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NASA NTRS1996

Hyperbolic Methods for Surface and Field Grid Generation

This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.

Chan, William M.↗

NASA NTRS2001

SGBEM-FEM Alternating Method for Analyzing 3D Non-Planar Cracks and Their Growth in Structural Components

The highly accurate and efficient Symmetric Galerkin Boundary Element Method (SGBEM), a Finite Element Method (FEM)-based alternating method, is proposed for analyzing three-dimensional non-planar cracks and their growth. The cracks are modeled using the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, simulating an infinite medium. The finite element method only analyzes the stress for the uncracked body. The solution for the cracked structural component is determined by an iteration procedure. This process alternates between an FEM solution for the uncracked body and the SGBEM solution for a crack in an infinite body. Numerical analysis, and the Java code used, evaluate stress intensity factors and model fatigue crack growth. Examples of non-planar cracks in infinite media and planar cracks in finite bodies, as well as growth under fatigue, show the accuracy of the method.

Nikishkov, G. P.↗

NASA NTRS2002

Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum- exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Mei, Renwei↗

NASA NTRS2002

Measurement of Trailing Edge Noise Using Directional Array and Coherent Output Power Methods

The use of a directional (or phased) array of microphones for the measurement of trailing edge (TE) noise is described and tested. The capabilities of this method arc evaluated via measurements of TE noise from a NACA 63-215 airfoil model and from a cylindrical rod. This TE noise measurement approach is compared to one that is based on thc cross spectral analysis of output signals from a pair of microphones placed on opposite sides of an airframe model (COP method). Advantages and limitations of both methods arc examined. It is shown that the microphone array can accurately measures TE noise and captures its two-dimensional characteristic over a large frequency range for any TE configuration as long as noise contamination from extraneous sources is within bounds. The COP method is shown to also accurately measure TE noise but over a more limited frequency range that narrows for increased TE thickness. Finally, the applicability and generality of an airfoil self-noise prediction method was evaluated via comparison to the experimental data obtained using the COP and array measurement methods. The predicted and experimental results are shown to agree over large frequency ranges.

Hutcheson, Florence V.↗

NASA NTRS2002

Measurement Of Trailing Edge Noise using Directional Array and Coherent Output Power Methods

The use of a directional array of microphones for the measurement of trailing edge (TE) noise is described. The capabilities of this method are evaluated via measurements of TE noise from a NACA 63-215 airfoil model and from a cylindrical rod. This TE noise measurement approach is compared to one that is based on the cross spectral analysis of output signals from a pair of microphones (COP method). Advantages and limitations of both methods are examined. It is shown that the microphone array can accurately measures TE noise and captures its two-dimensional characteristic over a large frequency range for any TE configuration as long as noise contamination from extraneous sources is within bounds. The COP method is shown to also accurately measure TE noise but over a more limited frequency range that narrows for increased TE thickness. Finally, the applicability and generality of an airfoil self-noise prediction method was evaluated via comparison to the experimental data obtained using the COP and array measurement methods. The predicted and experimental results are shown to agree over large frequency ranges.

Hutcheson, Florence V.↗

NASA NTRS2003

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Zang, Thomas A.↗

NASA NTRS2004

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel Benchmarks (NPB). In this paper, we present some interesting performance results of ow OpenMP parallel implementation on different architectures such as the SGI Origin2000, SGI Altix, and Cray MTA-2.

Feng, Huiyu↗

NASA NTRS2005

Multi-Dimensional Spectral Difference Method for Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.

Liu, Yen↗

NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, 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.

Nemec, Marian↗

NASA NTRS2003

Application of a data-mining method based on Bayesian networks to lesion-deficit analysis

Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.

NASA Discipline Neuroscience↗

NASA NTRS2002

Methods for semi-automated indexing for high precision information retrieval

OBJECTIVE: To evaluate a new system, ISAID (Internet-based Semi-automated Indexing of Documents), and to generate textbook indexes that are more detailed and more useful to readers. DESIGN: Pilot evaluation: simple, nonrandomized trial comparing ISAID with manual indexing methods. Methods evaluation: randomized, cross-over trial comparing three versions of ISAID and usability survey. PARTICIPANTS: Pilot evaluation: two physicians. Methods evaluation: twelve physicians, each of whom used three different versions of the system for a total of 36 indexing sessions. MEASUREMENTS: Total index term tuples generated per document per minute (TPM), with and without adjustment for concordance with other subjects; inter-indexer consistency; ratings of the usability of the ISAID indexing system. RESULTS: Compared with manual methods, ISAID decreased indexing times greatly. Using three versions of ISAID, inter-indexer consistency ranged from 15% to 65% with a mean of 41%, 31%, and 40% for each of three documents. Subjects using the full version of ISAID were faster (average TPM: 5.6) and had higher rates of concordant index generation. There were substantial learning effects, despite our use of a training/run-in phase. Subjects using the full version of ISAID were much faster by the third indexing session (average TPM: 9.1). There was a statistically significant increase in three-subject concordant indexing rate using the full version of ISAID during the second indexing session (p < 0.05). SUMMARY: Users of the ISAID indexing system create complex, precise, and accurate indexing for full-text documents much faster than users of manual methods. Furthermore, the natural language processing methods that ISAID uses to suggest indexes contributes substantially to increased indexing speed and accuracy.

Evaluation Studies↗

NASA NTRS1998

Initial Results of an MDO Method Evaluation Study

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to

Alexandrov, Natalia M.↗

NASA NTRS2004

A Wall Correction Program Based on Classical Methods for the National Transonic Facility (Solid Wall or Slotted Wall) and the 14x22-Ft Subsonic Tunnel at NASA LaRC

A Fortran subroutine CMWALL is described, which is an implementation of the collective information from classical methods-based wall corrections. These methods use established closed-form expressions which were developed based on simple linear potential-based methods. This is a simple and rapid tool to calculate corrections due to wall interference in the National Transonic Facility (Solid Wall or Slotted Wall) or the 14x22-Ft Subsonic Tunnel at NASA LaRC. It is designed to be easily implemented in the existing tunnel data reduction programs, either as real-time or post-point. It is however important to realize that the method is based on the simplifying assumptions of linearity, small model and attached flow. The computed results are thus to be viewed as first-cut estimates, to be refined further using more complex methods based on measured wall pressures (known as wall signature methods).

Hemsch, Michael J.↗

NASA NTRS2004

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Nelson, Andrea↗

NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

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.

Nemec, Marian↗

NASA NTRS2000

Atomistic Method Applied to Computational Modeling of Surface Alloys

The formation of surface alloys is a growing research field that, in terms of the surface structure of multicomponent systems, defines the frontier both for experimental and theoretical techniques. Because of the impact that the formation of surface alloys has on surface properties, researchers need reliable methods to predict new surface alloys and to help interpret unknown structures. The structure of surface alloys and when, and even if, they form are largely unpredictable from the known properties of the participating elements. No unified theory or model to date can infer surface alloy structures from the constituents properties or their bulk alloy characteristics. In spite of these severe limitations, a growing catalogue of such systems has been developed during the last decade, and only recently are global theories being advanced to fully understand the phenomenon. None of the methods used in other areas of surface science can properly model even the already known cases. Aware of these limitations, the Computational Materials Group at the NASA Glenn Research Center at Lewis Field has developed a useful, computationally economical, and physically sound methodology to enable the systematic study of surface alloy formation in metals. This tool has been tested successfully on several known systems for which hard experimental evidence exists and has been used to predict ternary surface alloy formation (results to be published: Garces, J.E.; Bozzolo, G.; and Mosca, H.: Atomistic Modeling of Pd/Cu(100) Surface Alloy Formation. Surf. Sci., 2000 (in press); Mosca, H.; Garces J.E.; and Bozzolo, G.: Surface Ternary Alloys of (Cu,Au)/Ni(110). (Accepted for publication in Surf. Sci., 2000.); and Garces, J.E.; Bozzolo, G.; Mosca, H.; and Abel, P.: A New Approach for Atomistic Modeling of Pd/Cu(110) Surface Alloy Formation. (Submitted to Appl. Surf. Sci.)). Ternary alloy formation is a field yet to be fully explored experimentally. The computational tool, which is based on the BFS (Bozzolo, Ferrante, and Smith) method for the calculation of the energetics, consists of a small number of simple PCbased computer codes that deal with the different aspects of surface alloy formation. Two analysis modes are available within this package. The first mode provides an atom-by-atom description of real and virtual stages 1. during the process of surface alloying, based on the construction of catalogues of configurations where each configuration describes one possible atomic distribution. BFS analysis of this catalogue provides information on accessible states, possible ordering patterns, and details of island formation or film growth. More importantly, it provides insight into the evolution of the system. Software developed by the Computational Materials Group allows for the study of an arbitrary number of elements forming surface alloys, including an arbitrary number of surface atomic layers. The second mode involves large-scale temperature-dependent computer 2. simulations that use the BFS method for the energetics and provide information on the dynamic processes during surface alloying. These simulations require the implementation of Monte-Carlo-based codes with high efficiency within current workstation environments. This methodology capitalizes on the advantages of the BFS method: there are no restrictions on the number or type of elements or on the type of crystallographic structure considered. This removes any restrictions in the definition of the configuration catalogues used in the analytical calculations, thus allowing for the study of arbitrary ordering patterns, ultimately leading to the actual surface alloy structure. Moreover, the Monte Carlo numerical technique used for the large-scale simulations allows for a detailed visualization of the simulated process, the main advantage of this type of analysis being the ability to understand the underlying features that drive these processes. Because of the simplicity of the BFS method for e energetics used in these calculations, a detailed atom-by-atom analysis can be performed at any point in the simulation, providing necessary insight on the details of the process. The main objective of this research program is to develop a tool to guide experimenters in understanding and interpreting often unexpected results in alloy formation experiments. By reducing the computational effort without losing physical accuracy, we expect that powerful simulation tools will be developed in the immediate future, which will allow material scientists to easily visualize and analyze processes at a level not achievable experimentally.

Bozzolo, Guillermo H.↗

NASA NTRS2005

Stirling Analysis Comparison of Commercial Versus High-Order Methods

Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's compact scheme and Dyson's Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model with sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

Dyson, Rodger W.↗

NASA NTRS2004

International Space Station (ISS) Airlock Crewlock Depressurization Methods

The International Space Station (ISS) Airlock Crewlock can be depressurized via various methods. The ISS Airlock is divided into two major sections, the Equipment Lock and Crewlock. The Equipment Lock, as the name indicates, contains the equipment to support EVA activities including Extravehicular Maneuvering/Mobility Unit (EMU) maintenance and refurbishment. The Equipment Lock also contains basic life support equipment in order to support denitrogenzation protocols while the Airlock is isolated from the rest of the ISS. The Crewlock is the section of the Airlock that is depressurized to allow for Extravehicular Activity (EVA) crewmembers to exit the ISS for performance of EVAs. As opposed to the Equipment Lock, the Crewlock is quite simple and basically just contains lights and an assembly to provide services, oxygen, coolant, etc, to the EMUs. For operational flexibility, various methods were derived for Crewlock depressurization. Herein these various different methods of ISS Airlock Crewlock depressurization will be described including their performance, impacts, and risks associated with each method. Each of the different methods will be discussed with flight data, if it exists. Models will be applied to flight cases and to other methods that have not been used on-orbit at this time.

Williams, David E.↗