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Application of advanced grid generation techniques for flow field computations about complex configurations

In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.

Kathong, Monchai↗

Application of a variational method for generating adaptive grids

The application of variational methods for generating adaptive grids is not as straightforward as one is led to believe. Proper scaling, suitable weight functions and appropriate clustering on boundaries must be employed to obtain a satisfactory grid. This work, which is based on the framework developed by Brackbill and Saltzman, provides simple methods for determining scaling and investigates possible options for selecting the weight function and clustering points on the boundaries. The concepts developed here are applied to two two-dimensional problems: a model problem based on Burger's equation which contains two length scales and, transonic flow past airfoils using the Euler equations.

Kreis, R. I.↗

GRID3C: Computer program for generation of C type multilevel, three dimensional and boundary conforming periodic grids

A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.

Dulikravich, D. S.↗

Fast Generation of body conforming grids for 3-D

A fast algorithm was developed for accurately generating boundary conforming, three dimensional, consecutively refined, computational grids applicable to arbitrary axial turbomachinery geometry. The method is based on using a single analytic function to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the hub and the shroud. These grids are of the "O" type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flowfield. Due to the built in additional nonorthogonal coordinate stretching and shearing, the grid lines leaving the trailing of the blade end at downstream infinity, thus simplifying the numerical treatment of the three dimensional trailing vortex sheet.

Dulikravich, O.↗

An Application of Overset Grids to Payload/Fairing Three-Dimensional Internal Flow CFD Analysis

The application of overset grids to the computational fluid dynamics analysis of three-dimensional internal flow in the payload/fairing of an expendable launch vehicle is described. In conjunction with the overset grid system, the flowfield in the payload/fairing configuration is obtained with the aid of OVERFLOW Navier-Stokes code. The solution exhibits a highly three dimensional complex flowfield with swirl, separation, and vortices. Some of the computed flow features are compared with the measured Laser-Doppler Velocimetry (LDV) data on a 1/5th scale model of the payload/fairing configuration. The counter-rotating vortex structures and the location of the saddle point predicted by the CFD analysis are in general agreement with the LDV data. Comparisons of the computed (CFD) velocity profiles on horizontal and vertical lines in the LDV measurement plane in the faring nose region show reasonable agreement with the LDV data.

Kandula, Max↗

Proof-of-Concept Experiments on a Gallium-Based Ignitron for Pulsed Power Applications

Ignitrons are electrical switching devices that operate at switching times that are on the order of microseconds, can conduct high currents of thousands of amps, and are capable of holding off tens of thousands of volts between pulses. They consist of a liquid metal pool within an evacuated tube that serves both the cathode and the source of atoms and electrons for an arc discharge. Facing the liquid metal pool is an anode suspended above the cathode, with a smaller ignitor electrode tip located just above the surface of the cathode. The ignitron can be charged to significant voltages, with a potential difference of thousands of volts between anode and cathode. When an ignition pulse is delivered from the ignitor electrode to the cathode, a small amount of the liquid metal is vaporized and subsequently ionized, with the high voltage between the anode and cathode causing the gas to bridge the gap between the two electrodes. The electrons and ions move rapidly towards the anode and cathode, respectively, with the ions liberating still more atoms from the liquid metal cathode surface as a high-current plasma arc discharge is rapidly established. This arc continues in a self-sustaining fashion until the potential difference between the anode and cathode drops below some critical value. Ignitrons have been used in a variety of pulsed power applications, including the railroad industry, industrial chemical processing, and high-power arc welding. In addition, they might prove useful in terrestrial power grid applications, serving as high-current fault switches, quickly shunting dangerous high-current or high-voltage spikes safely to ground. The motivation for this work stemmed from the fact that high-power, high-reliability, pulsed power devices like the ignitron have been used for ground testing in-space pulsed electric thruster technologies, and the continued use of ignitrons could prove advantageous to the future development and testing of such thrusters. Previous ignitron designs have used mercury as the liquid metal cathode, owing to its presence as a liquid at room temperatures and a vapor pressure of 10 Pa (75 mtorr) at room temperature. While these are favorable properties, there are obvious environmental and personal safety concerns with the storage, handling, and use of mercury and its compounds. The purpose of the present work was to fabricate and test an ignitron that used as its cathode an alternate liquid metal that was safe to handle and store. To that end, an ignitron test article that used liquid gallium as the cathode material was developed and tested. Gallium is a metal that has a melting temperature of 29.76 C, which is slightly above room temperature, and a boiling point of over 2,300 C at atmospheric pressure. This property makes gallium the element with the largest relative difference between melting and boiling points. Gallium has a limited role in biology, and when ingested, it will be subsequently processed by the body and expelled rather than accumulating to toxic levels. The next section of this Technical Memorandum (TM) provides background information on the development of mercury-based ignitrons, which serves as the starting point for the development of the gallium-based variant. Afterwards, the experimental hardware and setup used in proof-of-concept testing of a basic gallium ignitron are presented. Experimental data, consisting of discharge voltage and current waveforms as well as high-speed imaging of the gallium arc discharge in the gallium ignitron test article, are presented to demonstrate the efficacy of the concept. Discussion of the data and suggestions on improvements for future iterations of the design are presented in the final two sections of this TM.

Ali, H. K.↗

GRID3O: Computer program for fast generation of multilevel, three-dimensional boundary-conforming O-type computational grids

A fast algorithm was developed for accurately generating boundary-conforming, three-dimensional, consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. The method is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing edge to end at downstream infinity, the numerical treatment of the three-dimensional trailing vortex sheets is simplified.

Dulikravich, D. S.↗

A Geometry Based Infra-Structure for Computational Analysis and Design

The computational steps traditionally taken for most engineering analysis suites (computational fluid dynamics (CFD), structural analysis, heat transfer and etc.) are: (1) Surface Generation -- usually by employing a Computer Assisted Design (CAD) system; (2) Grid Generation -- preparing the volume for the simulation; (3) Flow Solver -- producing the results at the specified operational point; (4) Post-processing Visualization -- interactively attempting to understand the results. For structural analysis, integrated systems can be obtained from a number of commercial vendors. These vendors couple directly to a number of CAD systems and are executed from within the CAD Graphical User Interface (GUI). It should be noted that the structural analysis problem is more tractable than CFD; there are fewer mesh topologies used and the grids are not as fine (this problem space does not have the length scaling issues of fluids). For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. In most cases, the output from a CAD system could go to Initial Graphics Exchange Specification (IGES) or Standard Exchange Program (STEP) files. The output from Grid Generators and Solvers do not really have standards though there are a couple of file formats that can be used for a subset of the gridding (i.e. PLOT3D data formats). The user would have to patch up the data or translate from one format to another to move to the next step. Sometimes this could take days. Specifically the problems with this procedure are:(1) File based -- Information flows from one step to the next via data files with formats specified for that procedure. File standards, when they exist, are wholly inadequate. For example, geometry from CAD systems (transmitted via IGES files) is defined as disjoint surfaces and curves (as well as masses of other information of no interest for the Grid Generator). This is particularly onerous for modern CAD systems based on solid modeling. The part was a proper solid and in the translation to IGES has lost this important characteristic. STEP is another standard for CAD data that exists and supports the concept of a solid. The problem with STEP is that a solid modeling geometry kernel is required to query and manipulate the data within this type of file. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. Adroit multi-block methods are not far behind. This means that a million node steady-state solution can be computed on the order of hours (using current high performance computers) starting from this 'good' geometry. Unfortunately, the geometry usually transmitted from the CAD system is not 'good' in the grid generator sense. The grid generator needs smooth closed solid geometry. It can take a week (or more) of interaction with the CAD output (sometimes by hand) before the process can begin. One way Communication. (3) One-way Communication -- All information travels on from one phase to the next. This makes procedures like node adaptation difficult when attempting to add or move nodes that sit on bounding surfaces (when the actual surface data has been lost after the grid generation phase). Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive. There is also no way to easily deal with this system in a modular manner. One can only replace the grid generator, for example, if the software reads and writes the same files. Instead of the serial approach to analysis as described above, CAPRI takes a geometry centric approach. This makes the actual geometry (not a discretized version) accessible to all phases of the analysis. The connection to the geometry is made through an Application Programming Interface (API) and NOT a file system. This API isolates the top-level applications (grid generators, solvers and visualization components) from the geometry engine. Also this allows the replacement of one geometry kernel with another, without effecting these top-level applications. For example, if UniGraphics is used as the CAD package then Parasolid (UG's own geometry engine) can be used for all geometric queries so that no solid geometry information is lost in a translation. This is much better than STEP because when the data is queried, the same software is executed as used in the CAD system. Therefore, one analyzes the exact part that is in the CAD system. CAPRI uses the same idea as the commercial structural analysis codes but does not specify control. Software components of the CAD system are used, but the analysis suite, not the CAD operator, specifies the control of the software session. This also means that the license issues (may be) minimized and individuals need not have to know how to operate a CAD system in order to run the suite.

Haimes, Robert↗

On the applications of algebraic grid generation methods based on transfinite interpolation

Algebraic grid generation methods based on transfinite interpolation called the two-boundary and four-boundary methods are applied for generating grids with highly complex boundaries. These methods yield grid point distributions that allow for accurate application to regions of sharp gradients in the physical domain or time-dependent problems with small length scale phenomena. Algebraic grids are derived using the two-boundary and four-boundary methods for applications in both two- and three-dimensional domains. Grids are developed for distinctly different geometrical problems and the two-boundary and four-boundary methods are demonstrated to be applicable to a wide class of geometries.

Nguyen, Hung Lee↗

Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D showed that HPF has potential to be a high level language for parallelization of CFD applications. The use of HPF requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement and data granularity. Since HPF hides data movement from the user even with this knowledge it is easy to overlook pieces of the code causing low performance of the application. In order to simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and partially implemented ADAPT (Automatic Data Distribution and Placement Tool). The ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level or inter application level. ADAPT is designed to annotate existing CFD FORTRAN application performing computations on single or multiple grids. On each grid the application can considered as a sequence of operators each applied to a set of variables defined in a particular grid domain. The operators can be classified as implicit, having data dependences, and explicit, without data dependences. In order to parallelize an explicit operator it is sufficient to create a template for the domain of the operator, align arrays used in the operator with the template, distribute the template, and declare the loops over the distributed dimensions as INDEPENDENT. In order to parallelize an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator then the loop which implements the operator can be declared as INDEPENDENT.

Frumkin, Michael↗

The multidimensional Self-Adaptive Grid code, SAGE, version 2

This new report on Version 2 of the SAGE code includes all the information in the original publication plus all upgrades and changes to the SAGE code since that time. The two most significant upgrades are the inclusion of a finite-volume option and the ability to adapt and manipulate zonal-matching multiple-grid files. In addition, the original SAGE code has been upgraded to Version 1.1 and includes all options mentioned in this report, with the exception of the multiple grid option and its associated features. Since Version 2 is a larger and more complex code, it is suggested (but not required) that Version 1.1 be used for single-grid applications. This document contains all the information required to run both versions of SAGE. The formulation of the adaption method is described in the first section of this document. The second section is presented in the form of a user guide that explains the input and execution of the code. The third section provides many examples. Successful application of the SAGE code in both two and three dimensions for the solution of various flow problems has proven the code to be robust, portable, and simple to use. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for complex grid structures. Modifications to the method and the simple but extensive input options make this a flexible and user-friendly code. The SAGE code can accommodate two-dimensional and three-dimensional, finite-difference and finite-volume, single grid, and zonal-matching multiple grid flow problems.

Davies, Carol B.↗

A Hierarchical and Distributed Approach for Mapping Large Applications to Heterogeneous Grids using Genetic Algorithms

In this paper, we propose a distributed approach for mapping a single large application to a heterogeneous grid environment. To minimize the execution time of the parallel application, we distribute the mapping overhead to the available nodes of the grid. This approach not only provides a fast mapping of tasks to resources but is also scalable. We adopt a hierarchical grid model and accomplish the job of mapping tasks to this topology using a scheduler tree. Results show that our three-phase algorithm provides high quality mappings, and is fast and scalable.

Sanyal, Soumya↗

A self-adaptive-grid method with application to airfoil flow

A self-adaptive-grid method is described that is suitable for multidimensional steady and unsteady computations. Based on variational principles, a spring analogy is used to redistribute grid points in an optimal sense to reduce the overall solution error. User-specified parameters, denoting both maximum and minimum permissible grid spacings, are used to define the all-important constants, thereby minimizing the empiricism and making the method self-adaptive. Operator splitting and one-sided controls for orthogonality and smoothness are used to make the method practical, robust, and efficient. Examples are included for both steady and unsteady viscous flow computations about airfoils in two dimensions, as well as for a steady inviscid flow computation and a one-dimensional case. These examples illustrate the precise control the user has with the self-adaptive method and demonstrate a significant improvement in accuracy and quality of the solutions.

Nakahashi, K.↗

A three-dimensional spacecraft-charging computer code

A computer code is described which simulates the interaction of the space environment with a satellite at geosynchronous altitude. Employing finite elements, a three-dimensional satellite model has been constructed with more than 1000 surface cells and 15 different surface materials. Free space around the satellite is modeled by nesting grids within grids. Applications of this NASA Spacecraft Charging Analyzer Program (NASCAP) code to the study of a satellite photosheath and the differential charging of the SCATHA (satellite charging at high altitudes) satellite in eclipse and in sunlight are discussed. In order to understand detector response when the satellite is charged, the code is used to trace the trajectories of particles reaching the SCATHA detectors. Particle trajectories from positive and negative emitters on SCATHA also are traced to determine the location of returning particles, to estimate the escaping flux, and to simulate active control of satellite potentials.

Rubin, A. G.↗

Charon Toolkit for Parallel, Implicit Structured-Grid Computations: Functional Design

In a previous report the design concepts of Charon were presented. Charon is a toolkit that aids engineers in developing scientific programs for structured-grid applications to be run on MIMD parallel computers. It constitutes an augmentation of the general-purpose MPI-based message-passing layer, and provides the user with a hierarchy of tools for rapid prototyping and validation of parallel programs, and subsequent piecemeal performance tuning. Here we describe the implementation of the domain decomposition tools used for creating data distributions across sets of processors. We also present the hierarchy of parallelization tools that allows smooth translation of legacy code (or a serial design) into a parallel program. Along with the actual tool descriptions, we will present the considerations that led to the particular design choices. Many of these are motivated by the requirement that Charon must be useful within the traditional computational environments of Fortran 77 and C. Only the Fortran 77 syntax will be presented in this report.

VanderWijngaart, Rob F.↗

Safe Grid

The biggest users of GRID technologies came from the science and technology communities. These consist of government, industry and academia (national and international). The NASA GRID is moving into a higher technology readiness level (TRL) today; and as a joint effort among these leaders within government, academia, and industry, the NASA GRID plans to extend availability to enable scientists and engineers across these geographical boundaries collaborate to solve important problems facing the world in the 21 st century. In order to enable NASA programs and missions to use IPG resources for program and mission design, the IPG capabilities needs to be accessible from inside the NASA center networks. However, because different NASA centers maintain different security domains, the GRID penetration across different firewalls is a concern for center security people. This is the reason why some IPG resources are been separated from the NASA center network. Also, because of the center network security and ITAR concerns, the NASA IPG resource owner may not have full control over who can access remotely from outside the NASA center. In order to obtain organizational approval for secured remote access, the IPG infrastructure needs to be adapted to work with the NASA business process. Improvements need to be made before the IPG can be used for NASA program and mission development. The Secured Advanced Federated Environment (SAFE) technology is designed to provide federated security across NASA center and NASA partner's security domains. Instead of one giant center firewall which can be difficult to modify for different GRID applications, the SAFE "micro security domain" provide large number of professionally managed "micro firewalls" that can allow NASA centers to accept remote IPG access without the worry of damaging other center resources. The SAFE policy-driven capability-based federated security mechanism can enable joint organizational and resource owner approved remote access from outside of NASA centers. A SAFE enabled IPG can enable IPG capabilities to be available to NASA mission design teams across different NASA center and partner company firewalls. This paper will first discuss some of the potential security issues for IPG to work across NASA center firewalls. We will then present the SAFE federated security model. Finally we will present the concept of the architecture of a SAFE enabled IPG and how it can benefit NASA mission development.

Chow, Edward T.↗

Application of multiple grids topology to supersonic internal/external flow interactions

For many aerodynamic applications, it is very difficult to construct a smooth body-fitted grid around complex configurations. An approach, called 'multiple grids' or 'zonal grids', which subdivides the entire physical domain into several subdomains, is used to overcome such difficulties. The approach is applied to obtain the solutions to the Euler equations for the supersonic internal/external flow around a fighter-aircraft configuration. Steady-state solutions are presented for Mach 2 at 0, 3.79, 7, and 10 deg angles-of-attack. The problem of conservative treatment at the zonal interfaces is also addressed.

Kathong, M.↗

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

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

Frumkin, Michael↗