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NASA NTRSDate not supplied

An Automated Marching Scheme for Overset Structured Surface Mesh Generation

Starting with a Boundary Representation (BRep) of the geometry of an aerospace vehicle, an automated marching scheme is presented for generation of structured overset surface meshes. First, a pre-processing step automatically generates discrete representations of the BRep faces and BRep edges by tessellating in parameter space. Topological connectivity between the discretized BRep edges is then established, followed by automatic grid point distribution on these edges based on local turning angle, proximity to sharp geometric features, and prescribed maximum stretching ratio and grid spacing. A set of initial curves for algebraic or hyperbolic marching on a surface is then derived from the redistributed edge curves. A spatially-variable marching distance together with a grid point distribution in the marching direction are automatically determined for each initial curve. A set of overset surface meshes that covers the entire geometry is then obtained by combining the surface meshes around the BRep edges, and the structured meshes derived from the discretized BRep faces

Shishir A Pandya↗

NASA NTRS1995

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Brislawn, Kristi D.↗

NASA NTRS1982

Prediction of sound radiation from different practical jet engine inlets

The computer codes necessary for this study were developed and checked against exact solutions generated by the point source method using the NASA Lewis QCSEE inlet geometry. These computer codes were used to predict the acoustic properties of the following five inlet configurations: the NASA Langley Bellmouth, the NASA Lewis JT15D-1 Ground Test Nacelle, and three finite hyperbolic inlets of 50, 70 and 90 degrees. Thirty-five computer runs were done for the NASA Langley Bellmouth. For each of these computer runs, the reflection coefficient at the duct exit plane was calculated as was the far field radiation pattern. These results are presented in both graphical and tabular form with many of the results cross plotted so that trends in the results verses cut-off ratio (wave number) and tangential mode number may be easily identified.

Zinn, B. T.↗

NASA NTRS1993

Numerical computation of complex multi-body Navier-Stokes flows with applications for the integrated Space Shuttle launch vehicle

An enhanced grid system for the Space Shuttle Orbiter was built by integrating CAD definitions from several sources and then generating the surface and volume grids. The new grid system contains geometric components not modeled previously plus significant enhancements on geometry that has been modeled in the old grid system. The new orbiter grids were then integrated with new grids for the rest of the launch vehicle. Enhancements were made to the hyperbolic grid generator HYPGEN and new tools for grid projection, manipulation, and modification, Cartesian box grid and far field grid generation and post-processing of flow solver data were developed.

Chan, William M.↗

NASA NTRSDate not supplied

Advances in Automation of Overset Structured Volume Mesh Generation and Domain Connectivity

Automation of overset structured surface mesh generation has recently been accomplished by the creation of face, edge, and node meshes based on Boundary Representation solids as the geometry input. The current work continues the automation effort in overset volume mesh generation and domain connectivity based on the auto-generated surface meshes. All near-body curvilinear volume meshes are automatically generated using hyperbolic methods. Automation of this step is enabled by appropriate surface grid point distribution, and selection of boundary-splay and smoothing parameters based on concave and convex surface features. The off-body domain is covered by two automatically generated grid systems. The first contains a single Cartesian mesh with a uniform core enclosing all near-body volume meshes and stretched layers that extend to the far field, while the second consists of a set of small stretched Cartesian grids covering pockets of off-body orphan points. With high quality mesh overlap mostly guaranteed by the surface meshing scheme, orphan points that need to be covered by the second Cartesian mesh system are located away from the fine grid spacing region near the wall. Using line-segment and ray-pierce tests against the surface grids, hole-cutting is accomplished on both near and off-body volume grids resulting in appropriate clearances from the wall. The complete mesh generation automation process is demonstrated on five test cases where flow solutions are also computed and compared with solutions obtained using other methods.

TTT↗

DOE OSTI2025

Effective Polarizability in Near-Field Microscopy of Phonon-Polariton Resonances

We investigate the resonant characteristics of planar surfaces and distinct edges of structures with the excitation of phonon-polaritons. We analyze two materials supporting phonon-polariton excitations in the mid-infrared spectrum: silicon carbide, characterized by an almost isotropic dielectric constant, and hexagonal boron nitride, notable for its pronounced anisotropy in a spectral region exhibiting hyperbolic dispersion. We formulate a theoretical framework that accurately captures the excitations of the structure involving phonon-polaritons, predicts the response in scattering-type near-field optical microscopy, and is effective for complex resonant geometries where the locations of hot spots are uncertain. We account for the tapping motion of the probe, perform analysis for different heights of the probe, and demodulate the signal using a fast Fourier transform. Using this Fourier demodulation analysis, we show that light enhancement across the entire apex is the most accurate characteristic for describing the response of all resonant excitations and hot spots. We demonstrate that computing the demodulation orders of light enhancement in the microscope probe accurately predicts its imaging.

Chemistry↗

NASA NTRS1989

The stability of a compressible stratified shear layer

The stability of a shear layer under the effect of gravity is investigated using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent the curvature effects of the flow and magnetic field line geometry. A general eigenmode equation is derived for a two-dimensional MHD fluid, and an energy-principle analysis to explain the effect of compressibility on the critical Richardson number is presented. For the case of a hyperbolic tangent shear flow and exponential density profile, it was found that, in the Boussinesq approximation, the compressibility raises the critical Richardson number from 1/4 to as much as 1/2, with the exact value depending on the value of the magnetic field at infinity. Under approximation of a strong asymptotic magnetic field, without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. The long-wavelength stability boundary for the Richardson number J = 0 is characterized by a normalized phase velocity c =

Wang, Z.↗

NASA NTRS2017

Strategies Toward Automation of Overset Structured Surface Grid Generation

An outline of a strategy for automation of overset structured surface grid generation on complex geometries is described. The starting point of the process consists of an unstructured surface triangulation representation of the geometry derived from a native CAD, STEP, or IGES definition, and a set of discretized surface curves that captures all geometric features of interest. The procedure for surface grid generation is decomposed into an algebraic meshing step, a hyperbolic meshing step, and a gap-filling step. This paper will focus primarily on the high-level plan with details on the algebraic step. The algorithmic procedure for the algebraic step involves analyzing the topology of the network of surface curves, distributing grid points appropriately on these curves, identifying domains bounded by four curves that can be meshed algebraically, concatenating the resulting grids into fewer patches, and extending appropriate boundaries of the concatenated grids to provide proper overlap. Results are presented for grids created on various aerospace vehicle components.

overset↗

NASA NTRS1992

Grid generation research at OSU

In the last two years, effort was concentrated on: (1) surface modeling; (2) surface grid generation; and (3) 3-D flow space grid generation. The surface modeling shares the same objectives as the surface modeling in computer aided design (CAD), so software available in CAD can in principle be used for solid modeling. Unfortunately, however, the CAD software cannot be easily used in practice for grid generation purposes, because they are not designed to provide appropriate data base for grid generation. Therefore, we started developing a generalized surface modeling software from scratch, that provides the data base for the surface grid generation. Generating surface grid is an important step in generating a 3-D space for flow space. To generate a surface grid on a given surface representation, we developed a unique algorithm that works on any non-smooth surfaces. Once the surface grid is generated, a 3-D space can be generated. For this purpose, we also developed a new algorithm, which is a hybrid of the hyperbolic and the elliptic grid generation methods. With this hybrid method, orthogonality of the grid near the solid boundary can be easily achieved without introducing empirical fudge factors. Work to develop 2-D and 3-D grids for turbomachinery blade geometries was performed, and as an extension of this research we are planning to develop an adaptive grid procedure with an interactive grid environment.

Nakamura, S.↗

NASA NTRS1985

Recent developments in FEM-CFD

The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.

Loehner, R.↗

NASA NTRS1979

Recent developments in finite element analysis for transonic airfoils

The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.

Hafez, M. M.↗

NASA NTRS1984

On the method of pseudo compressibility for numerically solving incompressible flows

Pseudo compressibility is used for numerically solving incompressible flows to achieve computational efficiency. The use of pseudo compressibility results in a system of hyperbolic-type equations of motion that introduce waves of finite speed. The interactions of the wave propagation and the vorticity spreading are analyzed. A criterion governing the dependence of the pseudo compressiblity on the Reynolds number and the characteristic length of the flow geometry is obtained that allows for a proper convergence. It is demonstrated that the solution does tend to the incompressible limit. External and internal viscous flow test problems are presented to verify the theory.

Chang, J. L. C.↗

DOE OSTI2025

Looking at extremal black holes from very far away

Near-extremal black holes are subject to large quantum effects, which modify their low-temperature thermodynamic behavior. Hitherto, these quantum effects were analyzed by separating the geometry into the near-horizon region and its exterior. It is desirable to understand and reproduce such corrections from the full higher-dimensional asymptotically flat or AdS geometry’s perspective. We address this question in this article and fill this gap. Specifically, we find off-shell eigenmodes of the quadratic fluctuation operator of the Euclidean gravitational dynamics, with eigenvalues that vanish linearly with temperature. We illustrate this for BTZ and neutral black holes with hyperbolic horizons in AdS in Einstein-Hilbert theory, and for the charged black holes in Einstein-Maxwell theory. The linear scaling with Matsubara frequency, which is a distinctive feature of the modes, together with the fact that their wavefunctions localize close to the horizon as we approach extremality, identifies them as responsible for the aforementioned quantum effects. We provide a contour prescription to deal with the sign indefiniteness of the Euclidean Einstein-Maxwell action, which we derive to aid our analysis. We also resolve a technical puzzle regarding modes associated with rotational isometries in stationary black hole spacetimes.

AdS-CFT Correspondence↗

NASA NTRS1986

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented.

Kopriva, D.↗

NASA NTRS1993

User's manual for the HYPGEN hyperbolic grid generator and the HGUI graphical user interface

The HYPGEN program is used to generate a 3-D volume grid over a user-supplied single-block surface grid. This is accomplished by solving the 3-D hyperbolic grid generation equations consisting of two orthogonality relations and one cell volume constraint. In this user manual, the required input files and parameters and output files are described. Guidelines on how to select the input parameters are given. Illustrated examples are provided showing a variety of topologies and geometries that can be treated. HYPGEN can be used in stand-alone mode as a batch program or it can be called from within a graphical user interface HGUI that runs on Silicon Graphics workstations. This user manual provides a description of the menus, buttons, sliders, and typein fields in HGUI for users to enter the parameters needed to run HYPGEN. Instructions are given on how to configure the interface to allow HYPGEN to run either locally or on a faster remote machine through the use of shell scripts on UNIX operating systems. The volume grid generated is copied back to the local machine for visualization using a built-in hook to PLOT3D.

Chan, William M.↗

NASA NTRS2002

The Overgrid Interface for Computational Simulations on Overset Grids

Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.

Chan, William M.↗

NASA NTRS1972

Crack shapes and stress intensity factors for edge-cracked specimens.

A simple stress intensity factor expression is given for a deep edge crack in a plate in tension. The shapes of cracks opened by tension or bending are approximated by conic sections, and the conic section coefficients are related to plate geometry by very simple empirical equations. The magnitude of the crack displacement is a function of applied load, plate geometry, and the elastic constants of the plate material. The shape of a loaded crack in a semiinfinite plate is, approximately, a portion of an ellipse whose semimajor axis is about three times the crack length. As the crack length (relative to the plate width) increases, the crack shape becomes parabolic, then hyperbolic, the acuity of the hyperbola increasing with the relative crack length.

Orange, T. W.↗

NASA NTRS1988

Grid generation for general 2-D regions using hyperbolic equations

A method for applying a hyperbolic grid generation scheme to the construction of meshes in general 2-D regions has been developed. This approach, which follows the theory developed by Steger and Chaussee (1980) and the algorithm outlined by Kinsey and Barth (1984), is based on improving local grid control. This is accomplished by adding an angle control source term to the equations and using a new algorithm for computing the volume source term. These modifications lead to superior methods for fixing the 'local' problems of hyperbolic grid generation, namely, propagation of initial discontinuities and formation of grid shocks (crossing grid lines). More importantly, a method for solving the global problem of constraining the grid with more than one boundary (internal grid generation) has been developed. These algorithms have been implemented in an interactive grid generation program and the results for several geometries are presented and discussed.

Cordova, Jeffrey Q.↗