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NASA NTRS1990

A three-dimensional space marching algorithm for the solution of the Euler equations on unstructured grids

A three-dimensional space marching algorithm using an unstructured discretization is proposed. The governing equations and the spatial discretization of the domain and the interpolation from one arbitrary unstructured mesh to another are discussed, and the grid generation technique is described. Solutions for several different geometries are presented, and the results are compared with existing numerical techniques and experimental results.

Mcgrory, W. D.↗

NASA NTRS1991

A staggered mesh finite difference scheme for the computation of hypersonic Euler flows

A shock capturing finite difference method for systems of hyperbolic conservation laws is presented which avoids the need to solve Riemann problems while being competitive in performance with other current methods. A staggered spatial mesh is employed, so that complicated nonlinear waves generated at cell interfaces are averaged over cell interiors at the next time level. The full method combines to form a conservative version of the modified method of characteristics. The advantages of the method are discussed, and numerical results are presented for the two-dimensional double ellipse problem.

Sanders, Richard↗

NASA NTRS2002

A Tool for Low Noise Procedures Design and Community Noise Impact Assessment: The Rotorcraft Noise Model (RNM)

To improve aircraft noise impact modeling capabilities and to provide a tool to aid in the development of low noise terminal area operations for rotorcraft and tiltrotors, the Rotorcraft Noise Model (RNM) was developed by the NASA Langley Research Center and Wyle Laboratories. RNM is a simulation program that predicts how sound will propagate through the atmosphere and accumulate at receiver locations located on flat ground or varying terrain, for single and multiple vehicle flight operations. At the core of RNM are the vehicle noise sources, input as sound hemispheres. As the vehicle "flies" along its prescribed flight trajectory, the source sound propagation is simulated and accumulated at the receiver locations (single points of interest or multiple grid points) in a systematic time-based manner. These sound signals at the receiver locations may then be analyzed to obtain single event footprints, integrated noise contours, time histories, or numerous other features. RNM may also be used to generate spectral time history data over a ground mesh for the creation of single event sound animation videos. Acoustic properties of the noise source(s) are defined in terms of sound hemispheres that may be obtained from theoretical predictions, wind tunnel experimental results, flight test measurements, or a combination of the three. The sound hemispheres may contain broadband data (source levels as a function of one-third octave band) and pure-tone data (in the form of specific frequency sound pressure levels and phase). A PC executable version of RNM is publicly available and has been adopted by a number of organizations for Environmental Impact Assessment studies of rotorcraft noise. This paper provides a review of the required input data, the theoretical framework of RNM's propagation model and the output results. Code validation results are provided from a NATO helicopter noise flight test as well as a tiltrotor flight test program that used the RNM as a tool to aid in the development of low noise approach profiles.

Conner, David A.↗

NASA NTRS1989

Theory of gearing

Basic mathematical problems on the theory of gearing are covered in this book, such as the necessary and sufficient conditions of envelope existence, relations between principal curvatures and directions for surfaces of mating gears. Also included are singularities of surfaces accompanied by undercutting the process of generation, the phenomena of envelope of lines of contact, and the principles for generation of conjugate surfaces. Special attention is given to the algorithms for computer aided simulation of meshing and tooth contact. This edition was complemented with the results of research recently performed by the author and his doctoral students. The book contains sample problems and also problems for the reader to solve.

Gear-tooth surface↗

NASA NTRS1992

Delaunay triangulation and computational fluid dynamics meshes

In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable for CFD calculations, particularly with regard to high aspect ratio, skewed quadrilateral elements.

Posenau, Mary-Anne K.↗

NASA NTRS1995

Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect-ratio AR = delta y/delta x is much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotopic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Morano, E.↗

NASA NTRS1996

Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e. the aspect-ratio AR = (delta)y/(delta)x much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Morano, E.↗

NASA NTRS1989

Topology of modified helical gears and Tooth Contact Analysis (TCA) program

The contents of this report covers: (1) development of optimal geometries for crowned helical gears; (2) a method for their generation; (3) tooth contact analysis (TCA) computer programs for the analysis of meshing and bearing contact of the crowned helical gears; and (4) modelling and simulation of gear shaft deflection. The developed method for synthesis was used to determine the optimal geometry for a crowned helical pinion surface and was directed to localize the bearing contact and guarantee favorable shape and a low level of transmission errors. Two new methods for generation of the crowned helical pinion surface are proposed. One is based on the application of a tool with a surface of revolution that slightly deviates from a regular cone surface. The tool can be used as a grinding wheel or as a shaver. The other is based on a crowning pinion tooth surface with predesigned transmission errors. The pinion tooth surface can be generated by a computer-controlled automatic grinding machine. The TCA program simulates the meshing and bearing contact of the misaligned gears. The transmission errors are also determined. The gear shaft deformation was modelled and investigated. It was found that the deflection of gear shafts has the same effect as gear misalignment.

Litvin, Faydor L.↗

NASA NTRSDate not supplied

Toward The Development of Hailstorm Climatologies Derived From Reanalyses and Infared/Passive Microwave Satellite Imagers

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) and Meteosat series, provide both historical and near-real-time observations of cloud top patterns that are commonly associated with severe convection. Environmental conditions favorable for severe weather are thought to be represented well by reanalyses. Predicting exactly where convection and costly storm hazards like hail will occur using models or satellite imagery alone, however, is extremely challenging. The multivariate combination of satellite-observed cloud patterns with reanalysis environmental parameters, linked to United States Next Generation Weather Radar- (NEXRAD-) estimated Maximum Expected Size of Hail (MESH) using a deep neural network (DNN), enables estimation of potentially severe hail likelihood for any observed storm cell. These estimates are specifically designed to make hail likelihood distinctions based on satellite-indicated points of deep convection within environments favorable for storm development. We seek an approach that can be used to estimate climatological hailstorm frequency and risk throughout the historical satellite data record. This presentation demonstrates that statistical distributions of convective parameters from satellite and reanalysis show separation between non-severe/severe hailstorm classes for predictors including overshooting cloud top temperature and area characteristics, convective available potential energy, vertical wind shear, 500 hPa temperature, mid-level lapse rate, precipitable water, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN to produce a hail likelihood metric with a critical success index of 0.504 and Heidke skill score of 0.403, which is exceptional among recent analogous hail studies. Furthermore, applications of the DNN to select case studies demonstrate good qualitative agreement between hail likelihood and MESH. These hail classifications are aggregated across an 11-year GOES-12/13 image database to derive a hail frequency and severity climatology, which denotes the Central Plains, the Midwest, and northwestern Mexico as being the most hail-prone regions within the domain studied. Opportunities for training and applying DNN-based hailstorm predictions to recently developed GOES-8/10/12/13/16 and Meteosat Second Generation convective storm detection and characterization climatologies over South America and South Africa, respectively, will also be presented.

Kristopher Bedka↗

NASA NTRS2002

Graph Partitioning for Parallel Applications in Heterogeneous Grid Environments

The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.

Bisws, Rupak↗

NASA NTRS1971

ELAS8 - Computer program for linear structure equilibrium problems

Program generates and solves governing equations for unknown deflection of mesh points as if problem were to locate stationary point of total potential function associated with given loading and unknown deflections. Solution is obtained by means of displacement method and finite element technique.

Utku, S.↗

NASA NTRS1988

Calculations Of Transonic Flow About A Wing

Report describes calculations of transonic airflows about wing in wind tunnel. Basic equations of flow used in study are Reynolds-averaged Navier-Stokes equations in strong conservation-law form. Equations of flow incorporated into finite-difference computer code called TNS (Transonic Navier-Stokes). Computational grid generated by solution of partial differential equations yielding smooth meshes conforming to surfaces of wing and wind tunnel.

Holst, Terry L.↗

NASA NTRS1992

A brief description of a new numerical framework for solving conservation laws: The method of space-time conservation element and solution element

A new numerical method for solving conservation laws is being developed. It differs substantially from the well established methods, i.e., finite difference, finite volume, finite element, and spectral methods, in both concept and methodology. It is much simpler than a typical high resolution method. No flux limiter or any technique related to characteristics is involved. No artificial viscosity or smoothing is introduced, and no moving mesh is used. Yet this method is capable of generating highly accurate shock tube solutions. The slight numerical overshoot and/or oscillations generated can be removed if a simple averaging formula initially used is replaced by a weighted formula. This modification has little effect on other parts of the solution. Because of its simplicity, generalization of this new method for multi-dimensional problems is straightforward.

Chang, Sin-Chung↗

NASA NTRS1997

HARP: A Dynamic Inertial Spectral Partitioner

Partitioning unstructured graphs is central to the parallel solution of computational science and engineering problems. Spectral partitioners, such recursive spectral bisection (RSB), have proven effecfive in generating high-quality partitions of realistically-sized meshes. The major problem which hindered their wide-spread use was their long execution times. This paper presents a new inertial spectral partitioner, called HARP. The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines. The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigerivectors of the original mesh. Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime. Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method. A parallel WI version of HARP has also been implemented on IBM SP2 and Cray T3E. Parallel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second. These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications.

Simon, Horst D.↗

NASA NTRS1998

CAPRI (Computational Analysis PRogramming Interface): A Solid Modeling Based Infra-Structure for Engineering Analysis and Design Simulations

CAPRI is a CAD-vendor neutral application programming interface designed for the construction of analysis and design systems. By allowing access to the geometry from within all modules (grid generators, solvers and post-processors) such tasks as meshing on the actual surfaces, node enrichment by solvers and defining which mesh faces are boundaries (for the solver and visualization system) become simpler. The overall reliance on file 'standards' is minimized. This 'Geometry Centric' approach makes multi-physics (multi-disciplinary) analysis codes much easier to build. By using the shared (coupled) surface as the foundation, CAPRI provides a single call to interpolate grid-node based data from the surface discretization in one volume to another. Finally, design systems are possible where the results can be brought back into the CAD system (and therefore manufactured) because all geometry construction and modification are performed using the CAD system's geometry kernel.

Haimes, Robert↗

NASA NTRS1993

NASA Lewis Meshed VSAT Workshop meeting summary

NASA Lewis Research Center's Space Electronics Division (SED) hosted a workshop to address specific topics related to future meshed very small-aperture terminal (VSAT) satellite communications networks. The ideas generated by this workshop will help to identify potential markets and focus technology development within the commercial satellite communications industry and NASA. The workshop resulted in recommendations concerning these principal points of interest: the window of opportunity for a meshed VSAT system; system availability; ground terminal antenna sizes; recommended multifrequency for time division multiple access (TDMA) uplink; a packet switch design concept for narrowband; and fault tolerance design concepts. This report presents a summary of group presentations and discussion associated with the technological, economic, and operational issues of meshed VSAT architectures that utilize processing satellites.

Ivancic, William↗

NASA NTRS1988

Spur gears: Optimal geometry, methods for generation and Tooth Contact Analysis (TCA) program

The contents of this report include the following: (1) development of optimal geometry for crowned spur gears; (2) methods for their generation; and (3) tooth contact analysis (TCA) computer programs for the analysis of meshing and bearing contact on the crowned spur gears. The method developed for synthesis is used for the determination of the optimal geometry for crowned pinion surface and is directed to reduce the sensitivity of the gears to misalignment, localize the bearing contact, and guarantee the favorable shape and low level of the transmission errors. A new method for the generation of the crowned pinion surface has been proposed. This method is based on application of the tool with a surface of revolution that slightly deviates from a regular cone surface. The tool can be used as a grinding wheel or as a shaver. The crowned pinion surface can also be generated by a generating plane whose motion is provided by an automatic grinding machine controlled by a computer. The TCA program simulates the meshing and bearing contact of the misaligned gears. The transmission errors are also determined.

Litvin, Faydor L.↗

NASA NTRS1996

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

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.

Williams, Tonya↗