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NASA NTRS1995

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

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.

Coirier, William J.↗

NASA NTRS1995

Parametric design and gridding through relational geometry

Relational Geometric Synthesis (RGS) is a new logical framework for building up precise definitions of complex geometric models from points, curves, surfaces and solids. RGS achieves unprecedented design flexibility by supporting a rich variety of useful curve and surface entities. During the design process, many qualitative and quantitative relationships between elementary objects may be captured and retained in a data structure equivalent to a directed graph, such that they can be utilized for automatically updating the complete model geometry following changes in the shape or location of an underlying object. Capture of relationships enables many new possibilities for parametric variations and optimization. Examples are given of panelization applications for submarines, sailing yachts, offshore structures, and propellers.

Letcher, John S., Jr.↗

NASA NTRS1993

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

Biswas, Rupak↗

NASA NTRS1994

New multigrid approach for three-dimensional unstructured, adaptive grids

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.

Parthasarathy, Vijayan↗

NASA NTRS1994

Design and implementation of a parallel unstructured Euler solver using software primitives

This paper is concerned with the implementation of a three-dimensional unstructured-grid Euler solver on massively parallel distributed-memory computer architectures. The goal is to minimize solution time by achieving high computational rates with a numerically efficient algorithm. An unstructured multigrid algorithm with an edge-based data structure has been adopted, and a number of optimizations have been devised and implemented to accelerate the parallel computational rates. The implementation is carried out by creating a set of software tools, which provide an interface between the parallelization issues and the sequential code, while providing a basis for future automatic run-time compilation support. Large practical unstructured grid problems are solved on the Intel iPSC/860 hypercube and Intel Touchstone Delta machine. The quantitative effects of the various optimizations are demonstrated, and we show that the combined effect of these optimizations leads to roughly a factor of 3 performance improvement. The overall solution efficiency is compared with that obtained on the Cray Y-MP vector supercomputer.

Das, R.↗

NASA NTRS1993

Adaptive-mesh algorithms for computational fluid dynamics

The basic goal of adaptive-mesh algorithms is to distribute computational resources wisely by increasing the resolution of 'important' regions of the flow and decreasing the resolution of regions that are less important. While this goal is one that is worthwhile, implementing schemes that have this degree of sophistication remains more of an art than a science. In this paper, the basic pieces of adaptive-mesh algorithms are described and some of the possible ways to implement them are discussed and compared. These basic pieces are the data structure to be used, the generation of an initial mesh, the criterion to be used to adapt the mesh to the solution, and the flow-solver algorithm on the resulting mesh. Each of these is discussed, with particular emphasis on methods suitable for the computation of compressible flows.

Powell, Kenneth G.↗

NASA NTRS1995

Client/server study

The goal of this project is to find cost-effective and efficient strategies/solutions to integrate existing databases, manage network, and improve productivity of users in a move towards client/server and Integrated Desktop Environment (IDE) at NASA LeRC. The project consisted of two tasks as follows: (1) Data collection, and (2) Database Development/Integration. Under task 1, survey questionnaires and a database were developed. Also, an investigation on commercially available tools for automated data-collection and net-management was performed. As requirements evolved, the main focus has been task 2 which involved the following subtasks: (1) Data gathering/analysis of database user requirements, (2) Database analysis and design, making recommendations for modification of existing data structures into relational database or proposing a common interface to access heterogeneous databases(INFOMAN system, CCNS equipment list, CCNS software list, USERMAN, and other databases), (3) Establishment of a client/server test bed at Central State University (CSU), (4) Investigation of multi-database integration technologies/ products for IDE at NASA LeRC, and (5) Development of prototypes using CASE tools (Object/View) for representative scenarios accessing multi-databases and tables in a client/server environment. Both CSU and NASA LeRC have benefited from this project. CSU team investigated and prototyped cost-effective/practical solutions to facilitate NASA LeRC move to a more productive environment. CSU students utilized new products and gained skills that could be a great resource for future needs of NASA.

Dezhgosha, Kamyar↗

NASA NTRS1990

CLIPS enhanced with objects, backward chaining and explanation facilities

In this project we extend C Language Production System (CLIPS), an existing Expert System shell, by creating three new options. Specifically, first we create a compatible with CLIPS environment that allows for defining objects and object hierarchies, second we provide means to implement backward chaining in a pure forward chaining environment, and finally we give some simple explanation facilities for the derivations the system has made. Objects and object hierarchies are extended so that facts can be automatically inferred, and placed in the fact base. Backward chaining is implemented by creating run time data structures which hold the derivation process allowing for a depth first search. The backward chaining mechanism works not only with ground facts, but also creates bindings for every query that involves variables, and returns the truth value of such a query as well as the relevant variable bindings. Finally, the WHY and HOW explanation facilities allow for a complete examination of the derivation process, the rules triggered, and the bindings created. The entire system is integrated with the original CLIPS code, and all of its routines can be invoked as CLIPS commands.

Aldrobi, M.↗

NASA NTRS1996

Stress and Damage in Polymer Matrix Composite Materials Due to Material Degradation at High Temperatures

This report describes analytical methods for calculating stresses and damage caused by degradation of the matrix constituent in polymer matrix composite materials. Laminate geometry, material properties, and matrix degradation states are specified as functions of position and time. Matrix shrinkage and property changes are modeled as functions of the degradation states. The model is incorporated into an existing composite mechanics computer code. Stresses, strains, and deformations at the laminate, ply, and micro levels are calculated, and from these calculations it is determined if there is failure of any kind. The rationale for the model (based on published experimental work) is presented, its integration into the laminate analysis code is outlined, and example results are given, with comparisons to existing material and structural data. The mechanisms behind the changes in properties and in surface cracking during long-term aging of polyimide matrix composites are clarified. High-temperature-material test methods are also evaluated.

McManus, Hugh L.↗

NASA NTRS1996

A User's Guide to AMR1D: An Instructional Adaptive Mesh Refinement Code for Unstructured Grids

This report documents the code AMR1D, which is currently posted on the World Wide Web (http://sdcd.gsfc.nasa.gov/ESS/exchange/contrib/de-fainchtein/adaptive _mesh_refinement.html). AMR1D is a one-dimensional finite element fluid-dynamics solver, capable of adaptive mesh refinement (AMR). It was written as an instructional tool for AMR on unstructured mesh codes. It is meant to illustrate the minimum requirements for AMR on more than one dimension. For that purpose, it uses the same type of data structure that would be necessary on a two-dimensional AMR code (loosely following the algorithm described by Lohner).

deFainchtein, Rosalinda↗

NASA NTRS1995

Fast Multipole Methods for Three-Dimensional N-body Problems

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Koumoutsakos, P.↗

NASA NTRS1995

Distributed and collaborative synthetic environments

Fast graphics workstations and increased computing power, together with improved interface technologies, have created new and diverse possibilities for developing and interacting with synthetic environments. A synthetic environment system is generally characterized by input/output devices that constitute the interface between the human senses and the synthetic environment generated by the computer; and a computation system running a real-time simulation of the environment. A basic need of a synthetic environment system is that of giving the user a plausible reproduction of the visual aspect of the objects with which he is interacting. The goal of our Shastra research project is to provide a substrate of geometric data structures and algorithms which allow the distributed construction and modification of the environment, efficient querying of objects attributes, collaborative interaction with the environment, fast computation of collision detection and visibility information for efficient dynamic simulation and real-time scene display. In particular, we address the following issues: (1) A geometric framework for modeling and visualizing synthetic environments and interacting with them. We highlight the functions required for the geometric engine of a synthetic environment system. (2) A distribution and collaboration substrate that supports construction, modification, and interaction with synthetic environments on networked desktop machines.

Bajaj, Chandrajit L.↗

NASA NTRS1996

An N-body Tree Algorithm for the Cray T3D

We describe in this paper an algorithm for solving the gravitational N-body problem using tree data structures on the Cray T3D parallel supercomputer. This implementation is an adaptation of previous work where this problem was solved using an SIMD, fine-grained parallel computer. We show here that this approach lends itself, with small modifications, to more coarse-grained parallelism as well. We also show that the performance of the algorithm on the Cray T3D parallel architecture scales adequately with the number of processors (up to 256). Specific levels to be reached using the Cray T3D parallel architecture. A peak performance level of 9.6 Gflop/s is reached on 256 processors for the time critical gravity computation.

Olson, Kevin M.↗

NASA NTRS1996

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

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.

Coirier, William J.↗

NASA NTRS1992

Sparse Matrices in MATLAB: Design and Implementation

The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

Gilbert, John R.↗

NASA NTRS1998

Parallel PAB3D: Experiences with a Prototype in MPI

PAB3D is a three-dimensional Navier Stokes solver that has gained acceptance in the research and industrial communities. It takes as computational domain, a set disjoint blocks covering the physical domain. This is the first report on the implementation of PAB3D using the Message Passing Interface (MPI), a standard for parallel processing. We discuss briefly the characteristics of tile code and define a prototype for testing. The principal data structure used for communication is derived from preprocessing "patching". We describe a simple interface (COMMSYS) for MPI communication, and some general techniques likely to be encountered when working on problems of this nature. Last, we identify levels of improvement from the current version and outline future work.

Guerinoni, Fabio↗

NASA NTRS1999

Object-Oriented Design for Sparse Direct Solvers

We discuss the object-oriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important structural and algorithmic classes in our design, and discuss the trade-offs we made for high performance. The kernels at the lower layers were optimized by hand. Our results show no performance loss from our object-oriented design, while providing flexibility, case of use, and extensibility over solvers using procedural design.

Dobrian, Florin↗

NASA NTRS1988

Identification of 15-15 Aeroelastic Modes using Frequency-Domain Methods

The XV-15 Tilt-Rotor wing has six major aeroelastic modes that are close in frequency. To precisely excite individual modes during flight test, dual flaperon exciters with automatic frequency-sweep controls were installed. The resulting structural data were analyzed in the frequency domain (Fourier-transformed). Modal frequencies and damping were determined by performing curve fits to frequency-response magnitude and phase data. Results are given for the XV-15 with its original metal rotor blades. Frequency and damping values are also compared with new predictions by two different programs, CAMRAD and ASAP.

Acree, C. W., Jr.↗