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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Jorgenson, Philip C. E.↗
NASA NTRS1978

The control net of Mars - May 1977

The development of planet-wide control nets of Mars is reviewed, and the May 1977 update is described. This updated control net was computed by means of a large single-block analytical triangulation incorporating the new direction of the spin axis and the new rotation rate of Mars, as determined from radio tracking data provided by the Viking lander spacecraft. The analytical triangulation adjusts for planimetric control only (areocentric latitude and longitude) and for the camera orientation angles. Most of the areocentric radii at the control points were interpolated from radio occultation measurements, but a few were determined photogrammetically, and a substantial number were derived from elevation contours on the 1976 USGS topographic series of Mars maps. A value of V, measured from Mars' vernal equinox along the equator to the prime meridian (Airy-0) is presented.

Davies, M. E.↗
NASA NTRS1995

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗
NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗
DOE OSTI2022

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

Here, we present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high-quality balanced mesh is produced.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications

A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.

Marcum, David L.↗
DOE OSTI2024

Fermions, quantum gravity, and holography in two dimensions

We study a model comprising N flavors of Kähler Dirac fermion propagating on a triangulated two-dimensional disk which is constrained to have a negative average bulk curvature. Dirichlet boundary conditions are chosen for the fermions. Quantum fluctuations of the geometry are included by summing over all possible triangulations consistent with these constraints. We show in the limit N → ∞ that the partition function is dominated by a regular triangulation of two-dimensional hyperbolic space. We use strong coupling expansions and Monte Carlo simulation to show that in this limit boundary correlators of the fermions have a power law dependence on boundary separation as one expects from holography. However, we argue that this behavior breaks down for any finite number of massive fields in the thermodynamic limit and quantum fluctuations of the bulk geometry drive the theory into a nonholographic phase. In contrast, for massless fermions, we find evidence that the boundary is conformal even for finite N . This is consistent with theoretical results in quantum Liouville theory. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
NASA NTRS1978

Detection of horizontal crustal movements by photogrammetric methods

The photogrammetric methods can be applied only if the horizontal displacements of the ground are of the order of several centimeters, because the standard error of the points so determined cannot, at the present time, be smaller than two centimeters. The procedure to be adopted, which has already been applied with satisfactory results for the densification of geodetic nets, is the aerial analytical triangulation. The taking can be executed with wide-angle cameras (f = 15 cm), or normal-angle cameras (f = 30 cm) and format 23 x 23 cm. Since the average scale of photos must be chosen in relation with the desired accuracy and then is independent of the principal distance of the cameras, the number of photos is constant, whereas the flying height varies according to the focal length.

Solaini, L.↗
NASA NTRS1962

Some Applications of Detailed Wind Profile Data to Launch Vehicle Response Problems

The response of a launch vehicle to a number of detailed wind profiles has been determined. The wind profiles were measured by two techniques which are briefly described. One of these techniques uses an angle-of-attack sensor in conjunction with guidance data to measure the wind profile traversed by some particular launch vehicle. The other wind-measuring technique is a photographic triangulation method, whereby two cameras take simultaneous pictures of a vertical trail of smoke left by a launch vehicle or sounding rocket. The response of a vehicle flying these detailed profiles is compared with the response of the same vehicle flying through balloon-measured profiles. The response to the detailed wind profiles, relative t o the balloon-measured profiles, is characterized by the large excitation of the rigid pitch and elastic bending modes. This is found to cause higher loads on the launch vehicle structure. Established design criteria which utilize balloon measured wind profiles have arbitrarily accounted-for this increased load by adding a load due to some type of discrete gust.

LAUNCH VEHICLE↗
DOE OSTI2023

A Level Set Model for Structured Mesh Representation of Fibrous Preforms used in Composites Manufacturing

Here, a model for implicit representation of fibrous and woven preforms used for composites manufacturing is described. The method is based on a level set function defined on a structured mesh to implicitly capture the complex fiber and weave geometries. Since most software packages used to model woven preforms are based on unstructured mesh, a numerical model for transforming a discretized surface to a structured mesh representation and vice-a-versa is presented. Specific emphasis is on scalable computation of a level set function for large and complex 3D woven structures from a triangulated surface of the smallest unit (yarn). The model is applied to capture a periodic 3D layered 5-harness satin (5HS) weave geometry on a structured mesh. Geometric transformations needed to efficiently compute the level set function for the 3D structure on a high resolution mesh are described. Effects of mesh resolution on the geometric features such as number of resolved fibers, effective fiber size, and the surface area to volume ratio of the iso-surface are analyzed. Using the distance property of the level set function, an approach to evaluate the structure function resulting from transient evolving topology representing densification due to matrix phase depositions is also presented. The approach captures transition of the geometric characteristic from fiber governed at early stages of densification to yarn governed at the terminal stage.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Towards the Gravituhedron: new expressions for NMHV gravity amplitudes

In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call G-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of G-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, the role of momentum twistors and the intricate web of spurious poles cancelation. Because of the close connection between R-invariants and the (tree-level) Amplituhedron for Yang-Mills amplitudes, we speculate that the new expansion for gravity amplitudes should correspond to the triangulation of the putative Gravituhedron geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1997

Some Experiences with High Order Discretization Schemes for Compressible Fluid Flow

It is widely recognized that the structure and complexity of compressible fluid flow places high demands on numerical discretization techniques for the fluid flow equations. Fluid flows arising in external aerodynamics often contain both flow field discontinuities and fluid boundary-layers. Both must be accurately resolved to provide useful information to aerodynamic design and analysis engineers. These accuracy requirements motivated the present author to examine a class of finite-volume techniques on arbitrary triangulated domains based on linear or quadratic reconstruction of integral-averaged data followed by upwind flux function evaluation and small time evolution. More recently, we have considered some new upwind techniques which yield compact discretizations while maintaining higher order accuracy. In the mini-symposium talk we will discuss both of these techniques as well as demonstrate the relative merits of each method by computing a number of aerodynamic flows containing shock waves and boundary-layers.

Barth, Timothy J.↗
NASA NTRS2002

Computing Axisymmetric Jet Screech Tones Using Unstructured Grids

The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

Jorgenson, Philip C. E.↗
DOE OSTI2022

Hybrid Curve Fitting For Reducing Motion Commands In Object Construction

Existing slicing software for additive manufacturing typically requires a triangulated mesh as its input. Triangulated meshes are approximate representations of exact CAD models. Despite the loss in dimensional accuracy, triangulated meshes are used because they are computationally easier to cross-section and offset than the exact geometry in CAD format. When a triangulated object is prepared, the resulting machine instructions include only linear motion commands. Numerous modern motion controllers can move in arc and spline motions; however, the absence of slicing software that supports curvature prevents these commands from being leveraged. To address this limitation, this paper presents a method for the hybrid reconstruction of arcs and splines as a post-processing step to traditional slicing. This method can greatly reduce the number of motion commands required to construct an object by printing smooth curved surfaces. This concise representation of tool-pathing allows for more even extrusion and is computed without a major impact on slicing time.

Wade, Charles↗
DOE OSTI2020

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

In this work, we present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress–energy tensor is evolved in flux-conservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Furthermore, radiation four-forces are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency-dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that Method of Characteristics Moment Closure converges at least as ~N -1 , rather than the canonical Monte Carlo N -1/2 , where N is the number of samples per zone.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1996

Preconditioning Operators on Unstructured Grids

We consider systems of mesh equations that approximate elliptic boundary value problems on arbitrary (unstructured) quasi-uniform triangulations and propose a method for constructing optimal preconditioning operators. The method is based upon two approaches: (1) the fictitious space method, i.e., the reduction of the original problem to a problem in an auxiliary (fictitious) space, and (2) the multilevel decomposition method, i.e., the construction of preconditioners by decomposing functions on hierarchical meshes. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh step. The preconditioner has an optimal computational cost: the number of arithmetic operations required for its implementation is proportional to the number of unknowns in the problem. The construction of the preconditioning operators for three dimensional problems can be done in the same way.

Nepomnyaschikh, S. V.↗