer study, a significant improvement was found in both soft tissue visibility and nonuniformity of scans when grid is used. The evaluated fiber-interspaced grid improved the image quality of the CBCT system for broad range of imaging conditions. Clinical scans show significant improvement in soft tissue visibility and uniformity without the need to increase the imaging dose.

Earth Science Data Grid System

NASA Astrophysics Data System (ADS)

Chi, Y.; Yang, R.; Kafatos, M.

2004-05-01

The Earth Science Data Grid System (ESDGS) is a software system in support of earth science data storage and access. It is built upon the Storage Resource Broker (SRB) data grid technology. We have developed a complete data grid system consistent of SRB server providing users uniform access to diverse storage resources in a heterogeneous computing environment and metadata catalog server (MCAT) managing the metadata associated with data set, users, and resources. We also develop the earth science application metadata; geospatial, temporal, and content-based indexing; and some other tools. In this paper, we will describe software architecture and components of the data grid system, and use a practical example in support of storage and access of rainfall data from the Tropical Rainfall Measuring Mission (TRMM) to illustrate its functionality and features.

High-resolution field shaping utilizing a masked multileaf collimator.

PubMed

Williams, P C; Cooper, P

2000-08-01

Multileaf collimators (MLCs) have become an important tool in the modern radiotherapy department. However, the current limit of resolution (1 cm at isocentre) can be too coarse for acceptable shielding of all fields. A number of mini- and micro-MLCs have been developed, with thinner leaves to achieve approved resolution. Currently however, such devices are limited to modest field sizes and stereotactic applications. This paper proposes a new method of high-resolution beam collimation by use of a tertiary grid collimator situated below the conventional MLC. The width of each slit in the grid is a submultiple of the MLC width. A composite shaped field is thus built up from a series of subfields, with the main MLC defining the length of each strip within each subfield. Presented here are initial findings using a prototype device. The beam uniformity achievable with such a device was examined by measuring transmission profiles through the grid using a diode. Profiles thus measured were then copied and superposed to generate composite beams, from which the uniformity achievable could be assessed. With the average dose across the profile normalized to 100%, hot spots up to 5.0% and troughs of 3% were identified for a composite beam of 2 x 5.0 mm grids, as measured at Dmax for a 6 MV beam. For a beam composed from 4 x 2.5 mm grids, the maximum across the profile was 3.0% above the average, and the minimum 2.5% below. Actual composite profiles were also formed using the integrating properties of film, with the subfield indexing performed using an engineering positioning stage. The beam uniformity for these fields compared well with that achieved in theory using the diode measurements. Finally sine wave patterns were generated to demonstrate the potential improvements in field shaping and conformity using this device as opposed to the conventional MLC alone. The scalloping effect on the field edge commonly seen on MLC fields was appreciably reduced by use of 2 x 5.0 mm grids, and still further by the use of 4 x 2.5 mm grids, as would be expected. This was also achieved with a small or negligible broadening of the beam penumbra as measured at Dmax.

Information Power Grid Posters

NASA Technical Reports Server (NTRS)

Vaziri, Arsi

2003-01-01

This document is a summary of the accomplishments of the Information Power Grid (IPG). Grids are an emerging technology that provide seamless and uniform access to the geographically dispersed, computational, data storage, networking, instruments, and software resources needed for solving large-scale scientific and engineering problems. The goal of the NASA IPG is to use NASA's remotely located computing and data system resources to build distributed systems that can address problems that are too large or complex for a single site. The accomplishments outlined in this poster presentation are: access to distributed data, IPG heterogeneous computing, integration of large-scale computing node into distributed environment, remote access to high data rate instruments,and exploratory grid environment.

GEOS-5 Seasonal Forecast System: ENSO Prediction Skill and Bias

NASA Technical Reports Server (NTRS)

Borovikov, Anna; Kovach, Robin; Marshak, Jelena

2018-01-01

The GEOS-5 AOGCM known as S2S-1.0 has been in service from June 2012 through January 2018 (Borovikov et al. 2017). The atmospheric component of S2S-1.0 is Fortuna-2.5, the same that was used for the Modern-Era Retrospective Analysis for Research and Applications (MERRA), but with adjusted parameterization of moist processes and turbulence. The ocean component is the Modular Ocean Model version 4 (MOM4). The sea ice component is the Community Ice CodE, version 4 (CICE). The land surface model is a catchment-based hydrological model coupled to the multi-layer snow model. The AGCM uses a Cartesian grid with a 1 deg × 1.25 deg horizontal resolution and 72 hybrid vertical levels with the upper most level at 0.01 hPa. OGCM nominal resolution of the tripolar grid is 1/2 deg, with a meridional equatorial refinement to 1/4 deg. In the coupled model initialization, selected atmospheric variables are constrained with MERRA. The Goddard Earth Observing System integrated Ocean Data Assimilation System (GEOS-iODAS) is used for both ocean state and sea ice initialization. SST, T and S profiles and sea ice concentration were assimilated.

ESMPy and OpenClimateGIS: Python Interfaces for High Performance Grid Remapping and Geospatial Dataset Manipulation

NASA Astrophysics Data System (ADS)

O'Kuinghttons, Ryan; Koziol, Benjamin; Oehmke, Robert; DeLuca, Cecelia; Theurich, Gerhard; Li, Peggy; Jacob, Joseph

2016-04-01

The Earth System Modeling Framework (ESMF) Python interface (ESMPy) supports analysis and visualization in Earth system modeling codes by providing access to a variety of tools for data manipulation. ESMPy started as a Python interface to the ESMF grid remapping package, which provides mature and robust high-performance and scalable grid remapping between 2D and 3D logically rectangular and unstructured grids and sets of unconnected data. ESMPy now also interfaces with OpenClimateGIS (OCGIS), a package that performs subsetting, reformatting, and computational operations on climate datasets. ESMPy exposes a subset of ESMF grid remapping utilities. This includes bilinear, finite element patch recovery, first-order conservative, and nearest neighbor grid remapping methods. There are also options to ignore unmapped destination points, mask points on source and destination grids, and provide grid structure in the polar regions. Grid remapping on the sphere takes place in 3D Cartesian space, so the pole problem is not an issue as it can be with other grid remapping software. Remapping can be done between any combination of 2D and 3D logically rectangular and unstructured grids with overlapping domains. Grid pairs where one side of the regridding is represented by an appropriate set of unconnected data points, as is commonly found with observational data streams, is also supported. There is a developing interoperability layer between ESMPy and OpenClimateGIS (OCGIS). OCGIS is a pure Python, open source package designed for geospatial manipulation, subsetting, and computation on climate datasets stored in local NetCDF files or accessible remotely via the OPeNDAP protocol. Interfacing with OCGIS has brought GIS-like functionality to ESMPy (i.e. subsetting, coordinate transformations) as well as additional file output formats (i.e. CSV, ESRI Shapefile). ESMPy is distinguished by its strong emphasis on open source, community governance, and distributed development. The user base has grown quickly, and the package is integrating with several other software tools and frameworks. These include the Ultrascale Visualization Climate Data Analysis Tools (UV-CDAT), Iris, PyFerret, cfpython, and the Community Surface Dynamics Modeling System (CSDMS). ESMPy minimum requirements include Python 2.6, Numpy 1.6.1 and an ESMF installation. Optional dependencies include NetCDF and OCGIS-related dependencies: GDAL, Shapely, and Fiona. ESMPy is regression tested nightly, and supported on Darwin, Linux and Cray systems with the GNU compiler suite and MPI communications. OCGIS is supported on Linux, and also undergoes nightly regression testing. Both packages are installable from Anaconda channels. Upcoming development plans for ESMPy involve development of a higher order conservative grid remapping method. Future OCGIS development will focus on mesh and location stream interoperability and streamlined access to ESMPy's MPI implementation.

Grid Convergence for Turbulent Flows(Invited)

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Rumsey, Christopher L.; Schwoppe, Axel

2015-01-01

A detailed grid convergence study has been conducted to establish accurate reference solutions corresponding to the one-equation linear eddy-viscosity Spalart-Allmaras turbulence model for two dimensional turbulent flows around the NACA 0012 airfoil and a flat plate. The study involved three widely used codes, CFL3D (NASA), FUN3D (NASA), and TAU (DLR), and families of uniformly refined structured grids that differ in the grid density patterns. Solutions computed by different codes on different grid families appear to converge to the same continuous limit, but exhibit different convergence characteristics. The grid resolution in the vicinity of geometric singularities, such as a sharp trailing edge, is found to be the major factor affecting accuracy and convergence of discrete solutions, more prominent than differences in discretization schemes and/or grid elements. The results reported for these relatively simple turbulent flows demonstrate that CFL3D, FUN3D, and TAU solutions are very accurate on the finest grids used in the study, but even those grids are not sufficient to conclusively establish an asymptotic convergence order.

Rethinking the birthing body: Cartesian dualism and perinatal nursing.

PubMed

Goldberg, Lisa

2002-03-01

This paper highlights the pervasive influence of a Cartesian metaphysics on the medical paradigm and its profound impact on the practice of perinatal nursing in North America. Modern perinatal health care practices are founded on a Cartesian metaphysics that reduce birthing women to the status of object. Such practices deny the holistic aims of perinatal nursing. A philosophical inquiry informs the tenets of this metaphysical discussion regarding the foundations of perinatal nursing practices. Although perinatal health care is founded on a Cartesian metaphysics, an alternative paradigm of embodied practice is suggested as a way of viewing birthing women as embodied subjects. If the foundations of health care, which have been built on a Cartesian metaphysics, are not re-examined, perinatal nurses will be providing care that further reduce women to the status of object.

Quantification of turbulence and velocity in stenotic flow using spiral three-dimensional phase-contrast MRI.

PubMed

Petersson, Sven; Dyverfeldt, Petter; Sigfridsson, Andreas; Lantz, Jonas; Carlhäll, Carl-Johan; Ebbers, Tino

2016-03-01

Evaluate spiral three-dimensional (3D) phase contrast MRI for the assessment of turbulence and velocity in stenotic flow. A-stack-of-spirals 3D phase contrast MRI sequence was evaluated in vitro against a conventional Cartesian sequence. Measurements were made in a flow phantom with a 75% stenosis. Both spiral and Cartesian imaging were performed using different scan orientations and flow rates. Volume flow rate, maximum velocity and turbulent kinetic energy (TKE) were computed for both methods. Moreover, the estimated TKE was compared with computational fluid dynamics (CFD) data. There was good agreement between the turbulent kinetic energy from the spiral, Cartesian and CFD data. Flow rate and maximum velocity from the spiral data agreed well with Cartesian data. As expected, the short echo time of the spiral sequence resulted in less prominent displacement artifacts compared with the Cartesian sequence. However, both spiral and Cartesian flow rate estimates were sensitive to displacement when the flow was oblique to the encoding directions. Spiral 3D phase contrast MRI appears favorable for the assessment of stenotic flow. The spiral sequence was more than three times faster and less sensitive to displacement artifacts when compared with a conventional Cartesian sequence. © 2015 Wiley Periodicals, Inc.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

NASA Astrophysics Data System (ADS)

Coco, Armando; Russo, Giovanni

2018-05-01

In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

Optimized Routing of Intelligent, Mobile Sensors for Dynamic, Data-Driven Sampling

DTIC Science & Technology

2016-09-27

nonstationary random process that requires nonuniform sampling. The ap- proach incorporates complementary representations of an unknown process: the first...lookup table as follows. A uniform grid is created in the r-domain and mapped to the R-domain, which produces a nonuniform grid of locations in the R...vehicle coverage algorithm that invokes the coor- dinate transformation from the previous section to generate nonuniform sampling trajectories [54]. We

Method and apparatus for jetting, manufacturing and attaching uniform solder balls

DOEpatents

Yost, F.G.; Frear, D.R.; Schmale, D.T.

1999-01-05

An apparatus and process are disclosed for jetting molten solder in the form of balls directly onto all the metallized interconnects lands for a ball grid array package in one step with no solder paste required. Molten solder is jetted out of a grid of holes using a piston attached to a piezoelectric crystal. When voltage is applied to the crystal it expands forcing the piston to extrude a desired volume of solder through holes in the aperture plate. When the voltage is decreased the piston reverses motion creating an instability in the molten solder at the aperture plate surface and thereby forming spherical solder balls that fall onto a metallized substrate. The molten solder balls land on the substrate and form a metallurgical bond with the metallized lands. The size of the solder balls is determined by a combination of the size of the holes in the aperture plate, the duration of the piston pulse, and the displacement of the piston. The layout of the balls is dictated by the location of the hooks in the grid. Changes in ball size and layout can be easily accomplished by changing the grid plate. This invention also allows simple preparation of uniform balls for subsequent supply to BGA users. 7 figs.

Method and apparatus for jetting, manufacturing and attaching uniform solder balls

DOEpatents

Yost, Frederick G.; Frear, Darrel R.; Schmale, David T.

1999-01-01

An apparatus and process for jetting molten solder in the form of balls directly onto all the metallized interconnects lands for a ball grid array package in one step with no solder paste required. Molten solder is jetted out of a grid of holes using a piston attached to a piezoelectric crystal. When voltage is applied to the crystal it expands forcing the piston to extrude a desired volume of solder through holes in the aperture plate. When the voltage is decreased the piston reverses motion creating an instability in the molten solder at the aperture plate surface and thereby forming spherical solder balls that fall onto a metallized substrate. The molten solder balls land on the substrate and form a metallurgical bond with the metallized lands. The size of the solder balls is determined by a combination of the size of the holes in the aperture plate, the duration of the piston pulse, and the displacement of the piston. The layout of the balls is dictated by the location of the hooks in the grid. Changes in ball size and layout can be easily accomplished by changing the grid plate. This invention also allows simple preparation of uniform balls for subsequent supply to BGA users.

An efficient spectral method for the simulation of dynamos in Cartesian geometry and its implementation on massively parallel computers

NASA Astrophysics Data System (ADS)

Stellmach, Stephan; Hansen, Ulrich

2008-05-01

Numerical simulations of the process of convection and magnetic field generation in planetary cores still fail to reach geophysically realistic control parameter values. Future progress in this field depends crucially on efficient numerical algorithms which are able to take advantage of the newest generation of parallel computers. Desirable features of simulation algorithms include (1) spectral accuracy, (2) an operation count per time step that is small and roughly proportional to the number of grid points, (3) memory requirements that scale linear with resolution, (4) an implicit treatment of all linear terms including the Coriolis force, (5) the ability to treat all kinds of common boundary conditions, and (6) reasonable efficiency on massively parallel machines with tens of thousands of processors. So far, algorithms for fully self-consistent dynamo simulations in spherical shells do not achieve all these criteria simultaneously, resulting in strong restrictions on the possible resolutions. In this paper, we demonstrate that local dynamo models in which the process of convection and magnetic field generation is only simulated for a small part of a planetary core in Cartesian geometry can achieve the above goal. We propose an algorithm that fulfills the first five of the above criteria and demonstrate that a model implementation of our method on an IBM Blue Gene/L system scales impressively well for up to O(104) processors. This allows for numerical simulations at rather extreme parameter values.

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, He; Luo, Li -Shi; Li, Rui

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE PAGES

Huang, He; Luo, Li -Shi; Li, Rui; ...

2018-05-17

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

Improved genetic algorithm for the protein folding problem by use of a Cartesian combination operator.

PubMed Central

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

Sinter of uniform, predictable, blemish-free nickel plaque for large aerospace nickel cadmium cells

NASA Technical Reports Server (NTRS)

Seiger, H. N.

1975-01-01

A series of nickel slurry compositions were tested. Important slurry parameters were found to be the nature of the binder, a pore former and the method of mixing. A slow roll mixing which is non-turbulent successfully eliminated entrapped air so that bubbles and pockets were avoided in the sinter. A slurry applicator was developed which enabled an equal quantity of slurry to be applied to both sides of the grid. Sintering in a furnace having a graded atmosphere characteristic, ranging from oxidizing to strongly reducing, improved adhesion of porous sinter to grid and resulted in a uniform welding of nickel particles to each other throughout the plaque. Sintering was carried out in a horizontal furnace having three heating zones and 16 heating control circuits. Tests used for plaque evaluation include (1) appearance, (2) grid location and adhesion, (3) mechanical strength, (4) thickness, (5) weight per unit area, (6) void volume per unit area, (7) surface area and (8) electrical resistance. Plaque material was impregnated using Heliotek proprietary processes and 100 AH cells were fabricated.

Accurate finite difference methods for time-harmonic wave propagation

NASA Technical Reports Server (NTRS)

Harari, Isaac; Turkel, Eli

1994-01-01

Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.

GENIE(++): A Multi-Block Structured Grid System

NASA Technical Reports Server (NTRS)

Williams, Tonya; Nadenthiran, Naren; Thornburg, Hugh; Soni, Bharat K.

1996-01-01

The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.

The Computing and Data Grid Approach: Infrastructure for Distributed Science Applications

NASA Technical Reports Server (NTRS)

Johnston, William E.

2002-01-01

With the advent of Grids - infrastructure for using and managing widely distributed computing and data resources in the science environment - there is now an opportunity to provide a standard, large-scale, computing, data, instrument, and collaboration environment for science that spans many different projects and provides the required infrastructure and services in a relatively uniform and supportable way. Grid technology has evolved over the past several years to provide the services and infrastructure needed for building 'virtual' systems and organizations. We argue that Grid technology provides an excellent basis for the creation of the integrated environments that can combine the resources needed to support the large- scale science projects located at multiple laboratories and universities. We present some science case studies that indicate that a paradigm shift in the process of science will come about as a result of Grids providing transparent and secure access to advanced and integrated information and technologies infrastructure: powerful computing systems, large-scale data archives, scientific instruments, and collaboration tools. These changes will be in the form of services that can be integrated with the user's work environment, and that enable uniform and highly capable access to these computers, data, and instruments, regardless of the location or exact nature of these resources. These services will integrate transient-use resources like computing systems, scientific instruments, and data caches (e.g., as they are needed to perform a simulation or analyze data from a single experiment); persistent-use resources. such as databases, data catalogues, and archives, and; collaborators, whose involvement will continue for the lifetime of a project or longer. While we largely address large-scale science in this paper, Grids, particularly when combined with Web Services, will address a broad spectrum of science scenarios. both large and small scale.

Aeroelastic Deflection of NURBS Geometry

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

1998-01-01

The purpose of this paper is to present an algorithm for using NonUniform Rational B-Spline (NURBS) representation in an aeroelastic loop. The algorithm is based on creating a least-squares NURBS surface representing the aeroelastic defection. The resulting NURBS surfaces are used to update either the original Computer- Aided Design (CAD) model, Computational Structural Mechanics (CSM) grid or the Computational Fluid Dynamics (CFD) grid. Results are presented for a generic High-Speed Civil Transport (HSCT).

The CRONOS Code for Astrophysical Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Kissmann, R.; Kleimann, J.; Krebl, B.; Wiengarten, T.

2018-06-01

We describe the magnetohydrodynamics (MHD) code CRONOS, which has been used in astrophysics and space-physics studies in recent years. CRONOS has been designed to be easily adaptable to the problem in hand, where the user can expand or exchange core modules or add new functionality to the code. This modularity comes about through its implementation using a C++ class structure. The core components of the code include solvers for both hydrodynamical (HD) and MHD problems. These problems are solved on different rectangular grids, which currently support Cartesian, spherical, and cylindrical coordinates. CRONOS uses a finite-volume description with different approximate Riemann solvers that can be chosen at runtime. Here, we describe the implementation of the code with a view toward its ongoing development. We illustrate the code’s potential through several (M)HD test problems and some astrophysical applications.

Design and implementation of a 3D-MR/CT geometric image distortion phantom/analysis system for stereotactic radiosurgery.

PubMed

Damyanovich, A Z; Rieker, M; Zhang, B; Bissonnette, J-P; Jaffray, D A

2018-03-27

The design, construction and application of a multimodality, 3D magnetic resonance/computed tomography (MR/CT) image distortion phantom and analysis system for stereotactic radiosurgery (SRS) is presented. The phantom is characterized by (1) a 1 × 1 × 1 (cm) 3 MRI/CT-visible 3D-Cartesian grid; (2) 2002 grid vertices that are 3D-intersections of MR-/CT-visible 'lines' in all three orthogonal planes; (3) a 3D-grid that is MR-signal positive/CT-signal negative; (4) a vertex distribution sufficiently 'dense' to characterize geometrical parameters properly, and (5) a grid/vertex resolution consistent with SRS localization accuracy. When positioned correctly, successive 3D-vertex planes along any orthogonal axis of the phantom appear as 1 × 1 (cm) 2 -2D grids, whereas between vertex planes, images are defined by 1 × 1 (cm) 2 -2D arrays of signal points. Image distortion is evaluated using a centroid algorithm that automatically identifies the center of each 3D-intersection and then calculates the deviations dx, dy, dz and dr for each vertex point; the results are presented as a color-coded 2D or 3D distribution of deviations. The phantom components and 3D-grid are machined to sub-millimeter accuracy, making the device uniquely suited to SRS applications; as such, we present it here in a form adapted for use with a Leksell stereotactic frame. Imaging reproducibility was assessed via repeated phantom imaging across ten back-to-back scans; 80%-90% of the differences in vertex deviations dx, dy, dz and dr between successive 3 T MRI scans were found to be  ⩽0.05 mm for both axial and coronal acquisitions, and over  >95% of the differences were observed to be  ⩽0.05 mm for repeated CT scans, clearly demonstrating excellent reproducibility. Applications of the 3D-phantom/analysis system are presented, using a 32-month time-course assessment of image distortion/gradient stability and statistical control chart for 1.5 T and 3 T GE TwinSpeed MRI systems.

Design and implementation of a 3D-MR/CT geometric image distortion phantom/analysis system for stereotactic radiosurgery

NASA Astrophysics Data System (ADS)

Damyanovich, A. Z.; Rieker, M.; Zhang, B.; Bissonnette, J.-P.; Jaffray, D. A.

2018-04-01

The design, construction and application of a multimodality, 3D magnetic resonance/computed tomography (MR/CT) image distortion phantom and analysis system for stereotactic radiosurgery (SRS) is presented. The phantom is characterized by (1) a 1 × 1 × 1 (cm)3 MRI/CT-visible 3D-Cartesian grid; (2) 2002 grid vertices that are 3D-intersections of MR-/CT-visible ‘lines’ in all three orthogonal planes; (3) a 3D-grid that is MR-signal positive/CT-signal negative; (4) a vertex distribution sufficiently ‘dense’ to characterize geometrical parameters properly, and (5) a grid/vertex resolution consistent with SRS localization accuracy. When positioned correctly, successive 3D-vertex planes along any orthogonal axis of the phantom appear as 1 × 1 (cm)2-2D grids, whereas between vertex planes, images are defined by 1 × 1 (cm)2-2D arrays of signal points. Image distortion is evaluated using a centroid algorithm that automatically identifies the center of each 3D-intersection and then calculates the deviations dx, dy, dz and dr for each vertex point; the results are presented as a color-coded 2D or 3D distribution of deviations. The phantom components and 3D-grid are machined to sub-millimeter accuracy, making the device uniquely suited to SRS applications; as such, we present it here in a form adapted for use with a Leksell stereotactic frame. Imaging reproducibility was assessed via repeated phantom imaging across ten back-to-back scans; 80%–90% of the differences in vertex deviations dx, dy, dz and dr between successive 3 T MRI scans were found to be  ⩽0.05 mm for both axial and coronal acquisitions, and over  >95% of the differences were observed to be  ⩽0.05 mm for repeated CT scans, clearly demonstrating excellent reproducibility. Applications of the 3D-phantom/analysis system are presented, using a 32-month time-course assessment of image distortion/gradient stability and statistical control chart for 1.5 T and 3 T GE TwinSpeed MRI systems.

On the improvement for charging large-scale flexible electrostatic actuators

NASA Astrophysics Data System (ADS)

Liao, Hsu-Ching; Chen, Han-Long; Su, Yu-Hao; Chen, Yu-Chi; Ko, Wen-Ching; Liou, Chang-Ho; Wu, Wen-Jong; Lee, Chih-Kung

2011-04-01

Recently, the development of flexible electret based electrostatic actuator has been widely discussed. The devices was shown to have high sound quality, energy saving, flexible structure and can be cut to any shape. However, achieving uniform charge on the electret diaphragm is one of the most critical processes needed to have the speaker ready for large-scale production. In this paper, corona discharge equipment contains multi-corona probes and grid bias was set up to inject spatial charges within the electret diaphragm. The optimal multi-corona probes system was adjusted to achieve uniform charge distribution of electret diaphragm. The processing conditions include the distance between the corona probes, the voltages of corona probe and grid bias, etc. We assembled the flexible electret loudspeakers first and then measured their sound pressure and beam pattern. The uniform charge distribution within the electret diaphragm based flexible electret loudspeaker provided us with the opportunity to shape the loudspeaker arbitrarily and to tailor the sound distribution per specifications request. Some of the potential futuristic applications for this device such as sound poster, smart clothes, and sound wallpaper, etc. were discussed as well.

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guba, O.; Taylor, M. A.; Ullrich, P. A.

2014-11-27

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, formore » regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

The spectral element method on variable resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE PAGES

Guba, O.; Taylor, M. A.; Ullrich, P. A.; ...

2014-06-25

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable resolution grids using the shallow water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution dependent coefficient. For the spectral element method with variable resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity ismore » constructed so that for regions of uniform resolution it matches the traditional constant coefficient hyperviscsosity. With the tensor hyperviscosity the large scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications where long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

A multigrid method for steady Euler equations on unstructured adaptive grids

NASA Technical Reports Server (NTRS)

Riemslagh, Kris; Dick, Erik

1993-01-01

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Aeroacoustic Simulations of a Nose Landing Gear with FUN3D: A Grid Refinement Study

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.; Khorrami, Mehdi R.; Lockard, David P.

2017-01-01

A systematic grid refinement study is presented for numerical simulations of a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise (Registered Trademark) grid generation software are used for numerical simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A set of grids was generated in this manner to create a family of uniformly refined grids. The finest grid was then modified to coarsen the wall-normal spacing to create a grid suitable for the wall-function implementation in FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence modeling approach is used for these simulations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. These CFD solutions are used as input to a FfowcsWilliams-Hawkings (FW-H) noise propagation code to compute the farfield noise levels. The agreement of the computed results with the experimental data improves as the grid is refined.

Estimating scatter in cone beam CT with striped ratio grids: A preliminary investigation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hsieh, Scott, E-mail: sshsieh@stanford.edu

2016-09-15

Purpose: To propose a new method for estimating scatter in x-ray imaging. Conventional antiscatter grids reject scatter at an efficiency that is constant or slowly varying over the surface of the grid. A striped ratio antiscatter grid, composed of stripes that alternate between high and low grid ratio, could be used instead. Such a striped ratio grid would reduce scatter-to-primary ratio as a conventional grid would, but more importantly, the signal discontinuities at the boundaries of stripes can be used to estimate local scatter content. Methods: Signal discontinuities provide information on scatter, but are contaminated by variation in primary radiation.more » A nonlinear image processing algorithm is used to estimate the scatter content in the presence of primary variation. We emulated a striped ratio grid by imaging phantoms with two sequential CT scans, one with and one without a conventional grid. These two scans are processed together to mimic a striped ratio grid. This represents a best case limit of the striped ratio grid, in that the extent of grid ratio modulation is very high and the scatter contrast is maximized. Results: In a uniform cylinder, the striped ratio grid virtually eliminates cupping. Artifacts from scatter are improved in an anthropomorphic phantom. Some banding artifacts are induced by the striped ratio grid. Conclusions: Striped ratio grids could be a simple and effective evolution of conventional antiscatter grids. Construction and validation of a physical prototype remains an important future step.« less

Regional Data Assimilation Using a Stretched-Grid Approach and Ensemble Calculations

NASA Technical Reports Server (NTRS)

Fox-Rabinovitz, M. S.; Takacs, L. L.; Govindaraju, R. C.; Atlas, Robert (Technical Monitor)

2002-01-01

The global variable resolution stretched grid (SG) version of the Goddard Earth Observing System (GEOS) Data Assimilation System (DAS) incorporating the GEOS SG-GCM (Fox-Rabinovitz 2000, Fox-Rabinovitz et al. 2001a,b), has been developed and tested as an efficient tool for producing regional analyses and diagnostics with enhanced mesoscale resolution. The major area of interest with enhanced regional resolution used in different SG-DAS experiments includes a rectangle over the U.S. with 50 or 60 km horizontal resolution. The analyses and diagnostics are produced for all mandatory levels from the surface to 0.2 hPa. The assimilated regional mesoscale products are consistent with global scale circulation characteristics due to using the SG-approach. Both the stretched grid and basic uniform grid DASs use the same amount of global grid-points and are compared in terms of regional product quality.

FDTD simulation of transmittance characteristics of one-dimensional conducting electrodes.

PubMed

Lee, Kilbock; Song, Seok Ho; Ahn, Jinho

2014-03-24

We investigated transparent conducting electrodes consisting of periodic one-dimensional Ag or Al grids with widths from 25 nm to 5 μm via the finite-difference time-domain method. To retain high transmittance, two grid configurations with opening ratios of 90% and 95% were simulated. Polarization-dependent characteristics of the transmission spectra revealed that the overall transmittance of micron-scale grid electrodes may be estimated by the sum of light power passing through the uncovered area and the light power penetrating the covered metal layer. However, several dominant physical phenomena significantly affect the transmission spectra of the nanoscale grids: Rayleigh anomaly, transmission decay in TE polarized mode, and localized surface plasmon resonance. We conclude that, for applications of transparent electrodes, the critical feature sizes of conducting 1D grids should not be less than the wavelength scale in order to maintain uniform and predictable transmission spectra and low electrical resistivity.

TU-H-BRC-07: Therapeutic Benefit in Spatially Fractionated Radiotherapy (GRID) Using Helical Tomotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narayanasamy, G; Zhang, X; Paudel, N

Purpose: The aim of this project is to study the therapeutic ratio (TR) for helical Tomotherapy (HT) based spatially fractionated radiotherapy (GRID). Estimation of TR was based on the linear-quadratic cell survival model by comparing the normal cell survival in a HT GRID to that of a uniform dose delivery in an open-field for the same tumor survival. Methods: HT GRID plan was generated using a patient specific virtual GRID block pattern of non-divergent, cylinder shaped holes using MLCs. TR was defined as the ratio of normal tissue surviving fraction (SF) under HT GRID irradiation to an open field irradiationmore » with an equivalent dose that result in the same tumor cell SF. The ratio was estimated from DVH data on ten patient plans with deep seated, bulky tumor approved by the treating radiation oncologist. Dependence of the TR values on radio-sensitivity of the tumor cells and prescription dose were also analyzed. Results: The mean ± standard deviation (SD) of TR was 4.0±0.7 (range: 3.1 to 5.5) for the 10 patients with single fraction dose of 20 Gy and tumor cell SF of 0.5 at 2 Gy. In addition, mean±SD of TR = 1±0.1 and 18.0±5.1 were found for tumor with SF of 0.3 and 0.7, respectively. Reducing the prescription dose to 15 and 10 Gy lowered the TR to 2.0±0.2 and 1.2±0.04 for a tumor cell SF of 0.5 at 2 Gy. In this study, the SF of normal cells was assumed to be 0.5 at 2 Gy. Conclusion: HT GRID displayed a significant therapeutic advantage over uniform dose from an open field irradiation. TR increases with the radioresistance of the tumor cells and with prescription dose.« less

Technical Report Series on Global Modeling and Data Assimilation. Volume 16; Filtering Techniques on a Stretched Grid General Circulation Model

NASA Technical Reports Server (NTRS)

Takacs, Lawrence L.; Sawyer, William; Suarez, Max J. (Editor); Fox-Rabinowitz, Michael S.

1999-01-01

This report documents the techniques used to filter quantities on a stretched grid general circulation model. Standard high-latitude filtering techniques (e.g., using an FFT (Fast Fourier Transformations) to decompose and filter unstable harmonics at selected latitudes) applied on a stretched grid are shown to produce significant distortions of the prognostic state when used to control instabilities near the pole. A new filtering technique is developed which accurately accounts for the non-uniform grid by computing the eigenvectors and eigenfrequencies associated with the stretching. A filter function, constructed to selectively damp those modes whose associated eigenfrequencies exceed some critical value, is used to construct a set of grid-spaced weights which are shown to effectively filter without distortion. Both offline and GCM (General Circulation Model) experiments are shown using the new filtering technique. Finally, a brief examination is also made on the impact of applying the Shapiro filter on the stretched grid.

Three-Dimensional Unsteady Separation at Low Reynolds Numbers

DTIC Science & Technology

1990-07-01

novel, robust adaptive- grid technique for incompressible flow (Shen & Reed 1990a "Shepard’s Interpolation for Solution-Adaptive Methods" submitted to...3-D adaptive- grid schemes developed for flat plate for full, unsteady, incompressible Navier Stokes. 4. 2-D and 3-D unsteady, vortex-lattice code...perforated to tailor suction through wall. Honeycomb and contractiong uide flow uniformly crons "a dn muwet a m Fiur32 c ic R n R ev lving -disc seals

Nonhydrostatic simulation of hyperpycnal river plumes on sloping continental shelves: Flow structures and nonhydrostatic effect

NASA Astrophysics Data System (ADS)

Tseng, Chien-Yung; Chou, Yi-Ju

2018-04-01

A three-dimensional nonhydrostatic coastal model SUNTANS is used to study hyperpycnal plumes on sloping continental shelves with idealized domain setup. The study aims to examine the nonhydrostatic effect of the plunging hyperpycnal plume and the associated flow structures on different shelf slopes. The unstructured triangular grid in SUNTANS allows for local refinement of the grid size for regions in which the flow varies abruptly, while retaining low-cost computation using the coarse grid resolution for regions in which the flow is more uniform. These nonhydrostatic simulations reveal detailed three-dimensional flow structures in both transient and steady states. Via comparison with the hydrostatic simulation, we show that the nonhydrostatic effect is particularly important before plunging, when the plume is subject to significant changes in both the along-shore and vertical directions. After plunging, where the plume becomes an undercurrent that is more spatially uniform, little difference is found between the hydrostatic and nonhydrostatic simulations in the present gentle- and mild-slope cases. A grid-dependence study shows that the nonhydrostatic effect can be seen only when the grid resolution is sufficiently fine that the calculation is not overly diffusive. A depth-integrated momentum budget analysis is then conducted to show that the flow convergence due to plunging is an important factor in the three-dimensional flow structures. Moreover, it shows that the nonhydrostatic effect becomes more important as the slope increases, and in the steep-slope case, neglect of transport of the vertical momentum during plunging in the hydrostatic case further leads to an erroneous prediction for the undercurrent.

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

Zhang, He; Huang, He; Li, Rui; ...

2017-03-06

Here, the fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor-based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed.

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

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

1993-01-01

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

Repeated surveys by acoustic Doppler current profiler for flow and sediment dynamics in a tidal river

USGS Publications Warehouse

Dinehart, R.L.; Burau, J.R.

2005-01-01

A strategy of repeated surveys by acoustic Doppler current profiler (ADCP) was applied in a tidal river to map velocity vectors and suspended-sediment indicators. The Sacramento River at the junction with the Delta Cross Channel at Walnut Grove, California, was surveyed over several tidal cycles in the Fall of 2000 and 2001 with a vessel-mounted ADCP. Velocity profiles were recorded along flow-defining survey paths, with surveys repeated every 27 min through a diurnal tidal cycle. Velocity vectors along each survey path were interpolated to a three-dimensional Cartesian grid that conformed to local bathymetry. A separate array of vectors was interpolated onto a grid from each survey. By displaying interpolated vector grids sequentially with computer animation, flow dynamics of the reach could be studied in three-dimensions as flow responded to the tidal cycle. Velocity streamtraces in the grid showed the upwelling of flow from the bottom of the Sacramento River channel into the Delta Cross Channel. The sequential display of vector grids showed that water in the canal briefly returned into the Sacramento River after peak flood tides, which had not been known previously. In addition to velocity vectors, ADCP data were processed to derive channel bathymetry and a spatial indicator for suspended-sediment concentration. Individual beam distances to bed, recorded by the ADCP, were transformed to yield bathymetry accurate enough to resolve small bedforms within the study reach. While recording velocity, ADCPs also record the intensity of acoustic backscatter from particles suspended in the flow. Sequential surveys of backscatter intensity were interpolated to grids and animated to indicate the spatial movement of suspended sediment through the study reach. Calculation of backscatter flux through cross-sectional grids provided a first step for computation of suspended-sediment discharge, the second step being a calibrated relation between backscatter intensity and sediment concentration. Spatial analyses of ADCP data showed that a strategy of repeated surveys and flow-field interpolation has the potential to simplify computation of flow and sediment discharge through complex waterways. The use of trade, product, industry, or firm names in this report is for descriptive purposes only and does not constitute endorsement of products by the US Government. ?? 2005 Elsevier B.V. All rights reserved.

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.

A Semi-implicit Treatment of Porous Media in Steady-State CFD.

PubMed

Domaingo, Andreas; Langmayr, Daniel; Somogyi, Bence; Almbauer, Raimund

There are many situations in computational fluid dynamics which require the definition of source terms in the Navier-Stokes equations. These source terms not only allow to model the physics of interest but also have a strong impact on the reliability, stability, and convergence of the numerics involved. Therefore, sophisticated numerical approaches exist for the description of such source terms. In this paper, we focus on the source terms present in the Navier-Stokes or Euler equations due to porous media-in particular the Darcy-Forchheimer equation. We introduce a method for the numerical treatment of the source term which is independent of the spatial discretization and based on linearization. In this description, the source term is treated in a fully implicit way whereas the other flow variables can be computed in an implicit or explicit manner. This leads to a more robust description in comparison with a fully explicit approach. The method is well suited to be combined with coarse-grid-CFD on Cartesian grids, which makes it especially favorable for accelerated solution of coupled 1D-3D problems. To demonstrate the applicability and robustness of the proposed method, a proof-of-concept example in 1D, as well as more complex examples in 2D and 3D, is presented.

High accuracy binary black hole simulations with an extended wave zone

NASA Astrophysics Data System (ADS)

Pollney, Denis; Reisswig, Christian; Schnetter, Erik; Dorband, Nils; Diener, Peter

2011-02-01

We present results from a new code for binary black hole evolutions using the moving-puncture approach, implementing finite differences in generalized coordinates, and allowing the spacetime to be covered with multiple communicating nonsingular coordinate patches. Here we consider a regular Cartesian near-zone, with adapted spherical grids covering the wave zone. The efficiencies resulting from the use of adapted coordinates allow us to maintain sufficient grid resolution to an artificial outer boundary location which is causally disconnected from the measurement. For the well-studied test case of the inspiral of an equal-mass nonspinning binary (evolved for more than 8 orbits before merger), we determine the phase and amplitude to numerical accuracies better than 0.010% and 0.090% during inspiral, respectively, and 0.003% and 0.153% during merger. The waveforms, including the resolved higher harmonics, are convergent and can be consistently extrapolated to r→∞ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to (ℓ,m)=(6,6)) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass Mirr=0.884355±20×10-6 and spin Sf/Mf2=0.686923±10×10-6.

a Marker-Based Eulerian-Lagrangian Method for Multiphase Flow with Supersonic Combustion Applications

NASA Astrophysics Data System (ADS)

Fan, Xiaofeng; Wang, Jiangfeng

2016-06-01

The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an Eulerian-Lagrangian computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (Lagrangian) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based Eulerian-Lagrangian method is effective and reliable.

Hybrid Solution-Adaptive Unstructured Cartesian Method for Large-Eddy Simulation of Detonation in Multi-Phase Turbulent Reactive Mixtures

DTIC Science & Technology

2012-03-27

pulse- detonation engines ( PDE ), stage separation, supersonic cav- ity oscillations, hypersonic aerodynamics, detonation induced structural...ADAPTIVE UNSTRUCTURED CARTESIAN METHOD FOR LARGE-EDDY SIMULATION OF DETONATION IN MULTI-PHASE TURBULENT REACTIVE MIXTURES 5b. GRANT NUMBER FA9550...CCL Report TR-2012-03-03 Hybrid Solution-Adaptive Unstructured Cartesian Method for Large-Eddy Simulation of Detonation in Multi-Phase Turbulent

Impact of grid size on uniform scanning and IMPT plans in XiO treatment planning system for brain cancer

PubMed Central

Zheng, Yuanshui

2015-01-01

The main purposes of this study are to: 1) evaluate the accuracy of XiO treatment planning system (TPS) for different dose calculation grid size based on head phantom measurements in uniform scanning proton therapy (USPT); and 2) compare the dosimetric results for various dose calculation grid sizes based on real computed tomography (CT) dataset of pediatric brain cancer treatment plans generated by USPT and intensity‐modulated proton therapy (IMPT) techniques. For phantom study, we have utilized the anthropomorphic head proton phantom provided by Imaging and Radiation Oncology Core (IROC). The imaging, treatment planning, and beam delivery were carried out following the guidelines provided by the IROC. The USPT proton plan was generated in the XiO TPS, and dose calculations were performed for grid size ranged from 1 to 3 mm. The phantom containing thermoluminescent dosimeter (TLDs) and films was irradiated using uniform scanning proton beam. The irradiated TLDs were read by the IROC. The calculated doses from the XiO for different grid sizes were compared to the measured TLD doses provided by the IROC. Gamma evaluation was done by comparing calculated planar dose distribution of 3 mm grid size with measured planar dose distribution. Additionally, IMPT plan was generated based on the same CT dataset of the IROC phantom, and IMPT dose calculations were performed for grid size ranged from 1 to 3 mm. For comparative purpose, additional gamma analysis was done by comparing the planar dose distributions of standard grid size (3 mm) with that of other grid sizes (1, 1.5, 2, and 2.5 mm) for both the USPT and IMPT plans. For patient study, USPT plans of three pediatric brain cancer cases were selected. IMPT plans were generated for each of three pediatric cases. All patient treatment plans (USPT and IMPT) were generated in the XiO TPS for a total dose of 54 Gy (relative biological effectiveness [RBE]). Treatment plans (USPT and IMPT) of each case was recalculated for grid sizes of 1, 1.5, 2, and 2.5 mm; these dosimetric results were then compared with that of 3 mm grid size. Phantom study results: There was no distinct trend exhibiting the dependence of grid size on dose calculation accuracy when calculated point dose of different grid sizes were compared to the measured point (TLD) doses. On average, the calculated point dose was higher than the measured dose by 1.49% and 2.63% for the right and left TLDs, respectively. The gamma analysis showed very minimal differences among planar dose distributions of various grid sizes, with percentage of points meeting gamma index criteria 1% and 1 mm to be from 97.92% to 99.97%. The gamma evaluation using 2% and 2 mm criteria showed both the IMPT and USPT plans have 100% points meeting the criteria. Patient study results: In USPT, there was no very distinct relationship between the absolute difference in mean planning target volume (PTV) dose and grid size, whereas in IMPT, it was found that the decrease in grid size slightly increased the PTV maximum dose and decreased the PTV mean dose and PTV D50%. For the PTV doses, the average differences were up to 0.35 Gy (RBE) and 1.47 Gy (RBE) in the USPT and IMPT plans, respectively. Dependency on grid size was not very clear for the organs at risk (OARs), with average difference ranged from −0.61 Gy (RBE) to 0.53 Gy (RBE) in the USPT plans and from −0.83 Gy (RBE) to 1.39 Gy (RBE) in the IMPT plans. In conclusion, the difference in the calculated point dose between the smallest grid size (1 mm) and the largest grid size (3 mm) in phantom for USPT was typically less than 0.1%. Patient study results showed that the decrease in grid size slightly increased the PTV maximum dose in both the USPT and IMPT plans. However, no distinct trend was obtained between the absolute difference in dosimetric parameter and dose calculation grid size for the OARs. Grid size has a large effect on dose calculation efficiency, and use of 2 mm or less grid size can increase the dose calculation time significantly. It is recommended to use grid size either 2.5 or 3 mm for dose calculations of pediatric brain cancer plans generated by USPT and IMPT techniques in XiO TPS. PACS numbers: 87.55.D‐, 87.55.ne, 87.55.dk PMID:26699310

Finite slice analysis (FINA) of sliced and velocity mapped images on a Cartesian grid

NASA Astrophysics Data System (ADS)

Thompson, J. O. F.; Amarasinghe, C.; Foley, C. D.; Rombes, N.; Gao, Z.; Vogels, S. N.; van de Meerakker, S. Y. T.; Suits, A. G.

2017-08-01

Although time-sliced imaging yields improved signal-to-noise and resolution compared with unsliced velocity mapped ion images, for finite slice widths as encountered in real experiments there is a loss of resolution and recovered intensities for the slow fragments. Recently, we reported a new approach that permits correction of these effects for an arbitrarily sliced distribution of a 3D charged particle cloud. This finite slice analysis (FinA) method utilizes basis functions that model the out-of-plane contribution of a given velocity component to the image for sequential subtraction in a spherical polar coordinate system. However, the original approach suffers from a slow processing time due to the weighting procedure needed to accurately model the out-of-plane projection of an anisotropic angular distribution. To overcome this issue we present a variant of the method in which the FinA approach is performed in a cylindrical coordinate system (Cartesian in the image plane) rather than a spherical polar coordinate system. Dubbed C-FinA, we show how this method is applied in much the same manner. We compare this variant to the polar FinA method and find that the processing time (of a 510 × 510 pixel image) in its most extreme case improves by a factor of 100. We also show that although the resulting velocity resolution is not quite as high as the polar version, this new approach shows superior resolution for fine structure in the differential cross sections. We demonstrate the method on a range of experimental and synthetic data at different effective slice widths.

Iterative Image Reconstruction for PROPELLER-MRI using the NonUniform Fast Fourier Transform

PubMed Central

Tamhane, Ashish A.; Anastasio, Mark A.; Gui, Minzhi; Arfanakis, Konstantinos

2013-01-01

Purpose To investigate an iterative image reconstruction algorithm using the non-uniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping parallEL Lines with Enhanced Reconstruction) MRI. Materials and Methods Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it to that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. Results It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased SNR, reduced artifacts, for similar spatial resolution, compared to gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. Conclusion An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter the new reconstruction technique may provide PROPELLER images with improved image quality compared to conventional gridding. PMID:20578028

Sink or Swim: The Cartesian Diver.

ERIC Educational Resources Information Center

Pinkerton, K. David

2001-01-01

Presents the activity of Cartesian divers which demonstrates the relationship between pressure, temperature, volume, and buoyancy. Includes both instructor information and student activity sheet. (YDS)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koh, S.K.; Song, S.K.; Choi, W.K.

A Kaufman-type 5 cm convex gridded ion-beam source is characterized in terms of angle-resolved ion-beam current density and beam uniformity at various discharge currents, electromagnet currents, and acceleration potentials. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

Effects of Discrete Charge Clustering in Simulations of Charged Interfaces.

PubMed

Grime, John M A; Khan, Malek O

2010-10-12

A system of counterions between charged surfaces is investigated, with the surfaces represented by uniform charged planes and three different arrangements of discrete surface charges - an equispaced grid and two different clustered arrangements. The behaviors of a series of systems with identical net surface charge density are examined, with particular emphasis placed on the long ranged corrections via the method of "charged slabs" and the effects of the simulation cell size. Marked differences are observed in counterion distributions and the osmotic pressure dependent on the particular representation of the charged surfaces; the uniformly charged surfaces and equispaced grids of discrete charge behave in a broadly similar manner, but the clustered systems display a pronounced decrease in osmotic pressure as the simulation size is increased. The influence of the long ranged correction is shown to be minimal for all but the very smallest of system sizes.

Accelerating the two-point and three-point galaxy correlation functions using Fourier transforms

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Eisenstein, Daniel J.

2016-01-01

Though Fourier transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight direction is not constant on the Cartesian grid. Here we show how FTs can be used to compute the multipole moments of the anisotropic 2PCF. We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein. In both cases, these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density of objects in the survey. With the upcoming large data sets of Dark Energy Spectroscopic Instrument, Euclid, and Large Synoptic Survey Telescope, FT techniques will therefore offer an important complement to simple pair or triplet counts.

A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics

NASA Astrophysics Data System (ADS)

Capecelatro, Jesse

2018-03-01

It has long been suggested that a purely Lagrangian solution to global-scale atmospheric/oceanic flows can potentially outperform tradition Eulerian schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully Lagrangian method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.

A framework for joint image-and-shape analysis

NASA Astrophysics Data System (ADS)

Gao, Yi; Tannenbaum, Allen; Bouix, Sylvain

2014-03-01

Techniques in medical image analysis are many times used for the comparison or regression on the intensities of images. In general, the domain of the image is a given Cartesian grids. Shape analysis, on the other hand, studies the similarities and differences among spatial objects of arbitrary geometry and topology. Usually, there is no function defined on the domain of shapes. Recently, there has been a growing needs for defining and analyzing functions defined on the shape space, and a coupled analysis on both the shapes and the functions defined on them. Following this direction, in this work we present a coupled analysis for both images and shapes. As a result, the statistically significant discrepancies in both the image intensities as well as on the underlying shapes are detected. The method is applied on both brain images for the schizophrenia and heart images for atrial fibrillation patients.

Accurate Measurements of Spectral Reflectance in Picasso's Guernica Painting.

PubMed

de Luna, Javier Muñoz; Fernandez-Balbuena, Antonio Alvarez; Vázquez, Daniel; Melgosa, Manuel; Durán, Humberto; García, Jorge; Muro, Carmen

2016-01-01

The use of non-invasive spectral measurements to control the conservation status is a part of the preventive conservation of artworks which nowadays is becoming increasingly interesting. This paper describes how to use a spectral measuring device and an illumination system specifically designed for such a task in a very large dimension artwork painting (7.8 m wide × 3.5 m high). The system, controlled by a Cartesian robot, allows spectral measurements in a spectral range of 400-780 nm. The measured data array has a total of 2201 circular regions with 5.5 mm spot diameter placed on a square grid. Colorimetric calculations performed from these spectral measurements may be used to characterize color shifts related to reflectance changes in specific areas of the paint. A color shifting from the expected gray has been shown. © The Author(s) 2015.

Numerical modeling of the acoustic wave propagation across a homogenized rigid microstructure in the time domain

NASA Astrophysics Data System (ADS)

Lombard, Bruno; Maurel, Agnès; Marigo, Jean-Jacques

2017-04-01

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt the Explicit Simplified Interface Method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in a homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem.

Sonic boom prediction for the Langley Mach 2 low-boom configuration

NASA Technical Reports Server (NTRS)

Madson, Michael D.

1992-01-01

Sonic boom pressure signatures and aerodynamic force data for the Langley Mach 2 low sonic boom configuration were computed using the TranAir full-potential code. A solution-adaptive Cartesian grid scheme is utilized to compute off-body flow field data. Computations were performed with and without nacelles at several angles of attack. Force and moment data were computed to measure nacelle effects on the aerodynamic characteristics and sonic boom footprints of the model. Pressure signatures were computed both on and off ground-track. Near-field pressure signature computations on ground-track were in good agreement with experimental data. Computed off ground-track signatures showed that maximum pressure peaks were located off ground-track and were significantly higher than the signatures on ground-track. Bow shocks from the nacelle inlets increased lift and drag, and also increased the magnitude of the maximum pressure both on and off ground-track.

MODFLOW equipped with a new method for the accurate simulation of axisymmetric flow

NASA Astrophysics Data System (ADS)

Samani, N.; Kompani-Zare, M.; Barry, D. A.

2004-01-01

Axisymmetric flow to a well is an important topic of groundwater hydraulics, the simulation of which depends on accurate computation of head gradients. Groundwater numerical models with conventional rectilinear grid geometry such as MODFLOW (in contrast to analytical models) generally have not been used to simulate aquifer test results at a pumping well because they are not designed or expected to closely simulate the head gradient near the well. A scaling method is proposed based on mapping the governing flow equation from cylindrical to Cartesian coordinates, and vice versa. A set of relationships and scales is derived to implement the conversion. The proposed scaling method is then embedded in MODFLOW 2000. To verify the accuracy of the method steady and unsteady flows in confined and unconfined aquifers with fully or partially penetrating pumping wells are simulated and compared with the corresponding analytical solutions. In all cases a high degree of accuracy is achieved.

Direct Numerical Simulation of Passive Scalar Mixing in Shock Turbulence Interaction

NASA Astrophysics Data System (ADS)

Gao, Xiangyu; Bermejo-Moreno, Ivan; Larsson, Johan

2017-11-01

Passive scalar mixing in the canonical shock-turbulence interaction configuration is investigated through shock-capturing Direct Numerical Simulations (DNS). Scalar fields with different Schmidt numbers are transported by an initially isotropic turbulent flow field passing across a nominally planar shock wave. A solution-adaptive hybrid numerical scheme on Cartesian structured grids is used, that combines a fifth-order WENO scheme near shocks and a sixth-order central-difference scheme away from shocks. The simulations target variations in the shock Mach number, M (from 1.5 to 3), turbulent Mach number, Mt (from 0.1 to 0.4, including wrinkled- and broken-shock regimes), and scalar Schmidt numbers, Sc (from 0.5 to 2), while keeping the Taylor microscale Reynolds number constant (Reλ 40). The effects on passive scalar statistics are investigated, including the streamwise evolution of scalar variance budgets, pdfs and spectra, in comparison with their temporal evolution in decaying isotropic turbulence.

A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensions

NASA Astrophysics Data System (ADS)

Exl, Lukas

2017-12-01

An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled, the overall computation error is driven by the convergence of the finite Fourier series of the density. For smooth and fast-decaying densities the proposed method will be spectrally accurate. The method scales with O(N log N) operations, where N is the total number of discretization points in the Cartesian grid. The majority of the computational costs come from fast Fourier transforms (FFT), which makes it ideal for GPU computation. Several numerical computations on CPU and GPU validate the method and show efficiency and convergence behavior. Tests are performed using the Vienna Scientific Cluster 3 (VSC3). A free MATLAB implementation for CPU and GPU is provided to the interested community.

Modeling Complex Biological Flows in Multi-Scale Systems using the APDEC Framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trebotich, D

We have developed advanced numerical algorithms to model biological fluids in multiscale flow environments using the software framework developed under the SciDAC APDEC ISIC. The foundation of our computational effort is an approach for modeling DNA-laden fluids as ''bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity, leveraging algorithms and solvers in the APDEC Framework. Our Cartesian grid embedded boundary approach to incompressible viscousmore » flow in irregular geometries has also been interfaced to a fast and accurate level-sets method within the APDEC Framework for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.« less

Asynchronous discrete event schemes for PDEs

NASA Astrophysics Data System (ADS)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

Modeling complex biological flows in multi-scale systems using the APDEC framework

NASA Astrophysics Data System (ADS)

Trebotich, David

2006-09-01

We have developed advanced numerical algorithms to model biological fluids in multiscale flow environments using the software framework developed under the SciDAC APDEC ISIC. The foundation of our computational effort is an approach for modeling DNA laden fluids as ''bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity, leveraging algorithms and solvers in the APDEC Framework. Our Cartesian grid embedded boundary approach to incompressible viscous flow in irregular geometries has also been interfaced to a fast and accurate level-sets method within the APDEC Framework for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.

Grid cells form a global representation of connected environments.

PubMed

Carpenter, Francis; Manson, Daniel; Jeffery, Kate; Burgess, Neil; Barry, Caswell

2015-05-04

The firing patterns of grid cells in medial entorhinal cortex (mEC) and associated brain areas form triangular arrays that tessellate the environment [1, 2] and maintain constant spatial offsets to each other between environments [3, 4]. These cells are thought to provide an efficient metric for navigation in large-scale space [5-8]. However, an accurate and universal metric requires grid cell firing patterns to uniformly cover the space to be navigated, in contrast to recent demonstrations that environmental features such as boundaries can distort [9-11] and fragment [12] grid patterns. To establish whether grid firing is determined by local environmental cues, or provides a coherent global representation, we recorded mEC grid cells in rats foraging in an environment containing two perceptually identical compartments connected via a corridor. During initial exposures to the multicompartment environment, grid firing patterns were dominated by local environmental cues, replicating between the two compartments. However, with prolonged experience, grid cell firing patterns formed a single, continuous representation that spanned both compartments. Thus, we provide the first evidence that in a complex environment, grid cell firing can form the coherent global pattern necessary for them to act as a metric capable of supporting large-scale spatial navigation. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Grid Cells Form a Global Representation of Connected Environments

PubMed Central

Carpenter, Francis; Manson, Daniel; Jeffery, Kate; Burgess, Neil; Barry, Caswell

2015-01-01

Summary The firing patterns of grid cells in medial entorhinal cortex (mEC) and associated brain areas form triangular arrays that tessellate the environment [1, 2] and maintain constant spatial offsets to each other between environments [3, 4]. These cells are thought to provide an efficient metric for navigation in large-scale space [5–8]. However, an accurate and universal metric requires grid cell firing patterns to uniformly cover the space to be navigated, in contrast to recent demonstrations that environmental features such as boundaries can distort [9–11] and fragment [12] grid patterns. To establish whether grid firing is determined by local environmental cues, or provides a coherent global representation, we recorded mEC grid cells in rats foraging in an environment containing two perceptually identical compartments connected via a corridor. During initial exposures to the multicompartment environment, grid firing patterns were dominated by local environmental cues, replicating between the two compartments. However, with prolonged experience, grid cell firing patterns formed a single, continuous representation that spanned both compartments. Thus, we provide the first evidence that in a complex environment, grid cell firing can form the coherent global pattern necessary for them to act as a metric capable of supporting large-scale spatial navigation. PMID:25913404

A Greedy Double Auction Mechanism for Grid Resource Allocation

NASA Astrophysics Data System (ADS)

Ding, Ding; Luo, Siwei; Gao, Zhan

To improve the resource utilization and satisfy more users, a Greedy Double Auction Mechanism(GDAM) is proposed to allocate resources in grid environments. GDAM trades resources at discriminatory price instead of uniform price, reflecting the variance in requirements for profits and quantities. Moreover, GDAM applies different auction rules to different cases, over-demand, over-supply and equilibrium of demand and supply. As a new mechanism for grid resource allocation, GDAM is proved to be strategy-proof, economically efficient, weakly budget-balanced and individual rational. Simulation results also confirm that GDAM outperforms the traditional one on both the total trade amount and the user satisfaction percentage, specially as more users are involved in the auction market.

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

NASA Technical Reports Server (NTRS)

Campbell, W.

1981-01-01

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

Parallel hyperbolic PDE simulation on clusters: Cell versus GPU

NASA Astrophysics Data System (ADS)

Rostrup, Scott; De Sterck, Hans

2010-12-01

Increasingly, high-performance computing is looking towards data-parallel computational devices to enhance computational performance. Two technologies that have received significant attention are IBM's Cell Processor and NVIDIA's CUDA programming model for graphics processing unit (GPU) computing. In this paper we investigate the acceleration of parallel hyperbolic partial differential equation simulation on structured grids with explicit time integration on clusters with Cell and GPU backends. The message passing interface (MPI) is used for communication between nodes at the coarsest level of parallelism. Optimizations of the simulation code at the several finer levels of parallelism that the data-parallel devices provide are described in terms of data layout, data flow and data-parallel instructions. Optimized Cell and GPU performance are compared with reference code performance on a single x86 central processing unit (CPU) core in single and double precision. We further compare the CPU, Cell and GPU platforms on a chip-to-chip basis, and compare performance on single cluster nodes with two CPUs, two Cell processors or two GPUs in a shared memory configuration (without MPI). We finally compare performance on clusters with 32 CPUs, 32 Cell processors, and 32 GPUs using MPI. Our GPU cluster results use NVIDIA Tesla GPUs with GT200 architecture, but some preliminary results on recently introduced NVIDIA GPUs with the next-generation Fermi architecture are also included. This paper provides computational scientists and engineers who are considering porting their codes to accelerator environments with insight into how structured grid based explicit algorithms can be optimized for clusters with Cell and GPU accelerators. It also provides insight into the speed-up that may be gained on current and future accelerator architectures for this class of applications. Program summaryProgram title: SWsolver Catalogue identifier: AEGY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL v3 No. of lines in distributed program, including test data, etc.: 59 168 No. of bytes in distributed program, including test data, etc.: 453 409 Distribution format: tar.gz Programming language: C, CUDA Computer: Parallel Computing Clusters. Individual compute nodes may consist of x86 CPU, Cell processor, or x86 CPU with attached NVIDIA GPU accelerator. Operating system: Linux Has the code been vectorised or parallelized?: Yes. Tested on 1-128 x86 CPU cores, 1-32 Cell Processors, and 1-32 NVIDIA GPUs. RAM: Tested on Problems requiring up to 4 GB per compute node. Classification: 12 External routines: MPI, CUDA, IBM Cell SDK Nature of problem: MPI-parallel simulation of Shallow Water equations using high-resolution 2D hyperbolic equation solver on regular Cartesian grids for x86 CPU, Cell Processor, and NVIDIA GPU using CUDA. Solution method: SWsolver provides 3 implementations of a high-resolution 2D Shallow Water equation solver on regular Cartesian grids, for CPU, Cell Processor, and NVIDIA GPU. Each implementation uses MPI to divide work across a parallel computing cluster. Additional comments: Sub-program numdiff is used for the test run.

Earth Science Data Grid System

NASA Astrophysics Data System (ADS)

Chi, Y.; Yang, R.; Kafatos, M.

2004-12-01

The Earth Science Data Grid System (ESDGS) is a software in support of earth science data storage and access. It is built upon the Storage Resource Broker (SRB) data grid technology. We have developed a complete data grid system consistent of SRB server providing users uniform access to diverse storage resources in a heterogeneous computing environment and metadata catalog server (MCAT) managing the metadata associated with data set, users, and resources. We are also developing additional services of 1) metadata management, 2) geospatial, temporal, and content-based indexing, and 3) near/on site data processing, in response to the unique needs of Earth science applications. In this paper, we will describe the software architecture and components of the system, and use a practical example in support of storage and access of rainfall data from the Tropical Rainfall Measuring Mission (TRMM) to illustrate its functionality and features.

Oregon Magnetic and Gravity Maps and Data: A Web Site for Distribution of Data

USGS Publications Warehouse

Roberts, Carter W.; Kucks, Robert P.; Hill, Patricia L.

2008-01-01

This web site gives the results of a USGS project to acquire the best available, public-domain, aeromagnetic and gravity data in the United States and merge these data into uniform, composite grids for each State. The results for the State of Oregon are presented here on this site. Files of aeromagnetic and gravity grids and images are available for these States for downloading. In Oregon, 49 magnetic surveys have been knit together to form a single digital grid and map. Also, a complete Bouguer gravity anomaly grid and map was generated from 40,665 gravity station measurements in and adjacent to Oregon. In addition, a map shows the location of the aeromagnetic surveys, color-coded to the survey flight-line spacing. This project was supported by the Mineral Resource Program of the USGS.

Vortex Filaments in Grids for Scalable, Fine Smoke Simulation.

PubMed

Meng, Zhang; Weixin, Si; Yinling, Qian; Hanqiu, Sun; Jing, Qin; Heng, Pheng-Ann

2015-01-01

Vortex modeling can produce attractive visual effects of dynamic fluids, which are widely applicable for dynamic media, computer games, special effects, and virtual reality systems. However, it is challenging to effectively simulate intensive and fine detailed fluids such as smoke with fast increasing vortex filaments and smoke particles. The authors propose a novel vortex filaments in grids scheme in which the uniform grids dynamically bridge the vortex filaments and smoke particles for scalable, fine smoke simulation with macroscopic vortex structures. Using the vortex model, their approach supports the trade-off between simulation speed and scale of details. After computing the whole velocity, external control can be easily exerted on the embedded grid to guide the vortex-based smoke motion. The experimental results demonstrate the efficiency of using the proposed scheme for a visually plausible smoke simulation with macroscopic vortex structures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakaguchi, Koichi; Leung, Lai-Yung R.; Zhao, Chun

This study presents a diagnosis of a multi-resolution approach using the Model for Prediction Across Scales - Atmosphere (MPAS-A) for simulating regional climate. Four AMIP experiments are conducted for 1999-2009. In the first two experiments, MPAS-A is configured using global quasi-uniform grids at 120 km and 30 km grid spacing. In the other two experiments, MPAS-A is configured using variable-resolution (VR) mesh with local refinement at 30 km over North America and South America embedded inside a quasi-uniform domain at 120 km elsewhere. Precipitation and related fields in the four simulations are examined to determine how well the VR simulationsmore » reproduce the features simulated by the globally high-resolution model in the refined domain. In previous analyses of idealized aqua-planet simulations, the characteristics of the global high-resolution simulation in moist processes only developed near the boundary of the refined region. In contrast, the AMIP simulations with VR grids are able to reproduce the high-resolution characteristics across the refined domain, particularly in South America. This indicates the importance of finely resolved lower-boundary forcing such as topography and surface heterogeneity for the regional climate, and demonstrates the ability of the MPAS-A VR to replicate the large-scale moisture transport as simulated in the quasi-uniform high-resolution model. Outside of the refined domain, some upscale effects are detected through large-scale circulation but the overall climatic signals are not significant at regional scales. Our results provide support for the multi-resolution approach as a computationally efficient and physically consistent method for modeling regional climate.« less

TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE

NASA Technical Reports Server (NTRS)

Vu, B. T.

1994-01-01

TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

Fibonacci Grids

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.

Shallow Water Propagation

DTIC Science & Technology

2014-09-30

improvements in single-scattering treatments at stair-step risers in approximations for range dependence; non-uniform depth gridding to treat thin layers...turns out for such problems that preserving accuracy requires conceptually splitting a stair- riser interface into two interfaces separated by a very

Filtering and Gridding Satellite Observations of Cloud Variables to Compare with Climate Model Output

NASA Astrophysics Data System (ADS)

Pitts, K.; Nasiri, S. L.; Smith, N.

2013-12-01

Global climate models have improved considerably over the years, yet clouds still represent a large factor of uncertainty for these models. Comparisons of model-simulated cloud variables with equivalent satellite cloud products are the best way to start diagnosing the differences between model output and observations. Gridded (level 3) cloud products from many different satellites and instruments are required for a full analysis, but these products are created by different science teams using different algorithms and filtering criteria to create similar, but not directly comparable, cloud products. This study makes use of a recently developed uniform space-time gridding algorithm to create a new set of gridded cloud products from each satellite instrument's level 2 data of interest which are each filtered using the same criteria, allowing for a more direct comparison between satellite products. The filtering is done via several variables such as cloud top pressure/height, thermodynamic phase, optical properties, satellite viewing angle, and sun zenith angle. The filtering criteria are determined based on the variable being analyzed and the science question at hand. Each comparison of different variables may require different filtering strategies as no single approach is appropriate for all problems. Beyond inter-satellite data comparison, these new sets of uniformly gridded satellite products can also be used for comparison with model-simulated cloud variables. Of particular interest to this study are the differences in the vertical distributions of ice and liquid water content between the satellite retrievals and model simulations, especially in the mid-troposphere where there are mixed-phase clouds to consider. This presentation will demonstrate the proof of concept through comparisons of cloud water path from Aqua MODIS retrievals and NASA GISS-E2-[R/H] model simulations archived in the CMIP5 data portal.

Frequency-Offset Cartesian Feedback Based on Polyphase Difference Amplifiers

PubMed Central

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

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

NASA Technical Reports Server (NTRS)

Myhill, Elizabeth A.; Boss, Alan P.

1993-01-01

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eldred, Christopher; Randall, David

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

DPW-VI Results Using FUN3D with Focus on k-kL-MEAH2015 (k-kL) Turbulence Model

NASA Technical Reports Server (NTRS)

Abdol-Hamid, K. S.; Carlson, Jan-Renee; Rumsey, Christopher L.; Lee-Rausch, Elizabeth M.; Park, Michael A.

2017-01-01

The Common Research Model wing-body configuration is investigated with the k-kL-MEAH2015 turbulence model implemented in FUN3D. This includes results presented at the Sixth Drag Prediction Workshop and additional results generated after the workshop with a nonlinear Quadratic Constitutive Relation (QCR) variant of the same turbulence model. The workshop provided grids are used, and a uniform grid refinement study is performed at the design condition. A large variation between results with and without a reconstruction limiter is exhibited on "medium" grid sizes, indicating that the medium grid size is too coarse for drawing conclusions in comparison with experiment. This variation is reduced with grid refinement. At a fixed angle of attack near design conditions, the QCR variant yielded decreased lift and drag compared with the linear eddy-viscosity model by an amount that was approximately constant with grid refinement. The k-kL-MEAH2015 turbulence model produced wing root junction flow behavior consistent with wind tunnel observations.

Material souls and imagination in late Aristotelian embryology.

PubMed

Blank, Andreas

2010-04-01

This article explores some continuities between Late Aristotelian and Cartesian embryology. In particular, it argues that there is an interesting consilience between some accounts of the role of imagination in trait acquisition in Late Aristotelian and Cartesian embryology. Evidence for this thesis is presented using the extensive biological writings of the Padua-based philosopher and physician, Fortunio Liceti (1577-1657). Like the Cartesian physiologists, Liceti believed that animal souls are material beings and that acts of imagination result in material images that can be transmitted by means of medical spirits to the embryo. Moreover, while the Cartesian embryologists accepted such a view in a quite speculative way, one finds penetrating criticism of imagination theories of trait acquisition in the Late Aristotelian tradition. Evidence for this thesis is presented using the no less extensive biological writings of Liceti's contemporary, Emilio Parisano (1567-1643). In conclusion, the Late Aristotelian tradition itself provides the theoretical tools for excising immaterial formative forces from embryology and at the same time evinces a much more acute sense for the problems inherent in imagination theories of trait acquisition than the Cartesian tradition.

The influence of jet-grid turbulence on heat transfer from the stagnation region of a cylinder in crossflow

NASA Technical Reports Server (NTRS)

Obrien, J. E.; Vanfossen, G. J., Jr.

1985-01-01

The effect of high-intensity turbulence on heat transfer from the stagnation region of a circular cylinder in crossflow was studied. The work was motivated by the desire to be able to more fully understand and predict the heat transfer to the leading edge of a turbine airfoil. In order to achieve high levels of turbulence with a reasonable degree of isotropy and homogeneity, a jet-injection turbulence grid was used. The jet grid provided turbulence intensities of 10 to 12 percent, measured at the test cylinder location, for downstream blowing with the blowing rate adjusted to an optimal value for flow uniformity. Heat transfer augmentation above the zeroturbulence case ranged from 37 to 53 percent for the test cylinder behind the jet grid for a cylinder Reynolds number range of 48,000 to 180,000, respectively. The level of heat transfer augmentation was found to be fairly uniform with respect to circumferential distance from the stagnation line. Stagnation point heat transfer results (expressed in terms of the Frossling number) were found to be somewhat low with respect to previous studies, when compared on the basis of equal values of the parameter Tu Re(1/2), indicating an additional Reynolds number effect as observed by previous investigators. Consequently, for a specified value of Tu Re(1/2), data obtained with a relatively high turbulence intensity will have a lower value of the Frossling number.

Pressure wave propagation studies for oscillating cascades

NASA Technical Reports Server (NTRS)

Huff, Dennis L.

1992-01-01

The unsteady flow field around an oscillating cascade of flat plates is studied using a time marching Euler code. Exact solutions based on linear theory serve as model problems to study pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step is demonstrated. Results show that an approximate non-reflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer than cases using reflective boundary conditions. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates does a better job of capturing the unsteady flow field than cases using uniform grids as long as the CFL number is less than one for a sufficient portion of the grid. Results for various stagger angles and oscillation frequencies show good agreement with linear theory as long as the grid is properly resolved.

Generating grids directly on CAD database surfaces using a parametric evaluator approach

NASA Technical Reports Server (NTRS)

Gatzhe, Timothy D.; Melson, Thomas G.

1995-01-01

A very important, but often overlooked step in grid generation is acquiring a suitable geometry definition of the vehicle to be analyzed. In the past, geometry was usually obtained by generating a number of cross-sections of each component. A number of recent efforts have focussed on non-uniform rational B-spline surfaces (NURBS) to provide as single type of analytic surface to deal with inside the grid generator. This approach has required the development of tools to read other types of surfaces and convert them, either exactly or by approximation, into a NURBS surface. This paper describes a more generic parametric evaluator approach, which does not rely on a particular surface type internal to the grid generation system and is less restrictive in the number of surface types that can be represented exactly. This approach has been implemented in the McDonnell Douglas grid generation system, MACGS, and offers direct access to all types of surfaces from a Unigraphics part file.

On computations of the integrated space shuttle flowfield using overset grids

NASA Technical Reports Server (NTRS)

Chiu, I-T.; Pletcher, R. H.; Steger, J. L.

1990-01-01

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield.

Uniform function constants of motion and their first-order perturbation

NASA Astrophysics Data System (ADS)

Prato, Domingo; Hamity, Victor H.

2005-05-01

The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

Higher-Order Containers

NASA Astrophysics Data System (ADS)

Altenkirch, Thorsten; Levy, Paul; Staton, Sam

Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications in generic programming and representation of higher order abstract syntax. We also show that the category of containers has finite limits, but it is not locally cartesian closed.

CFL3D, FUN3d, and NSU3D Contributions to the Fifth Drag Prediction Workshop

NASA Technical Reports Server (NTRS)

Park, Michael A.; Laflin, Kelly R.; Chaffin, Mark S.; Powell, Nicholas; Levy, David W.

2013-01-01

Results presented at the Fifth Drag Prediction Workshop using CFL3D, FUN3D, and NSU3D are described. These are calculations on the workshop provided grids and drag adapted grids. The NSU3D results have been updated to reflect an improvement to skin friction calculation on skewed grids. FUN3D results generated after the workshop are included for custom participant generated grids and a grid from a previous workshop. Uniform grid refinement at the design condition shows a tight grouping in calculated drag, where the variation in the pressure component of drag is larger than the skin friction component. At this design condition, A fine-grid drag value was predicted with a smaller drag adjoint adapted grid via tetrahedral adaption to a metric and mixed-element subdivision. The buffet study produced larger variation than the design case, which is attributed to large differences in the predicted side-of-body separation extent. Various modeling and discretization approaches had a strong impact on predicted side-of-body separation. This large wing root separation bubble was not observed in wind tunnel tests indicating that more work is necessary in modeling wing root juncture flows to predict experiments.

Illinois, Indiana, and Ohio Magnetic and Gravity Maps and Data: A Website for Distribution of Data

USGS Publications Warehouse

Daniels, David L.; Kucks, Robert P.; Hill, Patricia L.

2008-01-01

This web site gives the results of a USGS project to acquire the best available, public-domain, aeromagnetic and gravity data in the United States and merge these data into uniform, composite grids for each state. The results for the three states, Illinois, Indiana, and Ohio are presented here in one site. Files of aeromagnetic and gravity grids and images are available for these states for downloading. In Illinois, Indiana, and Ohio, 19 magnetic surveys have been knit together to form a single digital grid and map. And, a complete Bouguer gravity anomaly grid and map was generated from 128,227 gravity station measurements in and adjacent to Illinois, Indiana, and Ohio. In addition, a map shows the location of the aeromagnetic surveys, color-coded to the survey flight-line spacing. This project was supported by the Mineral Resource Program of the USGS.

An Alternative Method of Computing Altitude Adjustment Corrected Geomagnetic Coordinates as Applied to IGRF Epoch 2005

DTIC Science & Technology

2007-07-20

science.msfc.nasa.gov/ss/pad/ sppb /workshoV7/&eoma&ne/Reo cgn/geo c&m.for. See also the GEOPACK library at http:/nssdcftp.gsfc.na-a.gov/models...calculations, fed into the inverse computation, should reproduce the original coordinate grid. This test of the consistency of the direct and inverse...algorithm. A test of this type was performed for a uniform grid, for line traces from 7200 km to the ground, and for 800 km to the ground. The maximum

A Cartesian parametrization for the numerical analysis of material instability

DOE PAGES

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

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

A Cartesian parametrization for the numerical analysis of material instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.

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

Mouse manipulation through single-switch scanning.

PubMed

Blackstien-Adler, Susie; Shein, Fraser; Quintal, Janet; Birch, Shae; Weiss, Patrice L Tamar

2004-01-01

Given the current extensive reliance on the graphical user interface, independent access to computer software requires that users be able to manipulate a pointing device of some type (e.g., mouse, trackball) or be able to emulate a mouse by some other means (e.g., scanning). The purpose of the present study was to identify one or more optimal single-switch scanning mouse emulation strategies. Four alternative scanning strategies (continuous Cartesian, discrete Cartesian, rotational, and hybrid quadrant/continuous Cartesian) were selected for testing based on current market availability as well as on theoretical considerations of their potential speed and accuracy. Each strategy was evaluated using a repeated measures study design by means of a test program that permitted mouse emulation via any one of four scanning strategies in a motivating environment; response speed and accuracy could be automatically recorded and considered in view of the motor, cognitive, and perceptual demands of each scanning strategy. Ten individuals whose disabilities required them to operate a computer via single-switch scanning participated in the study. Results indicated that Cartesian scanning was the preferred and most effective scanning strategy. There were no significant differences between results from the Continuous Cartesian and Discrete Cartesian scanning strategies. Rotational scanning was quite slow with respect to the other strategies, although it was equally accurate. Hybrid Quadrant scanning improved access time but at the cost of fewer correct selections. These results demonstrated the importance of testing and comparing alternate single-switch scanning strategies.

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehe, Remi; Kirchen, Manuel; Godfrey, Brendan B.

Particle-in-cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including, e.g., laser-wakefield acceleration, when viewed in a Lorentz-boosted frame) but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover,more » it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.« less

Tensorial Basis Spline Collocation Method for Poisson's Equation

NASA Astrophysics Data System (ADS)

Plagne, Laurent; Berthou, Jean-Yves

2000-01-01

This paper aims to describe the tensorial basis spline collocation method applied to Poisson's equation. In the case of a localized 3D charge distribution in vacuum, this direct method based on a tensorial decomposition of the differential operator is shown to be competitive with both iterative BSCM and FFT-based methods. We emphasize the O(h4) and O(h6) convergence of TBSCM for cubic and quintic splines, respectively. We describe the implementation of this method on a distributed memory parallel machine. Performance measurements on a Cray T3E are reported. Our code exhibits high performance and good scalability: As an example, a 27 Gflops performance is obtained when solving Poisson's equation on a 2563 non-uniform 3D Cartesian mesh by using 128 T3E-750 processors. This represents 215 Mflops per processors.

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates

DOE PAGES

Lehe, Remi; Kirchen, Manuel; Godfrey, Brendan B.; ...

2016-11-14

Particle-in-cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including, e.g., laser-wakefield acceleration, when viewed in a Lorentz-boosted frame) but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover,more » it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.« less

CALIPSO V1.00 L3 IceCloud Formal Release Announcement

Atmospheric Science Data Center

2018-06-13

... The Atmospheric Science Data Center (ASDC) at NASA Langley Research Center in collaboration with the CALIPSO mission team announces the ... distributions of ice cloud extinction coefficients and ice water content histograms on a uniform spatial grid.  All parameters are ...

Real-space microscopic electrical imaging of n+-p junction beneath front-side Ag contact of multicrystalline Si solar cells

NASA Astrophysics Data System (ADS)

Jiang, C.-S.; Li, Z. G.; Moutinho, H. R.; Liang, L.; Ionkin, A.; Al-Jassim, M. M.

2012-04-01

We investigated the quality of the n+-p diffused junction beneath the front-side Ag contact of multicrystalline Si solar cells by characterizing the uniformities of electrostatic potential and doping concentration across the junction using the atomic force microscopy-based electrical imaging techniques of scanning Kelvin probe force microscopy and scanning capacitance microscopy. We found that Ag screen-printing metallization fired at the over-fire temperature significantly degrades the junction uniformity beneath the Ag contact grid, whereas metallization at the optimal- and under-fire temperatures does not cause degradation. Ag crystallites with widely distributed sizes were found at the Ag-grid/emitter-Si interface of the over-fired cell, which is associated with the junction damage beneath the Ag grid. Large crystallites protrude into Si deeper than the junction depth. However, the junction was not broken down; instead, it was reformed on the entire front of the crystallite/Si interface. We propose a mechanism of junction-quality degradation, based on emitter Si melting at the temperature around the Ag-Si eutectic point during firing, and subsequent re-crystallization with incorporation of Ag and other impurities and with formation of crystallographic defects during quenching. The effect of this junction damage on solar cell performance is discussed.

Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR (Adaptive-Mesh Refinement) and Results from Special and General Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Dönmez, Orhan

2004-09-01

In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.

Real-Space Microscopic Electrical Imaging of n+-p Junction Beneath Front-Side Ag Contact of Multicrystalline Si Solar Cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, C. S.; Li, Z. G.; Moutinho, H. R.

2012-04-15

We investigated the quality of the n+-p diffused junction beneath the front-side Ag contact of multicrystalline Si solar cells by characterizing the uniformities of electrostatic potential and doping concentration across the junction using the atomic force microscopy-based electrical imaging techniques of scanning Kelvin probe force microscopy and scanning capacitance microscopy. We found that Ag screen-printing metallization fired at the over-fire temperature significantly degrades the junction uniformity beneath the Ag contact grid, whereas metallization at the optimal- and under-fire temperatures does not cause degradation. Ag crystallites with widely distributed sizes were found at the Ag-grid/emitter-Si interface of the over-fired cell, whichmore » is associated with the junction damage beneath the Ag grid. Large crystallites protrude into Si deeper than the junction depth. However, the junction was not broken down; instead, it was reformed on the entire front of the crystallite/Si interface. We propose a mechanism of junction-quality degradation, based on emitter Si melting at the temperature around the Ag-Si eutectic point during firing, and subsequent re-crystallization with incorporation of Ag and other impurities and with formation of crystallographic defects during quenching. The effect of this junction damage on solar cell performance is discussed.« less

Dynamic federation of grid and cloud storage

NASA Astrophysics Data System (ADS)

Furano, Fabrizio; Keeble, Oliver; Field, Laurence

2016-09-01

The Dynamic Federations project ("Dynafed") enables the deployment of scalable, distributed storage systems composed of independent storage endpoints. While the Uniform Generic Redirector at the heart of the project is protocol-agnostic, we have focused our effort on HTTP-based protocols, including S3 and WebDAV. The system has been deployed on testbeds covering the majority of the ATLAS and LHCb data, and supports geography-aware replica selection. The work done exploits the federation potential of HTTP to build systems that offer uniform, scalable, catalogue-less access to the storage and metadata ensemble and the possibility of seamless integration of other compatible resources such as those from cloud providers. Dynafed can exploit the potential of the S3 delegation scheme, effectively federating on the fly any number of S3 buckets from different providers and applying a uniform authorization to them. This feature has been used to deploy in production the BOINC Data Bridge, which uses the Uniform Generic Redirector with S3 buckets to harmonize the BOINC authorization scheme with the Grid/X509. The Data Bridge has been deployed in production with good results. We believe that the features of a loosely coupled federation of open-protocolbased storage elements open many possibilities of smoothly evolving the current computing models and of supporting new scientific computing projects that rely on massive distribution of data and that would appreciate systems that can more easily be interfaced with commercial providers and can work natively with Web browsers and clients.

Domain decomposition methods in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Gropp, William D.; Keyes, David E.

1991-01-01

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

NASA Astrophysics Data System (ADS)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

Visualization of Octree Adaptive Mesh Refinement (AMR) in Astrophysical Simulations

NASA Astrophysics Data System (ADS)

Labadens, M.; Chapon, D.; Pomaréde, D.; Teyssier, R.

2012-09-01

Computer simulations are important in current cosmological research. Those simulations run in parallel on thousands of processors, and produce huge amount of data. Adaptive mesh refinement is used to reduce the computing cost while keeping good numerical accuracy in regions of interest. RAMSES is a cosmological code developed by the Commissariat à l'énergie atomique et aux énergies alternatives (English: Atomic Energy and Alternative Energies Commission) which uses Octree adaptive mesh refinement. Compared to grid based AMR, the Octree AMR has the advantage to fit very precisely the adaptive resolution of the grid to the local problem complexity. However, this specific octree data type need some specific software to be visualized, as generic visualization tools works on Cartesian grid data type. This is why the PYMSES software has been also developed by our team. It relies on the python scripting language to ensure a modular and easy access to explore those specific data. In order to take advantage of the High Performance Computer which runs the RAMSES simulation, it also uses MPI and multiprocessing to run some parallel code. We would like to present with more details our PYMSES software with some performance benchmarks. PYMSES has currently two visualization techniques which work directly on the AMR. The first one is a splatting technique, and the second one is a custom ray tracing technique. Both have their own advantages and drawbacks. We have also compared two parallel programming techniques with the python multiprocessing library versus the use of MPI run. The load balancing strategy has to be smartly defined in order to achieve a good speed up in our computation. Results obtained with this software are illustrated in the context of a massive, 9000-processor parallel simulation of a Milky Way-like galaxy.

Three-dimensional body-wave model of Nepal using finite difference tomography

NASA Astrophysics Data System (ADS)

Ho, T. M.; Priestley, K.; Roecker, S. W.

2017-12-01

The processes occurring during continent-continent collision are still poorly understood. Ascertaining the seismic properties of the crust and uppermost mantle in such settings provides insight into continental rheology and geodynamics. The most active present-day continent-continent collision is that of India with Eurasia which has created the Himalayas and the Tibetan Plateau. Nepal provides an ideal laboratory for imaging the crustal processes resulting from the Indo-Eurasia collision. We build body wave models using local body wave arrivals picked at stations in Nepal deployed by the Department of Mining and Geology of Nepal. We use the tomographic inversion method of Roecker et al. [2006], the key feature of which is that the travel times are generated using a finite difference solution to the eikonal equation. The advantage of this technique is increased accuracy in the highly heterogeneous medium expected for the Himalayas. Travel times are calculated on a 3D Cartesian grid with a grid spacing of 6 km and intragrid times are estimated by trilinear interpolation. The gridded area spans a region of 80-90o longitude and 25-30o latitude. For a starting velocity model, we use IASP91. Inversion is performed using the LSQR algorithm. Since the damping parameter can have a significant effect on the final solution, we tested a range of damping parameters to fully explore its effect. Much of the seismicity is clustered to the West of Kathmandu at depths < 30 km. Small areas of strong fast wavespeeds exist in the centre of the region in the upper 30 km of the crust. At depths of 40-50 km, large areas of slow wavespeeds are present which track along the plate boundary.

A Hybrid Numerical Method for Turbulent Mixing Layers. Degree awarded by Case Western Reserve Univ.

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.

2001-01-01

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental data.

An adaptive mesh refinement-multiphase lattice Boltzmann flux solver for simulation of complex binary fluid flows

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Wang, Y.; Shu, C.

2017-12-01

This paper presents an adaptive mesh refinement-multiphase lattice Boltzmann flux solver (AMR-MLBFS) for effective simulation of complex binary fluid flows at large density ratios. In this method, an AMR algorithm is proposed by introducing a simple indicator on the root block for grid refinement and two possible statuses for each block. Unlike available block-structured AMR methods, which refine their mesh by spawning or removing four child blocks simultaneously, the present method is able to refine its mesh locally by spawning or removing one to four child blocks independently when the refinement indicator is triggered. As a result, the AMR mesh used in this work can be more focused on the flow region near the phase interface and its size is further reduced. In each block of mesh, the recently proposed MLBFS is applied for the solution of the flow field and the level-set method is used for capturing the fluid interface. As compared with existing AMR-lattice Boltzmann models, the present method avoids both spatial and temporal interpolations of density distribution functions so that converged solutions on different AMR meshes and uniform grids can be obtained. The proposed method has been successfully validated by simulating a static bubble immersed in another fluid, a falling droplet, instabilities of two-layered fluids, a bubble rising in a box, and a droplet splashing on a thin film with large density ratios and high Reynolds numbers. Good agreement with the theoretical solution, the uniform-grid result, and/or the published data has been achieved. Numerical results also show its effectiveness in saving computational time and virtual memory as compared with computations on uniform meshes.

Applications of an exponential finite difference technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

NASA Technical Reports Server (NTRS)

Batina, John T.

2005-01-01

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Stability of stagnation via an expanding accretion shock wave

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Murakami, M.; Taylor, B. D.; Giuliani, J. L.; Zalesak, S. T.; Iwamoto, Y.

2016-05-01

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett. 111, 035001 (2013)] to the experiments in support of the recently suggested concept of impact ignition in ICF [Azechi et al., Phys. Rev. Lett. 102, 235002 (2009); Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case, the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a power-law, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydrocode verification in two and three dimensions.

Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates

NASA Astrophysics Data System (ADS)

Milić, Ivan; Atanacković, Olga

2014-10-01

State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration (FBILI), developed earlier for 1D geometry. In order to present the method and examine its convergence properties we use the well-known instance of the two-level atom line formation with complete frequency redistribution. In the formal solution of the RT equation we employ short characteristics with two-point algorithm. Using an implicit representation of the source function in the computation of the specific intensities, we compute and store the coefficients of the linear relations J=a+bS between the mean intensity J and the corresponding source function S. The use of iteration factors in the ‘local’ coefficients of these implicit relations in two ‘inward’ sweeps of 2D grid, along with the update of the source function in other two ‘outward’ sweeps leads to four times faster solution than the Jacobi’s one. Moreover, the update made in all four consecutive sweeps of the grid leads to an acceleration by a factor of 6-7 compared to the Jacobi iterative scheme.

High order solution of Poisson problems with piecewise constant coefficients and interface jumps

NASA Astrophysics Data System (ADS)

Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben

2017-04-01

We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains-which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity.

SEAWAT-based simulation of axisymmetric heat transport.

PubMed

Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele

2014-01-01

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. © 2013, National Ground Water Association.

Stability of stagnation via an expanding accretion shock wave

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velikovich, A. L.; Giuliani, J. L.; Murakami, M.

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett. 111, 035001 (2013)] to the experiments in support of the recently suggested concept of impact ignition in ICF [Azechi et al., Phys. Rev. Lett. 102, 235002 (2009); Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never beenmore » studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case, the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a power-law, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydrocode verification in two and three dimensions.« less

Improvement of uniformity of the negative ion beams by tent-shaped magnetic field in the JT-60 negative ion source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoshida, Masafumi, E-mail: yoshida.masafumi@jaea.go.jp; Hanada, Masaya; Kojima, Atsushi

2014-02-15

Non-uniformity of the negative ion beams in the JT-60 negative ion source with the world-largest ion extraction area was improved by modifying the magnetic filter in the source from the plasma grid (PG) filter to a tent-shaped filter. The magnetic design via electron trajectory calculation showed that the tent-shaped filter was expected to suppress the localization of the primary electrons emitted from the filaments and created uniform plasma with positive ions and atoms of the parent particles for the negative ions. By modifying the magnetic filter to the tent-shaped filter, the uniformity defined as the deviation from the averaged beammore » intensity was reduced from 14% of the PG filter to ∼10% without a reduction of the negative ion production.« less

A climatically-derived global soil moisture data set for use in the GLAS atmospheric circulation model seasonal cycle experiment

NASA Technical Reports Server (NTRS)

Willmott, C. J.; Field, R. T.

1984-01-01

Algorithms for point interpolation and contouring on the surface of the sphere and in Cartesian two-space are developed from Shepard's (1968) well-known, local search method. These mapping procedures then are used to investigate the errors which appear on small-scale climate maps as a result of the all-too-common practice of of interpolating, from irregularly spaced data points to the nodes of a regular lattice, and contouring Cartesian two-space. Using mean annual air temperatures field over the western half of the northern hemisphere is estimated both on the sphere, assumed to be correct, and in Cartesian two-space. When the spherically- and Cartesian-approximted air temperature fields are mapped and compared, the magnitudes (as large as 5 C to 10 C) and distribution of the errors associated with the latter approach become apparent.

The Sensitivity of Numerical Simulations of Cloud-Topped Boundary Layers to Cross-Grid Flow

NASA Astrophysics Data System (ADS)

Wyant, Matthew C.; Bretherton, Christopher S.; Blossey, Peter N.

2018-02-01

In mesoscale and global atmospheric simulations with large horizontal domains, strong horizontal flow across the grid is often unavoidable, but its effects on cloud-topped boundary layers have received comparatively little study. Here the effects of cross-grid flow on large-eddy simulations of stratocumulus and trade-cumulus marine boundary layers are studied across a range of grid resolutions (horizontal × vertical) between 500 m × 20 m and 35 m × 5 m. Three cases are simulated: DYCOMS nocturnal stratocumulus, BOMEX trade cumulus, and a GCSS stratocumulus-to-trade cumulus case. Simulations are performed with a stationary grid (with 4-8 m s-1 horizontal winds blowing through the cyclic domain) and a moving grid (equivalent to subtracting off a fixed vertically uniform horizontal wind) approximately matching the mean boundary-layer wind speed. For stratocumulus clouds, cross-grid flow produces two primary effects on stratocumulus clouds: a filtering of fine-scale resolved turbulent eddies, which reduces stratocumulus cloud-top entrainment, and a vertical broadening of the stratocumulus-top inversion which enhances cloud-top entrainment. With a coarse (20 m) vertical grid, the former effect dominates and leads to strong increases in cloud cover and LWP, especially as horizontal resolution is coarsened. With a finer (5 m) vertical grid, the latter effect is stronger and leads to small reductions in cloud cover and LWP. For the BOMEX trade cumulus case, cross-grid flow tends to produce fewer and larger clouds with higher LWP, especially for coarser vertical grid spacing. The results presented are robust to choice of scalar advection scheme and Courant number.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

NASA Astrophysics Data System (ADS)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

FDD Massive MIMO Channel Estimation With Arbitrary 2D-Array Geometry

NASA Astrophysics Data System (ADS)

Dai, Jisheng; Liu, An; Lau, Vincent K. N.

2018-05-01

This paper addresses the problem of downlink channel estimation in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. The existing methods usually exploit hidden sparsity under a discrete Fourier transform (DFT) basis to estimate the cdownlink channel. However, there are at least two shortcomings of these DFT-based methods: 1) they are applicable to uniform linear arrays (ULAs) only, since the DFT basis requires a special structure of ULAs, and 2) they always suffer from a performance loss due to the leakage of energy over some DFT bins. To deal with the above shortcomings, we introduce an off-grid model for downlink channel sparse representation with arbitrary 2D-array antenna geometry, and propose an efficient sparse Bayesian learning (SBL) approach for the sparse channel recovery and off-grid refinement. The main idea of the proposed off-grid method is to consider the sampled grid points as adjustable parameters. Utilizing an in-exact block majorization-minimization (MM) algorithm, the grid points are refined iteratively to minimize the off-grid gap. Finally, we further extend the solution to uplink-aided channel estimation by exploiting the angular reciprocity between downlink and uplink channels, which brings enhanced recovery performance.

Grid Application Meta-Repository System: Repository Interconnectivity and Cross-domain Application Usage in Distributed Computing Environments

NASA Astrophysics Data System (ADS)

Tudose, Alexandru; Terstyansky, Gabor; Kacsuk, Peter; Winter, Stephen

Grid Application Repositories vary greatly in terms of access interface, security system, implementation technology, communication protocols and repository model. This diversity has become a significant limitation in terms of interoperability and inter-repository access. This paper presents the Grid Application Meta-Repository System (GAMRS) as a solution that offers better options for the management of Grid applications. GAMRS proposes a generic repository architecture, which allows any Grid Application Repository (GAR) to be connected to the system independent of their underlying technology. It also presents applications in a uniform manner and makes applications from all connected repositories visible to web search engines, OGSI/WSRF Grid Services and other OAI (Open Archive Initiative)-compliant repositories. GAMRS can also function as a repository in its own right and can store applications under a new repository model. With the help of this model, applications can be presented as embedded in virtual machines (VM) and therefore they can be run in their native environments and can easily be deployed on virtualized infrastructures allowing interoperability with new generation technologies such as cloud computing, application-on-demand, automatic service/application deployments and automatic VM generation.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Magnetic Field Would Reduce Electron Backstreaming in Ion Thrusters

NASA Technical Reports Server (NTRS)

Foster, John E.

2003-01-01

The imposition of a magnetic field has been proposed as a means of reducing the electron backstreaming problem in ion thrusters. Electron backstreaming refers to the backflow of electrons into the ion thruster. Backstreaming electrons are accelerated by the large potential difference that exists between the ion-thruster acceleration electrodes, which otherwise accelerates positive ions out of the engine to develop thrust. The energetic beam formed by the backstreaming electrons can damage the discharge cathode, as well as other discharge surfaces upstream of the acceleration electrodes. The electron-backstreaming condition occurs when the center potential of the ion accelerator grid is no longer sufficiently negative to prevent electron diffusion back into the ion thruster. This typically occurs over extended periods of operation as accelerator-grid apertures enlarge due to erosion. As a result, ion thrusters are required to operate at increasingly negative accelerator-grid voltages in order to prevent electron backstreaming. These larger negative voltages give rise to higher accelerator grid erosion rates, which in turn accelerates aperture enlargement. Electron backstreaming due to accelerator-gridhole enlargement has been identified as a failure mechanism that will limit ionthruster service lifetime. The proposed method would make it possible to not only reduce the electron backstreaming current at and below the backstreaming voltage limit, but also reduce the backstreaming voltage limit itself. This reduction in the voltage at which electron backstreaming occurs provides operating margin and thereby reduces the magnitude of negative voltage that must be placed on the accelerator grid. Such a reduction reduces accelerator- grid erosion rates. The basic idea behind the proposed method is to impose a spatially uniform magnetic field downstream of the accelerator electrode that is oriented transverse to the thruster axis. The magnetic field must be sufficiently strong to impede backstreaming electrons, but not so strong as to significantly perturb ion trajectories. An electromagnet or permanent magnetic circuit can be used to impose the transverse magnetic field downstream of the accelerator-grid electrode. For example, in the case of an accelerator grid containing straight, parallel rows of apertures, one can apply nearly uniform magnetic fields across all the apertures by the use of permanent magnets of alternating polarity connected to pole pieces laid out parallel to the rows, as shown in the left part of the figure. For low-temperature operation, the pole pieces can be replaced with bar magnets of alternating polarity. Alternatively, for the same accelerator grid, one could use an electromagnet in the form of current-carrying rods laid out parallel to the rows.

Topology and grid adaption for high-speed flow computations

NASA Technical Reports Server (NTRS)

Abolhassani, Jamshid S.; Tiwari, Surendra N.

1989-01-01

This study investigates the effects of grid topology and grid adaptation on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption.

Considering the Spatial Layout Information of Bag of Features (BoF) Framework for Image Classification.

PubMed

Mu, Guangyu; Liu, Ying; Wang, Limin

2015-01-01

The spatial pooling method such as spatial pyramid matching (SPM) is very crucial in the bag of features model used in image classification. SPM partitions the image into a set of regular grids and assumes that the spatial layout of all visual words obey the uniform distribution over these regular grids. However, in practice, we consider that different visual words should obey different spatial layout distributions. To improve SPM, we develop a novel spatial pooling method, namely spatial distribution pooling (SDP). The proposed SDP method uses an extension model of Gauss mixture model to estimate the spatial layout distributions of the visual vocabulary. For each visual word type, SDP can generate a set of flexible grids rather than the regular grids from the traditional SPM. Furthermore, we can compute the grid weights for visual word tokens according to their spatial coordinates. The experimental results demonstrate that SDP outperforms the traditional spatial pooling methods, and is competitive with the state-of-the-art classification accuracy on several challenging image datasets.

Interactive algebraic grid-generation technique

NASA Technical Reports Server (NTRS)

Smith, R. E.; Wiese, M. R.

1986-01-01

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Unsteady-flow-field predictions for oscillating cascades

NASA Technical Reports Server (NTRS)

Huff, Dennis L.

1991-01-01

The unsteady flow field around an oscillating cascade of flat plates with zero stagger was studied by using a time marching Euler code. This case had an exact solution based on linear theory and served as a model problem for studying pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step size was shown for a moderate reduced frequency. Results show that an approximate nonreflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer to the airfoils than when reflective boundaries are used. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates captures the unsteady flow field better than when uniform grids are used as long as the 'Courant Friedrichs Levy' (CFL) number is less than 1 for a sufficient portion of the grid. Finally, a solution based on an optimization of grid, CFL number, and boundary conditions shows good agreement with linear theory.

Solution adaptive grids applied to low Reynolds number flow

NASA Astrophysics Data System (ADS)

de With, G.; Holdø, A. E.; Huld, T. A.

2003-08-01

A numerical study has been undertaken to investigate the use of a solution adaptive grid for flow around a cylinder in the laminar flow regime. The main purpose of this work is twofold. The first aim is to investigate the suitability of a grid adaptation algorithm and the reduction in mesh size that can be obtained. Secondly, the uniform asymmetric flow structures are ideal to validate the mesh structures due to mesh refinement and consequently the selected refinement criteria. The refinement variable used in this work is a product of the rate of strain and the mesh cell size, and contains two variables Cm and Cstr which determine the order of each term. By altering the order of either one of these terms the refinement behaviour can be modified.

[Mental interiority in the early-modern age. The "Cartesian theater"].

PubMed

Gillot, Pascale

2010-01-01

This paper looks into the notion of mental interiority in the early-modern age and, more specifically, into the Cartesian conception of the mind as an "inner theater". The main claim emphasizes a close connexion at work between the representative theory of the mind, associated with internalism, on the one hand, and a "neuropsychological" view on the other hand. Cartesian mentalism, in so far as it is based upon a disjunction between representation and resemblance, can therefore not be separated from the general project, already at work in the Dioptrique, of an intra-cerebral localization of the mental.

Dual redundant arm system operational quality measures and their applications - Dynamic measures

NASA Technical Reports Server (NTRS)

Lee, Sukhan; Kim, Sungbok

1990-01-01

Dual-arm dynamic operation quality measures are presented which quantify the efficiency and capability of generating Cartesian accelerations by two cooperative arms based on the analysis of dual-arm dynamic interactions. Dual-arm dynamic manipulability is defined as the efficiency of generating Cartesian accelerations under the dynamic and kinematic interactions between individual arms and an object under manipulation. The analysis of dual-arm dynamic interactions is based on the so-called Cartesian space agent model of an arm, which represents an individual arm as a force source acting upon a point mass with the effective Cartesian space arm dynamics and an environment or an object under manipulation. The Cartesian space agent model of an arm makes it possible to derive the dynamic and kinematic constraints involved in the transport, assembly and grasping modes of dual-arm cooperation. A task-oriented operational quality measure, (TOQd) is defined by evaluating dual-arm dynamic manipulability in terms of given task requirements. TOQd is used in dual-arm joint configuration optimization. Simulation results are shown. A complete set of forward dynamic equations for a dual-arm system is derived, and dual-arm dynamic operational quality measures for various modes of dual-arm cooperation allowing sliding contacts are established.

Multiscale Simulations of Magnetic Island Coalescence

NASA Technical Reports Server (NTRS)

Dorelli, John C.

2010-01-01

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

The vacuum platform

NASA Astrophysics Data System (ADS)

McNab, A.

2017-10-01

This paper describes GridPP’s Vacuum Platform for managing virtual machines (VMs), which has been used to run production workloads for WLCG and other HEP experiments. The platform provides a uniform interface between VMs and the sites they run at, whether the site is organised as an Infrastructure-as-a-Service cloud system such as OpenStack, or an Infrastructure-as-a-Client system such as Vac. The paper describes our experience in using this platform, in developing and operating VM lifecycle managers Vac and Vcycle, and in interacting with VMs provided by LHCb, ATLAS, ALICE, CMS, and the GridPP DIRAC service to run production workloads.

Evaluation of acoustic telemetry grids for determining aquatic animal movement and survival

USGS Publications Warehouse

Kraus, Richard T.; Holbrook, Christopher; Vandergoot, Christopher; Stewart, Taylor R.; Faust, Matthew D.; Watkinson, Douglas A.; Charles, Colin; Pegg, Mark; Enders, Eva C.; Krueger, Charles C.

2018-01-01

Acoustic telemetry studies have frequently prioritized linear configurations of hydrophone receivers, such as perpendicular from shorelines or across rivers, to detect the presence of tagged aquatic animals. This approach introduces unknown bias when receivers are stationed for convenience at geographic bottlenecks (e.g., at the mouth of an embayment or between islands) as opposed to deployments following a statistical sampling design.We evaluated two-dimensional acoustic receiver arrays (grids: receivers spread uniformly across space) as an alternative approach to provide estimates of survival, movement, and habitat use. Performance of variably-spaced receiver grids (5–25 km spacing) was evaluated by simulating (1) animal tracks as correlated random walks (speed: 0.1–0.9 m/s; turning angle standard deviation: 5–30 degrees); (2) variable tag transmission intervals along each track (nominal delay: 15–300 seconds); and (3) probability of detection of each transmission based on logistic detection range curves (midpoint: 200–1500 m). From simulations, we quantified i) time between successive detections on any receiver (detection time), ii) time between successive detections on different receivers (transit time), and iii) distance between successive detections on different receivers (transit distance).In the most restrictive detection range scenario (200 m), the 95th percentile of transit time was 3.2 days at 5 km grid spacing, 5.7 days at 7 km, and 15.2 days at 25 km; for the 1500 m detection range scenario, it was 0.1 days at 5 km, 0.5 days at 7 km, and 10.8 days at 25 km. These values represented upper bounds on the expected maximum time that an animal could go undetected. Comparison of the simulations with pilot studies on three fishes (walleye Sander vitreus, common carp Cyprinus carpio, and channel catfish Ictalurus punctatus) from two independent large lake ecosystems (lakes Erie and Winnipeg) revealed shorter detection and transit times than what simulations predicted.By spreading effort uniformly across space, grids can improve understanding of fish migration over the commonly employed receiver line approach, but at increased time cost for maintaining grids.

GEM-AC, a stratospheric-tropospheric global and regional model for air quality and climate change: evaluation of gas phase properties

NASA Astrophysics Data System (ADS)

Kaminski, J. W.; Semeniuk, K.; McConnell, J. C.; Lupu, A.; Mamun, A.

2012-12-01

The Global Environmental Multiscale model for Air Quality and climate change (GEM-AC) is a global general circulation model based on the GEM model developed by the Meteorological Service of Canada for operational weather forecasting. It can be run with a global uniform (GU) grid or a global variable (GV) grid where the core has uniform grid spacing and the exterior grid expands. With a GV grid high resolution regional runs can be accomplished without a concern for boundary conditions. The work described here uses GEM version 3.3.2. The gas-phase chemistry consists in detailed reactions of Ox, NOx, HOx, CO, CH4, NMVOCs, halocarbons, ClOx and BrO. We have recently added elements of the Global Modal-aerosol eXtension (GMXe) scheme to address aerosol microphysics and gas-aerosol partitioning. The evaluation of the MESSY GMXe aerosol scheme is addressed in another poster. The Canadian aerosol module (CAM) is also available. Tracers are advected using the semi-Lagrangian scheme native to GEM. The vertical transport includes parameterized subgrid scale turbulence and large scale convection. Dry deposition is implemented as a flux boundary condition in the vertical diffusion equation. For climate runs the GHGs CO2, CH4, N2O, CFCs in the radiation scheme are adjusted to the scenario considered. In GV regional mode at high resolutions a lake model, FLAKE is also included. Wet removal comprises both in-cloud and below-cloud scavenging. With the gas phase chemistry the model has been run for a series of ten year time slices on a 3°×3° global grid with 77 hybrid levels from the surface to 0.15 hPa. The tropospheric and stratospheric gas phase results are compared with satellite measurements including, ACE, MIPAS, MOPITT, and OSIRIS. Current evaluations of the ozone field and other stratospheric fields are encouraging and tropospheric lifetimes for CH4 and CH3CCl3 are in reasonable accord with tropospheric models. We will present results for current and future climate conditions forced by SST for 2050.

One-dimensional nonlinear theory for rectangular helix traveling-wave tube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong

A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numericallymore » using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.« less

Retrospectively gated intracardiac 4D flow MRI using spiral trajectories.

PubMed

Petersson, Sven; Sigfridsson, Andreas; Dyverfeldt, Petter; Carlhäll, Carl-Johan; Ebbers, Tino

2016-01-01

To develop and evaluate retrospectively gated spiral readout four-dimensional (4D) flow MRI for intracardiac flow analysis. Retrospectively gated spiral 4D flow MRI was implemented on a 1.5-tesla scanner. The spiral sequence was compared against conventional Cartesian 4D flow (SENSE [sensitivity encoding] 2) in seven healthy volunteers and three patients (only spiral). In addition to comparing flow values, linear regression was used to assess internal consistency of aortic versus pulmonary net volume flows and left ventricular inflow versus outflow using quantitative pathlines analysis. Total scan time with spiral 4D flow was 44% ± 6% of the Cartesian counterpart (13 ± 3 vs. 31 ± 7 min). Aortic versus pulmonary flow correlated strongly for the spiral sequence (P < 0.05, slope = 1.03, R(2) = 0.88, N = 10), whereas the linear relationship for the Cartesian sequence was not significant (P = 0.06, N = 7). Pathlines analysis indicated good data quality for the spiral (P < 0.05, slope = 1.02, R(2) = 0.90, N = 10) and Cartesian sequence (P < 0.05, slope = 1.10, R(2) = 0.93, N = 7). Spiral and Cartesian peak flow rate (P < 0.05, slope = 0.96, R(2) = 0.72, N = 14), peak velocity (P < 0.05, slope = 1.00, R(2) = 0.81, N = 14), and pathlines flow components (P < 0.05, slope = 1.04, R(2) = 0.87, N = 28) correlated well. Retrospectively gated spiral 4D flow MRI permits more than two-fold reduction in scan time compared to conventional Cartesian 4D flow MRI, while maintaining similar data quality. © 2015 Wiley Periodicals, Inc.

Application of overlay modeling and control with Zernike polynomials in an HVM environment

NASA Astrophysics Data System (ADS)

Ju, JaeWuk; Kim, MinGyu; Lee, JuHan; Nabeth, Jeremy; Jeon, Sanghuck; Heo, Hoyoung; Robinson, John C.; Pierson, Bill

2016-03-01

Shrinking technology nodes and smaller process margins require improved photolithography overlay control. Generally, overlay measurement results are modeled with Cartesian polynomial functions for both intra-field and inter-field models and the model coefficients are sent to an advanced process control (APC) system operating in an XY Cartesian basis. Dampened overlay corrections, typically via exponentially or linearly weighted moving average in time, are then retrieved from the APC system to apply on the scanner in XY Cartesian form for subsequent lot exposure. The goal of the above method is to process lots with corrections that target the least possible overlay misregistration in steady state as well as in change point situations. In this study, we model overlay errors on product using Zernike polynomials with same fitting capability as the process of reference (POR) to represent the wafer-level terms, and use the standard Cartesian polynomials to represent the field-level terms. APC calculations for wafer-level correction are performed in Zernike basis while field-level calculations use standard XY Cartesian basis. Finally, weighted wafer-level correction terms are converted to XY Cartesian space in order to be applied on the scanner, along with field-level corrections, for future wafer exposures. Since Zernike polynomials have the property of being orthogonal in the unit disk we are able to reduce the amount of collinearity between terms and improve overlay stability. Our real time Zernike modeling and feedback evaluation was performed on a 20-lot dataset in a high volume manufacturing (HVM) environment. The measured on-product results were compared to POR and showed a 7% reduction in overlay variation including a 22% terms variation. This led to an on-product raw overlay Mean + 3Sigma X&Y improvement of 5% and resulted in 0.1% yield improvement.

Neural coding of image structure and contrast polarity of Cartesian, hyperbolic, and polar gratings in the primary and secondary visual cortex of the tree shrew.

PubMed

Poirot, Jordan; De Luna, Paolo; Rainer, Gregor

2016-04-01

We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. Copyright © 2016 the American Physiological Society.

Numerical modelling of needle-grid electrodes for negative surface corona charging system

NASA Astrophysics Data System (ADS)

Zhuang, Y.; Chen, G.; Rotaru, M.

2011-08-01

Surface potential decay measurement is a simple and low cost tool to examine electrical properties of insulation materials. During the corona charging stage, a needle-grid electrodes system is often used to achieve uniform charge distribution on the surface of the sample. In this paper, a model using COMSOL Multiphysics has been developed to simulate the gas discharge. A well-known hydrodynamic drift-diffusion model was used. The model consists of a set of continuity equations accounting for the movement, generation and loss of charge carriers (electrons, positive and negative ions) coupled with Poisson's equation to take into account the effect of space and surface charges on the electric field. Four models with the grid electrode in different positions and several mesh sizes are compared with a model that only has the needle electrode. The results for impulse current and surface charge density on the sample clearly show the effect of the extra grid electrode with various positions.

Parallel Adaptive High-Order CFD Simulations Characterizing Cavity Acoustics for the Complete SOFIA Aircraft

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.; Biswas, Rupak

2014-01-01

This paper presents one-of-a-kind MPI-parallel computational fluid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft of a Boeing 747SP. These simulations focus on how the unsteady flow field inside and over the cavity interferes with the optical path and mounting of the telescope. A temporally fourth-order Runge-Kutta, and spatially fifth-order WENO-5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh refinement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32,000 cores and 4 billion cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregularities caused by the highly complex geometry. Limits to scaling beyond 32K cores are identified, and targeted code optimizations are discussed.

Technical Note: Robust measurement of the slice-sensitivity profile in breast tomosynthesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maki, Aili K., E-mail: aili.maki@sri.utoronto.ca

2016-08-15

Purpose: The purpose of this work is to improve the repeatability of the measurement of the slice-sensitivity profile (SSP) in reconstructed breast tomosynthesis volumes. Methods: A grid of aluminum ball-bearings (BBs) within a PMMA phantom was imaged on breast tomosynthesis systems from three different manufacturers. The full-width half-maximum (FWHM) values were measured for the SSPs of the BBs in the reconstructed volumes. The effect of transforming the volumes from a Cartesian coordinate system (CCS) to a cone-beam coordinate system (CBCS) on the variability in the FWHM values was assessed. Results: Transforming the volumes from a CCS to a CBCS beforemore » measuring the SSPs reduced the coefficient of variation (COV) in the measurements of FWHM in repeated measurements by 56% and reduced the dependence of the FWHM values on the location of the BBs within the reconstructed volume by 76%. Conclusions: Measuring the SSP in the volumes in a CBCS improves the robustness of the measurement.« less

Implementation of polyatomic MCTDHF capability

NASA Astrophysics Data System (ADS)

Haxton, Daniel; Jones, Jeremiah; Rescigno, Thomas; McCurdy, C. William; Ibrahim, Khaled; Williams, Sam; Vecharynski, Eugene; Rouet, Francois-Henry; Li, Xiaoye; Yang, Chao

2015-05-01

The implementation of the Multiconfiguration Time-Dependent Hartree-Fock method for poly- atomic molecules using a cartesian product grid of sinc basis functions will be discussed. The focus will be on two key components of the method: first, the use of a resolution-of-the-identity approximation; sec- ond, the use of established techniques for triple Toeplitz matrix algebra using fast Fourier transform over distributed memory architectures (MPI 3D FFT). The scaling of two-electron matrix element transformations is converted from O(N4) to O(N log N) by including these components. Here N = n3, with n the number of points on a side. We test the prelim- inary implementation by calculating absorption spectra of small hydro- carbons, using approximately 16-512 points on a side. This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under the Early Career program, and by the offices of BES and Advanced Scientific Computing Research, under the SciDAC program.

Modified Polar-Format Software for Processing SAR Data

NASA Technical Reports Server (NTRS)

Chen, Curtis

2003-01-01

HMPF is a computer program that implements a modified polar-format algorithm for processing data from spaceborne synthetic-aperture radar (SAR) systems. Unlike prior polar-format processing algorithms, this algorithm is based on the assumption that the radar signal wavefronts are spherical rather than planar. The algorithm provides for resampling of SAR pulse data from slant range to radial distance from the center of a reference sphere that is nominally the local Earth surface. Then, invoking the projection-slice theorem, the resampled pulse data are Fourier-transformed over radial distance, arranged in the wavenumber domain according to the acquisition geometry, resampled to a Cartesian grid, and inverse-Fourier-transformed. The result of this process is the focused SAR image. HMPF, and perhaps other programs that implement variants of the algorithm, may give better accuracy than do prior algorithms for processing strip-map SAR data from high altitudes and may give better phase preservation relative to prior polar-format algorithms for processing spotlight-mode SAR data.

Numerical Methodology for Coupled Time-Accurate Simulations of Primary and Secondary Flowpaths in Gas Turbines

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Athavale, M. M.; Hendricks, R. C.; Steinetz, B. M.

2006-01-01

Detailed information of the flow-fields in the secondary flowpaths and their interaction with the primary flows in gas turbine engines is necessary for successful designs with optimized secondary flow streams. Present work is focused on the development of a simulation methodology for coupled time-accurate solutions of the two flowpaths. The secondary flowstream is treated using SCISEAL, an unstructured adaptive Cartesian grid code developed for secondary flows and seals, while the mainpath flow is solved using TURBO, a density based code with capability of resolving rotor-stator interaction in multi-stage machines. An interface is being tested that links the two codes at the rim seal to allow data exchange between the two codes for parallel, coupled execution. A description of the coupling methodology and the current status of the interface development is presented. Representative steady-state solutions of the secondary flow in the UTRC HP Rig disc cavity are also presented.

Analysis of digital images into energy-angular momentum modes.

PubMed

Vicent, Luis Edgar; Wolf, Kurt Bernardo

2011-05-01

The measurement of continuous wave fields by a digital (pixellated) screen of sensors can be used to assess the quality of a beam by finding its formant modes. A generic continuous field F(x, y) sampled at an N × N Cartesian grid of point sensors on a plane yields a matrix of values F(q(x), q(y)), where (q(x), q(y)) are integer coordinates. When the approximate rotational symmetry of the input field is important, one may use the sampled Laguerre-Gauss functions, with radial and angular modes (n, m), to analyze them into their corresponding coefficients F(n, m) of energy and angular momentum (E-AM). The sampled E-AM modes span an N²-dimensional space, but are not orthogonal--except for parity. In this paper, we propose the properly orthonormal "Laguerre-Kravchuk" discrete functions Λ(n, m)(q(x), q(y)) as a convenient basis to analyze the sampled beams into their E-AM polar modes, and with them synthesize the input image exactly.

Cart3D Simulations for the First AIAA Sonic Boom Prediction Workshop

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Nemec, Marian

2014-01-01

Simulation results for the First AIAA Sonic Boom Prediction Workshop (LBW1) are presented using an inviscid, embedded-boundary Cartesian mesh method. The method employs adjoint-based error estimation and adaptive meshing to automatically determine resolution requirements of the computational domain. Results are presented for both mandatory and optional test cases. These include an axisymmetric body of revolution, a 69deg delta wing model and a complete model of the Lockheed N+2 supersonic tri-jet with V-tail and flow through nacelles. In addition to formal mesh refinement studies and examination of the adjoint-based error estimates, mesh convergence is assessed by presenting simulation results for meshes at several resolutions which are comparable in size to the unstructured grids distributed by the workshop organizers. Data provided includes both the pressure signals required by the workshop and information on code performance in both memory and processing time. Various enhanced techniques offering improved simulation efficiency will be demonstrated and discussed.

Higher Order Lagrange Finite Elements In M3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

J. Chen; H.R. Strauss; S.C. Jardin

The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemesmore » have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.« less

Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Bolster, Diogo

2017-04-01

We introduce a simple and efficient lattice Boltzmann method for immiscible multiphase flows, capable of handling large density and viscosity contrasts. The model is based on a diffuse-interface phase-field approach. Within this context we propose a new algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. The proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases. We test the model by applying it to four benchmark problems: (i) wetting and dewetting of a droplet on a flat surface and (ii) on a cylindrical surface, (iii) multiphase flow past a circular cylinder at an intermediate Reynolds number, and (iv) a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions. Where available, our results show good agreement with analytical solutions and/or existing experimental data, highlighting strengths of this new approach.

Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

PubMed Central

Towse, Benjamin W.; Barry, Caswell; Bush, Daniel; Burgess, Neil

2014-01-01

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues. PMID:24366144

Enhanced Representation of Turbulent Flow Phenomena in Large-Eddy Simulations of the Atmospheric Boundary Layer using Grid Refinement with Pseudo-Spectral Numerics

NASA Astrophysics Data System (ADS)

Torkelson, G. Q.; Stoll, R., II

2017-12-01

Large Eddy Simulation (LES) is a tool commonly used to study the turbulent transport of momentum, heat, and moisture in the Atmospheric Boundary Layer (ABL). For a wide range of ABL LES applications, representing the full range of turbulent length scales in the flow field is a challenge. This is an acute problem in regions of the ABL with strong velocity or scalar gradients, which are typically poorly resolved by standard computational grids (e.g., near the ground surface, in the entrainment zone). Most efforts to address this problem have focused on advanced sub-grid scale (SGS) turbulence model development, or on the use of massive computational resources. While some work exists using embedded meshes, very little has been done on the use of grid refinement. Here, we explore the benefits of grid refinement in a pseudo-spectral LES numerical code. The code utilizes both uniform refinement of the grid in horizontal directions, and stretching of the grid in the vertical direction. Combining the two techniques allows us to refine areas of the flow while maintaining an acceptable grid aspect ratio. In tests that used only refinement of the vertical grid spacing, large grid aspect ratios were found to cause a significant unphysical spike in the stream-wise velocity variance near the ground surface. This was especially problematic in simulations of stably-stratified ABL flows. The use of advanced SGS models was not sufficient to alleviate this issue. The new refinement technique is evaluated using a series of idealized simulation test cases of neutrally and stably stratified ABLs. These test cases illustrate the ability of grid refinement to increase computational efficiency without loss in the representation of statistical features of the flow field.

Towards a Comprehensive Computational Simulation System for Turbomachinery

NASA Technical Reports Server (NTRS)

Shih, Ming-Hsin

1994-01-01

The objective of this work is to develop algorithms associated with a comprehensive computational simulation system for turbomachinery flow fields. This development is accomplished in a modular fashion. These modules includes grid generation, visualization, network, simulation, toolbox, and flow modules. An interactive grid generation module is customized to facilitate the grid generation process associated with complicated turbomachinery configurations. With its user-friendly graphical user interface, the user may interactively manipulate the default settings to obtain a quality grid within a fraction of time that is usually required for building a grid about the same geometry with a general-purpose grid generation code. Non-Uniform Rational B-Spline formulations are utilized in the algorithm to maintain geometry fidelity while redistributing grid points on the solid surfaces. Bezier curve formulation is used to allow interactive construction of inner boundaries. It is also utilized to allow interactive point distribution. Cascade surfaces are transformed from three-dimensional surfaces of revolution into two-dimensional parametric planes for easy manipulation. Such a transformation allows these manipulated plane grids to be mapped to surfaces of revolution by any generatrix definition. A sophisticated visualization module is developed to al-low visualization for both grid and flow solution, steady or unsteady. A network module is built to allow data transferring in the heterogeneous environment. A flow module is integrated into this system, using an existing turbomachinery flow code. A simulation module is developed to combine the network, flow, and visualization module to achieve near real-time flow simulation about turbomachinery geometries. A toolbox module is developed to support the overall task. A batch version of the grid generation module is developed to allow portability and has been extended to allow dynamic grid generation for pitch changing turbomachinery configurations. Various applications with different characteristics are presented to demonstrate the success of this system.

Design of Multishell Sampling Schemes with Uniform Coverage in Diffusion MRI

PubMed Central

Caruyer, Emmanuel; Lenglet, Christophe; Sapiro, Guillermo; Deriche, Rachid

2017-01-01

Purpose In diffusion MRI, a technique known as diffusion spectrum imaging reconstructs the propagator with a discrete Fourier transform, from a Cartesian sampling of the diffusion signal. Alternatively, it is possible to directly reconstruct the orientation distribution function in q-ball imaging, providing so-called high angular resolution diffusion imaging. In between these two techniques, acquisitions on several spheres in q-space offer an interesting trade-off between the angular resolution and the radial information gathered in diffusion MRI. A careful design is central in the success of multishell acquisition and reconstruction techniques. Methods The design of acquisition in multishell is still an open and active field of research, however. In this work, we provide a general method to design multishell acquisition with uniform angular coverage. This method is based on a generalization of electrostatic repulsion to multishell. Results We evaluate the impact of our method using simulations, on the angular resolution in one and two bundles of fiber configurations. Compared to more commonly used radial sampling, we show that our method improves the angular resolution, as well as fiber crossing discrimination. Discussion We propose a novel method to design sampling schemes with optimal angular coverage and show the positive impact on angular resolution in diffusion MRI. PMID:23625329

A Velocity Distribution Model for Steady State Heat Transfer

NASA Technical Reports Server (NTRS)

Hall, Eric B.

1996-01-01

Consider a box that is filled with an ideal gas and that is aligned along Cartesian coordinates (x, y, z) having until length in the 'y' direction and unspecified length in the 'x' and 'z' directions. Heat is applied uniformly over the 'hot' end of the box (y = 1) and is removed uniformly over the 'cold' end (y = O) at a constant rate such that the ends of the box are maintained at temperatures T(sub 0) at y = O and T(sub 1) at y = 1. Let U, V, and W denote the respective velocity components of a molecule inside the box selected at some random time and at some location (x, y, z). If T(sub 0) = T(sub 1), then U, Y, and W are mutually independent and Gaussian, each with mean zero and variance RT(sub 0), where R is the gas constant. When T(sub 0) does not equal T(sub 1) the velocity components are not independent and are not Gaussian. Our objective is to characterize the joint distribution of the velocity components U, Y, and W as a function of y, and, in particular, to characterize the distribution of V given y. It is hoped that this research will lead to an increased physical understanding of the nature of turbulence.

The Cartesian Heritage of Bloom's Taxonomy

ERIC Educational Resources Information Center

Bertucio, Brett

2017-01-01

This essay seeks to contribute to the critical reception of "Bloom's Taxonomy of Educational Objectives" by tracing the Taxonomy's underlying philosophical assumptions. Identifying Bloom's work as consistent with the legacy of Cartesian thought, I argue that its hierarchy of behavioral objectives provides a framework for certainty and…

Reduction of respiratory ghosting motion artifacts in conventional two-dimensional multi-slice Cartesian turbo spin-echo: which k-space filling order is the best?

PubMed

Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi

2018-06-01

The two-dimensional Cartesian turbo spin-echo (TSE) sequence is widely used in routine clinical studies, but it is sensitive to respiratory motion. We investigated the k-space orders in Cartesian TSE that can effectively reduce motion artifacts. The purpose of this study was to demonstrate the relationship between k-space order and degree of motion artifacts using a moving phantom. We compared the degree of motion artifacts between linear and asymmetric k-space orders. The actual spacing of ghost artifacts in the asymmetric order was doubled compared with that in the linear order in the free-breathing situation. The asymmetric order clearly showed less sensitivity to incomplete breath-hold at the latter half of the imaging period. Because of the actual number of partitions of the k-space and the temporal filling order, the asymmetric k-space order of Cartesian TSE was superior to the linear k-space order for reduction of ghosting motion artifacts.

SU-E-P-30: Clinical Applications of Spatially Fractionated Radiation Therapy (GRID) Using Helical Tomotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, X; Liang, X; Penagaricano, J

2015-06-15

Purpose: To present the first clinical applications of Helical Tomotherapy-based spatially fractionated radiotherapy (HT-GRID) for deep seated tumors and associated dosimetric study. Methods: Ten previously treated GRID patients were selected (5 HT-GRID and 5 LINAC-GRID using a commercially available GRID block). Each case was re-planned either in HT-GRID or LINAC-GRID for a total of 10 plans for both techniques using same prescribed dose of 20 Gy to maximum point dose of GRID GTV. For TOMO-GRID, a programmable virtual TOMOGRID template mimicking a GRID pattern was generated. Dosimetric parameters compared included: GRID GTV mean dose (Dmean) and equivalent uniform dose (EUD),more » GRID GTV dose inhomogeneity (Ratio(valley/peak)), normal tissue Dmean and EUD, and other organs-at-risk(OARs) doses. Results: The median tumor volume was 634 cc, ranging from 182 to 4646 cc. Median distance from skin to the deepest part of tumor was 22cm, ranging from 8.9 to 38cm. The median GRID GTV Dmean and EUD was 10.65Gy (9.8–12.5Gy) and 7.62Gy (4.31–11.06Gy) for HT-GRID and was 6.73Gy (4.44–8.44Gy) and 3.95Gy (0.14–4.2Gy) for LINAC-GRID. The median Ratio(valley/peak) was 0.144(0.05–0.29) for HT-GRID and was 0.055(0.0001–0.14) for LINAC-GRID. For normal tissue in HT-GRID, the median Dmean and EUD was 1.24Gy (0.34–2.54Gy) and 5.45 Gy(3.45–6.89Gy) and was 0.61 Gy(0.11–1.52Gy) and 6Gy(4.45–6.82Gy) for LINAC-GRID. The OAR doses were comparable between the HT-GRID and LINAC-GRID. However, in some cases it was not possible to avoid a critical structure in LINAC-GRID; while HT-GRID can spare more tissue doses for certain critical structures. Conclusion: HT-GRID delivers higher GRID GTV Dmean, EUD and Ratio(valley/peak) compared to LINAC-GRID. HT-GRID delivers higher Dmean and lower EUD for normal tissue compared to LINAC-GRID. TOMOGRID template can be highly patient-specific and allows adjustment of the GRID pattern to different tumor sizes and shapes when they are deeply-seated and cannot be safely treated with LINAC-GRID.« less

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.

Creation of bioactive glass (13-93) scaffolds for structural bone repair using a combined finite element modeling and rapid prototyping approach.

PubMed

Xiao, Wei; Zaeem, Mohsen Asle; Bal, B Sonny; Rahaman, Mohamed N

2016-11-01

There is a clinical need for synthetic bioactive materials that can reliably repair intercalary skeletal tissue loss in load-bearing bones. Bioactive glasses have been investigated as one such material but their mechanical response has been a concern. Previously, we created bioactive silicate glass (13-93) scaffolds with a uniform grid-like microstructure which showed a compressive strength comparable to human cortical bone but a much lower flexural strength. In the present study, finite element modeling (FEM) was used to re-design the scaffold microstructure to improve its flexural strength without significantly lowering its compressive strength and ability to support bone infiltration in vivo. Then scaffolds with the requisite microstructures were created by a robotic deposition method and tested in four-point bending and compression to validate the FEM simulations. In general, the data validated the predictions of the FEM simulations. Scaffolds with a porosity gradient, composed of a less porous outer region and a more porous inner region, showed a flexural strength (34±5MPa) that was more than twice the value for the uniform grid-like microstructure (15±5MPa) and a higher compressive strength (88±20MPa) than the grid-like microstructure (72±10MPa). Upon implantation of the scaffolds for 12weeks in rat calvarial defects in vivo, the amount of new bone that infiltrated the pore space of the scaffolds with the porosity gradient (37±16%) was similar to that for the grid-like scaffolds (35±6%). These scaffolds with a porosity gradient that better mimics the microstructure of human long bone could provide more reliable implants for structural bone repair. Copyright © 2016 Elsevier B.V. All rights reserved.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels,' nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces, It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Astrophysics Data System (ADS)

Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.

2001-12-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2013-12-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed-sphere grids

NASA Astrophysics Data System (ADS)

Thuburn, J.; Cotter, C. J.; Dubos, T.

2014-05-01

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

Wide-range radioactive-gas-concentration detector

DOEpatents

Anderson, D.F.

1981-11-16

A wide-range radioactive-gas-concentration detector and monitor capable of measuring radioactive-gas concentrations over a range of eight orders of magnitude is described. The device is designed to have an ionization chamber sufficiently small to give a fast response time for measuring radioactive gases but sufficiently large to provide accurate readings at low concentration levels. Closely spaced parallel-plate grids provide a uniform electric field in the active region to improve the accuracy of measurements and reduce ion migration time so as to virtually eliminate errors due to ion recombination. The parallel-plate grids are fabricated with a minimal surface area to reduce the effects of contamination resulting from absorption of contaminating materials on the surface of the grids. Additionally, the ionization-chamber wall is spaced a sufficient distance from the active region of the ionization chamber to minimize contamination effects.

Two-Liquid Cartesian Diver

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.

Dynamic fisheye grids for binary black hole simulations

NASA Astrophysics Data System (ADS)

Zilhão, Miguel; Noble, Scott C.

2014-03-01

We present a new warped gridding scheme adapted to simulating gas dynamics in binary black hole spacetimes. The grid concentrates grid points in the vicinity of each black hole to resolve the smaller scale structures there, and rarefies grid points away from each black hole to keep the overall problem size at a practical level. In this respect, our system can be thought of as a ‘double’ version of the fisheye coordinate system, used before in numerical relativity codes for evolving binary black holes. The gridding scheme is constructed as a mapping between a uniform coordinate system—in which the equations of motion are solved—to the distorted system representing the spatial locations of our grid points. Since we are motivated to eventually use this system for circumbinary disc calculations, we demonstrate how the distorted system can be constructed to asymptote to the typical spherical polar coordinate system, amenable to efficiently simulating orbiting gas flows about central objects with little numerical diffusion. We discuss its implementation in the Harm3d code, tailored to evolve the magnetohydrodynamics equations in curved spacetimes. We evaluate the performance of the system’s implementation in Harm3d with a series of tests, such as the advected magnetic field loop test, magnetized Bondi accretion, and evolutions of hydrodynamic discs about a single black hole and about a binary black hole. Like we have done with Harm3d, this gridding scheme can be implemented in other unigrid codes as a (possibly) simpler alternative to adaptive mesh refinement.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods $-$ Part 1: Derivation and properties

DOE PAGES

Eldred, Christopher; Randall, David

2017-02-17

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restrictedmore » to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Lastly, detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.« less

Effect of frequency on the uniformity of symmetrical RF CCP discharges

NASA Astrophysics Data System (ADS)

Liu, Yue; Booth, Jean-Paul; Chabert, Pascal

2018-05-01

A 2D Cartesian electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) model presented previously (Liu et al 2018 Plasma Sources Sci. Technol. 27 025006) is used to investigate the effect of the driving frequency (over the range of 15–45 MHz) on the plasma uniformity in radio frequency (RF) capacitively coupled plasma (CCP) discharges in a geometrically symmetric reactor with a dielectric side wall in argon gas. The reactor size (12 cm electrode length, 2.5 cm gap) and driving frequency are sufficiently small that electromagnetic effects can be ignored. Previously, we showed (Liu et al 2018 Plasma Sources Sci. Technol. 27 025006) that for 15 MHz excitation, Ohmic heating of electrons by the electric field perpendicular to the electrodes is enhanced in a region in front of the dielectric side wall, leading to a maximum in electron density there. In this work we show that increasing the excitation frequency (at constant applied voltage amplitude) not only increases the overall electron heating and density but also causes a stronger, narrower peak in electron heating closer to the dielectric wall, improving the plasma uniformity along the electrodes. This heating peak comes both from enhanced perpendicular electron heating and from the appearance at high frequency of significant parallel heating. The latter is caused by the presence of a significant parallel-direction RF oscillating electric field in the corners. Whereas at the reactor center the sheaths oscillate perpendicularly to the electrodes, near the dielectric edge they move in and out of the corners and must be treated in two dimensions.

Vapor Cartesian Diver

ERIC Educational Resources Information Center

Grebenev, Igor V.; Lebedeva, Olga V.; Polushkina, Svetlana V.

2018-01-01

The article proposes a new research object for a general physics course--the vapour Cartesian diver, designed to study the properties of saturated water vapour. Physics education puts great importance on the study of the saturated vapour state, as it is related to many fundamental laws and theories. For example, the temperature dependence of the…

Naturalistic Inquiry: Politics and Implications for Special Education.

ERIC Educational Resources Information Center

Lincoln, Yvonna S.

The revolution in hard sciences is explored, from the Cartesian-Newtonian worldview to the Heisenbergian universe, and consideration is given to whether the conventional, Cartesian model is a serviceable one for research in the social/applied sciences. Five axioms comprising the existing paradigm of logical positivism are outlined (reality,…

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…

Plasma characteristics of direct current enhanced cylindrical inductively coupled plasma source

NASA Astrophysics Data System (ADS)

Yue, HUA; Jian, SONG; Zeyu, HAO; Chunsheng, REN

2018-06-01

Experimental results of a direct current enhanced inductively coupled plasma (DCE-ICP) source which consists of a typical cylindrical ICP source and a plate-to-grid DC electrode are reported. With the use of this new source, the plasma characteristic parameters, namely, electron density, electron temperature and plasma uniformity, are measured by Langmuir floating double probe. It is found that DC discharge enhances the electron density and decreases the electron temperature, dramatically. Moreover, the plasma uniformity is obviously improved with the operation of DC and radio frequency (RF) hybrid discharge. Furthermore, the nonlinear enhancement effect of electron density with DC + RF hybrid discharge is confirmed. The presented observation indicates that the DCE-ICP source provides an effective method to obtain high-density uniform plasma, which is desirable for practical industrial applications.

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

Evaluation of the UnTRIM model for 3-D tidal circulation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; ,

2001-01-01

A family of numerical models, known as the TRIM models, shares the same modeling philosophy for solving the shallow water equations. A characteristic analysis of the shallow water equations points out that the numerical instability is controlled by the gravity wave terms in the momentum equations and by the transport terms in the continuity equation. A semi-implicit finite-difference scheme has been formulated so that these terms and the vertical diffusion terms are treated implicitly and the remaining terms explicitly to control the numerical stability and the computations are carried out over a uniform finite-difference computational mesh without invoking horizontal or vertical coordinate transformations. An unstructured grid version of TRIM model is introduced, or UnTRIM (pronounces as "you trim"), which preserves these basic numerical properties and modeling philosophy, only the computations are carried out over an unstructured orthogonal grid. The unstructured grid offers the flexibilities in representing complex study areas so that fine grid resolution can be placed in regions of interest, and coarse grids are used to cover the remaining domain. Thus, the computational efforts are concentrated in areas of importance, and an overall computational saving can be achieved because the total number of grid-points is dramatically reduced. To use this modeling approach, an unstructured grid mesh must be generated to properly reflect the properties of the domain of the investigation. The new modeling flexibility in grid structure is accompanied by new challenges associated with issues of grid generation. To take full advantage of this new model flexibility, the model grid generation should be guided by insights into the physics of the problems; and the insights needed may require a higher degree of modeling skill.

A Comparison of Spectral Element and Finite Difference Methods Using Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem

NASA Astrophysics Data System (ADS)

Ng, C. S.; Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Bhattacharjee, A.

2009-04-01

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (\\ci) in two dimensions. \\ci is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.

Uniform tissue lesion formation induced by high-intensity focused ultrasound along a spiral pathway.

PubMed

Qian, Kui; Li, Chenghai; Ni, Zhengyang; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2017-05-01

Both theoretical and experimental studies were performed here to investigate the lesion formation induced by high-intensity focused ultrasound (HIFU) operating in continuous scanning mode along a spiral pathway. The Khokhlov-Zabolotskaya-Kuznetsov equation and bio-heat equation were combined in the current model to predict HIFU-induced temperature distribution and lesion formation. The shape of lesion and treatment efficiency were assessed for a given scanning speed at two different grid spacing (3mm and 4mm) in the gel phantom studies and further researched in ex vivo studies. The results show that uniform lesions can be generated with continuous HIFU scanning along a spiral pathway. The complete coverage of the entire treated volume can be achieved as long as the spacing grid of the spiral pathway is small enough for heat to diffuse and deposit, and the treatment efficiency can be optimized by selecting an appropriate scanning speed. This study can provide guidance for further optimization of the treatment efficiency and safety of HIFU therapy. Copyright © 2017 Elsevier B.V. All rights reserved.

High Power ECR Ion Thruster Discharge Characterization

NASA Technical Reports Server (NTRS)

Foster, John E.; Kamhawi, Hani; Haag, Thomas; Carpenter, Christian; Williams, George W.

2006-01-01

Electron cyclotron resonance (ECR) based ion thrusters with carbon based ion optics can potentially satisfy lifetime requirements for long duration missions (approximately 10 years) because grid erosion and cathode insert depletion issues are virtually eliminated. Though the ECR plasma discharge has been found to typically operate at slightly higher discharge losses than conventional DC ion thrusters (for high total thruster power applications), the discharge power fraction is small (less than 1 percent at 25 kW). In this regard, the benefits of increased life, low discharge plasma potentials, and reduced complexity are welcome tradeoffs for the associated discharge efficiency decrease. Presented here are results from discharge characterization of a large area ECR plasma source for gridded ion thruster applications. These measurements included load matching efficacy, bulk plasma properties via Langmuir probe, and plasma uniformity as measured using current probes distributed at the exit plane. A high degree of plasma uniformity was observed (flatness greater than 0.9). Additionally, charge state composition was qualitatively evaluated using emission spectroscopy. Plasma induced emission was dominated by xenon ion lines. No doubly charged xenon ions were detected.

Constrained evolution in numerical relativity

NASA Astrophysics Data System (ADS)

Anderson, Matthew William

The strongest potential source of gravitational radiation for current and future detectors is the merger of binary black holes. Full numerical simulation of such mergers can provide realistic signal predictions and enhance the probability of detection. Numerical simulation of the Einstein equations, however, is fraught with difficulty. Stability even in static test cases of single black holes has proven elusive. Common to unstable simulations is the growth of constraint violations. This work examines the effect of controlling the growth of constraint violations by solving the constraints periodically during a simulation, an approach called constrained evolution. The effects of constrained evolution are contrasted with the results of unconstrained evolution, evolution where the constraints are not solved during the course of a simulation. Two different formulations of the Einstein equations are examined: the standard ADM formulation and the generalized Frittelli-Reula formulation. In most cases constrained evolution vastly improves the stability of a simulation at minimal computational cost when compared with unconstrained evolution. However, in the more demanding test cases examined, constrained evolution fails to produce simulations with long-term stability in spite of producing improvements in simulation lifetime when compared with unconstrained evolution. Constrained evolution is also examined in conjunction with a wide variety of promising numerical techniques, including mesh refinement and overlapping Cartesian and spherical computational grids. Constrained evolution in boosted black hole spacetimes is investigated using overlapping grids. Constrained evolution proves to be central to the host of innovations required in carrying out such intensive simulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sidler, Rolf, E-mail: rsidler@gmail.com; Carcione, José M.; Holliger, Klaus

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 themore » 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.« less

Implementation of ADI: Schemes on MIMD parallel computers

NASA Technical Reports Server (NTRS)

Vanderwijngaart, Rob F.

1993-01-01

In order to simulate the effects of the impingement of hot exhaust jets of High Performance Aircraft on landing surfaces a multi-disciplinary computation coupling flow dynamics to heat conduction in the runway needs to be carried out. Such simulations, which are essentially unsteady, require very large computational power in order to be completed within a reasonable time frame of the order of an hour. Such power can be furnished by the latest generation of massively parallel computers. These remove the bottleneck of ever more congested data paths to one or a few highly specialized central processing units (CPU's) by having many off-the-shelf CPU's work independently on their own data, and exchange information only when needed. During the past year the first phase of this project was completed, in which the optimal strategy for mapping an ADI-algorithm for the three dimensional unsteady heat equation to a MIMD parallel computer was identified. This was done by implementing and comparing three different domain decomposition techniques that define the tasks for the CPU's in the parallel machine. These implementations were done for a Cartesian grid and Dirichlet boundary conditions. The most promising technique was then used to implement the heat equation solver on a general curvilinear grid with a suite of nontrivial boundary conditions. Finally, this technique was also used to implement the Scalar Penta-diagonal (SP) benchmark, which was taken from the NAS Parallel Benchmarks report. All implementations were done in the programming language C on the Intel iPSC/860 computer.

Numerical preservation of symmetry properties of continuum problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caramana, E.J.; Whalen, P.

1997-12-31

The authors investigate the problem of perfectly preserving a symmetry associated naturally with one coordinate system when calculated in a different coordinate system. This allows a much wider range of problems that may be viewed as perturbations of the given symmetry to be investigated. They study the problem of preserving cylindrical symmetry in two-dimensional cartesian geometry and spherical symmetry in two-dimensional cylindrical geometry. They show that this can be achieved by a simple modification of the gradient operator used to compute the force in a staggered grid Lagrangian hydrodynamics algorithm. In the absence of the supposed symmetry they show thatmore » the new operator produces almost no change in the results because it is always close to the original gradient operator. Their technique this results in a subtle manipulation of the spatial truncation error in favor of the assumed symmetry but only to the extent that it is naturally present in the physical situation. This not only extends the range of previous algorithms and the use of new ones for these studies, but for spherical or cylindrical calculations reduces the sensitivity of the results to grid setup with equal angular zoning that has heretofore been necessary with these problems. Although this work is in two-dimensions, it does point the way to solving this problem in three-dimensions. This is particularly important for the ASCI initiative. The manner in which these results can be extended to three-dimensions will be discussed.« less

Overview of Transonic to Hypersonic Stage Separation Tool Development for Multi-Stage-to-Orbit Concepts

NASA Technical Reports Server (NTRS)

Murphy, Kelly J.; Bunning, Pieter G.; Pamadi, Bandu N.; Scallion, William I.; Jones, Kenneth M.

2004-01-01

An overview of research efforts at NASA in support of the stage separation and ascent aerothermodynamics research program is presented. The objective of this work is to develop a synergistic suite of experimental, computational, and engineering tools and methods to apply to vehicle separation across the transonic to hypersonic speed regimes. Proximity testing of a generic bimese wing-body configuration is on-going in the transonic (Mach numbers 0.6, 1.05, and 1.1), supersonic (Mach numbers 2.3, 3.0, and 4.5) and hypersonic (Mach numbers 6 and 10) speed regimes in four wind tunnel facilities at the NASA Langley Research Center. An overset grid, Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of the bimese configuration. Steady-state predictions with this solver were in excellent agreement with wind tunnel data at Mach 3 as were predictions via a Cartesian-grid Euler solver. Experimental and computational data have been used to evaluate multi-body enhancements to the widely-used Aerodynamic Preliminary Analysis System, an engineering methodology, and to develop a new software package, SepSim, for the simulation and visualization of vehicle motions in a stage separation scenario. Web-based software will be used for archiving information generated from this research program into a database accessible to the user community. Thus, a framework has been established to study stage separation problems using coordinated experimental, computational, and engineering tools.

KINETIC ENERGY FROM SUPERNOVA FEEDBACK IN HIGH-RESOLUTION GALAXY SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simpson, Christine M.; Bryan, Greg L.; Ostriker, Jeremiah P.

We describe a new method for adding a prescribed amount of kinetic energy to simulated gas modeled on a cartesian grid by directly altering grid cells’ mass and velocity in a distributed fashion. The method is explored in the context of supernova (SN) feedback in high-resolution (∼10 pc) hydrodynamic simulations of galaxy formation. Resolution dependence is a primary consideration in our application of the method, and simulations of isolated explosions (performed at different resolutions) motivate a resolution-dependent scaling for the injected fraction of kinetic energy that we apply in cosmological simulations of a 10{sup 9} M{sub ⊙} dwarf halo. Wemore » find that in high-density media (≳50 cm{sup −3}) with coarse resolution (≳4 pc per cell), results are sensitive to the initial kinetic energy fraction due to early and rapid cooling. In our galaxy simulations, the deposition of small amounts of SN energy in kinetic form (as little as 1%) has a dramatic impact on the evolution of the system, resulting in an order-of-magnitude suppression of stellar mass. The overall behavior of the galaxy in the two highest resolution simulations we perform appears to converge. We discuss the resulting distribution of stellar metallicities, an observable sensitive to galactic wind properties, and find that while the new method demonstrates increased agreement with observed systems, significant discrepancies remain, likely due to simplistic assumptions that neglect contributions from SNe Ia and stellar winds.« less

Brillouin zone grid refinement for highly resolved ab initio THz optical properties of graphene

NASA Astrophysics Data System (ADS)

Warmbier, Robert; Quandt, Alexander

2018-07-01

Optical spectra of materials can in principle be calculated within numerical frameworks based on Density Functional Theory. The huge numerical effort involved in these methods severely constraints the accuracy achievable in practice. In the case of the THz spectrum of graphene the primary limitation lays in the density of the reciprocal space sampling. In this letter we have developed a non-uniform sampling using grid refinement to achieve a high local sampling density with only moderate numerical effort. The resulting THz electron energy loss spectrum shows a plasmon signal below 50 meV with a ω(q) ∝√{ q } dispersion relation.

Effect of Contraction on Turbulence and Temperature Fluctuations Generated by a Warm Grid

NASA Technical Reports Server (NTRS)

Mills, Robert R., Jr.; Corrsin, Stanley

1959-01-01

Hot-wire anemometer measurements were made of several statistical properties of approximately homogeneous and isotropic fields of turbulence and temperature fluctuations generated by a warm grid in a uniform airstream sent through a 4-to-1 contraction. These measurements were made both in the contraction and in the axisymmetric domain farther downstream. In addition to confirming the well-known turbulence anisotropy induced by strain, the data show effects on the skewnesses of both longitudinal velocity fluctuation (which has zero skewness in isotropic turbulence) and its derivative. The concomitant anisotropy in the temperature field accelerates the decay of temperature fluctuations.

Use of photostress and strain gages to analyze behavior of weldments

NASA Astrophysics Data System (ADS)

Gambrell, S. C., Jr.

1993-09-01

Tensile and pure bending tests were conducted on specimens having welded joints made from 2219-T87 aluminum alloy and 2319 filler. Data were collected using photoelastic coatings and strain gages. Stress-strain relationships and contraction ratios were determined at several points in a grid covering the weld material and heat affected zone. Material behavior was nonlinear and nonuniform at all points in the grid and contraction ratios did not conform to those predicted by Chakrabarty's plasticity theory. Yielding in joints made using four new welding procedures was examined. None of the new procedures produced more uniform yielding in the joint.

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.

2012-01-01

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herrnstein, Aaron R.

An ocean model with adaptive mesh refinement (AMR) capability is presented for simulating ocean circulation on decade time scales. The model closely resembles the LLNL ocean general circulation model with some components incorporated from other well known ocean models when appropriate. Spatial components are discretized using finite differences on a staggered grid where tracer and pressure variables are defined at cell centers and velocities at cell vertices (B-grid). Horizontal motion is modeled explicitly with leapfrog and Euler forward-backward time integration, and vertical motion is modeled semi-implicitly. New AMR strategies are presented for horizontal refinement on a B-grid, leapfrog time integration,more » and time integration of coupled systems with unequal time steps. These AMR capabilities are added to the LLNL software package SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) and validated with standard benchmark tests. The ocean model is built on top of the amended SAMRAI library. The resulting model has the capability to dynamically increase resolution in localized areas of the domain. Limited basin tests are conducted using various refinement criteria and produce convergence trends in the model solution as refinement is increased. Carbon sequestration simulations are performed on decade time scales in domains the size of the North Atlantic and the global ocean. A suggestion is given for refinement criteria in such simulations. AMR predicts maximum pH changes and increases in CO 2 concentration near the injection sites that are virtually unattainable with a uniform high resolution due to extremely long run times. Fine scale details near the injection sites are achieved by AMR with shorter run times than the finest uniform resolution tested despite the need for enhanced parallel performance. The North Atlantic simulations show a reduction in passive tracer errors when AMR is applied instead of a uniform coarse resolution. No dramatic or persistent signs of error growth in the passive tracer outgassing or the ocean circulation are observed to result from AMR.« less

Submarine Periscope Depth Course Selection Tactical Decision Aid

DTIC Science & Technology

1997-12-01

are translated to Cartesian coordinates. Co is own ship’s course. 8 X0 = DMho. cos(Co) Yo = DAho . sin(Co) Xc = DMht- cos(Ct) Yc = DMhbt sin(Ct) These...Display Graph. The input parameters of DAho , Ct, and DMiht along with Co as generated by the simulation are used to determine the Cartesian

Supporting Generative Thinking about Number Lines, the Cartesian Plane, and Graphs of Linear Functions

ERIC Educational Resources Information Center

Earnest, Darrell Steven

2012-01-01

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

Sign(al)s: Living and Learning as Semiotic Engagement

ERIC Educational Resources Information Center

Stables, Andrew

2006-01-01

Cartesian mind-body dualism, while often explicitly denied, has left a legacy of conceptions that remain highly influential in education. I argue that trends in both analytic and continental philosophy of language point towards a post-Cartesian settlement in which the distinction between "signs" and "signals" is collapsed, and which thus construes…