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NASA NTRS1999

On the Use of CAD-Native Predicates and Geometry in Surface Meshing

Several paradigms for accessing CAD geometry during surface meshing for CFD are discussed. File translation, inconsistent geometry engines and non-native point construction are all identified as sources of non-robustness. The paper argues in favor of accessing CAD parts and assemblies in their native format, without translation, and for the use of CAD-native predicates and constructors in surface mesh generation. The discussion also emphasizes the importance of examining the computational requirements for exact evaluation of triangulation predicates during surface meshing. The native approach is demonstrated through an algorithm for the generation of closed manifold surface triangulations from CAD geometry. CAD parts and assemblies are used in their native format, and a part's native geometry engine is accessed through a modeler-independent application programming interface (API). In seeking a robust and fully automated procedure, the algorithm is based on a new physical space manifold triangulation technique specially developed to avoid robustness issues associated with poorly conditioned mappings. In addition, this approach avoids the usual ambiguities associated with floating-point predicate evaluation on constructed coordinate geometry in a mapped space. The technique is incremental, so that each new site improves the triangulation by some well defined quality measure. The algorithm terminates after achieving a prespecified measure of mesh quality and produces a triangulation such that no angle is less than a given angle bound, a or greater than pi - 2alpha. This result also sets bounds on the maximum vertex degree, triangle aspect-ratio and maximum stretching rate for the triangulation. In addition to the output triangulations for a variety of CAD parts, the discussion presents related theoretical results which assert the existence of such an angle bound, and demonstrate that maximum bounds of between 25 deg and 30 deg may be achieved in practice.

Aftosmis, M. J.↗

NASA NTRS2001

Unstructured Mesh Methods for the Simulation of Hypersonic Flows

This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite element algorithm for the solution of the viscous compressible flow equations which can solve flows all the way down to the incompressible limit and that can use higher order (quadratic) approximations leading to highly accurate answers, and 3) and iterative algebraic multigrid solution techniques.

Peraire, Jaime↗

NASA NTRS2001

A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.

Zhang, Zeng-Chan↗

NASA NTRS2001

Spaceborne Microwave Instrument for High Resolution Remote Sensing of the Earth's Surface Using a Large-Aperture Mesh Antenna

This report describes a two-year study of a large-aperture, lightweight, deployable mesh antenna system for radiometer and radar remote sensing of the Earth from space. The study focused specifically on an instrument to measure ocean salinity and Soil moisture. Measurements of ocean salinity and soil moisture are of critical . importance in improving knowledge and prediction of key ocean and land surface processes, but are not currently obtainable from space. A mission using this instrument would be the first demonstration of deployable mesh antenna technology for remote sensing and could lead to potential applications in other remote sensing disciplines that require high spatial resolution measurements. The study concept features a rotating 6-m-diameter deployable mesh antenna, with radiometer and radar sensors, to measure microwave emission and backscatter from the Earth's surface. The sensors operate at L and S bands, with multiple polarizations and a constant look angle, scanning across a wide swath. The study included detailed analyses of science requirements, reflector and feedhorn design and performance, microwave emissivity measurements of mesh samples, design and test of lightweight radar electronic~., launch vehicle accommodations, rotational dynamics simulations, and an analysis of attitude control issues associated with the antenna and spacecraft, The goal of the study was to advance the technology readiness of the overall concept to a level appropriate for an Earth science emission.

Njoku, E.↗

NASA NTRS2003

Analysis and Improvement of Upwind and Centered Schemes on Quadrilateral and Triangular Meshes

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (MUSCL approach) followed by an upwind step (Roe's flux-difference splitting). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the Nessyahu-Tadmor (N-T) scheme and the CE/SE method with epilson = 1/2. The upwind scheme is extended to the case of two spatial dimensions (2D) in a straightforward manner. The N-T and CE/SE schemes are extended in a manner similar to the 2D extensions of the CE/SE scheme by Wang and Chang for a triangular mesh and by Zhang, Yu, and Chang for a quadrilateral mesh. The slope estimates, however, are simplified. Fourier stability and accuracy analyses are carried out for these schemes for the standard 1D and the 2D quadrilateral mesh cases. In the nonstandard case of a triangular mesh, the triangles must be paired up when analyzing the upwind and N-T schemes. An observation resulting in an extended N-T scheme which is faster and uses only one-third of the storage for flow data compared with the CE/SE method is presented. Numerical results are shown. Other improvements to the schemes are discussed.

Huynh, H. T.↗

NASA NTRS2003

Development of a Flexible Framework of Common Hypersonic Navier-Strokes Meshes for the Space Shuttle Orbiter

A flexible framework for the development of block structured volume grids for hypersonic Navier-Stokes flow simulations was developed for analysis of the Shuttle Orbiter Columbia. The development of the flexible framework, resulted in an ability to quickly generate meshes to directly correlate solutions contributed by participating groups on a common surface mesh, providing confidence for the extension of the envelope of solutions and damage scenarios. The framework draws on the experience of NASA Langely and NASA Ames Research Centers in structured grid generation, and consists of a grid generation process that is implemented through a division of responsibilities. The nominal division of labor consisted of NASA Johnson Space Center coordinating the damage scenarios to be analyzed by the Aerothermodynamics Columbia Accident Investigation (CAI) team, Ames developing the surface grids that described the computational volume about the orbiter, and Langely improving grid quality of Ames generated data and constructing the final volume grids. Distributing the work among the participants in the Aerothermodynamic CIA team resulted in significantly less time required to construct complete meshes than possible by any individual participant. The approach demonstrated that the One-NASA grid generation team could sustain the demand for new meshes to explore new damage scenarios within a aggressive timeline.

Alter, Stephen J.↗

NASA NTRS2004

Surface Generation and Cartesian Mesh Support

This document serves as the final report for the grant titled Surface Generation and Cartesian Mesh Support . This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cart3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.

Haimes, Robert↗

NASA NTRS2005

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗

NASA NTRS1998

Numerical Differentiation for Adaptively Refined Finite Element Meshes

Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.

Borgioli, Andrea↗

NASA NTRS2005

A Hexapod Robot to Demonstrate Mesh Walking in a Microgravity Environment

The JPL Micro-Robot Explorer (MRE) Spiderbot is a robot that takes advantage of its small size to perform precision tasks suitable for space applications. The Spiderbot is a legged robot that can traverse harsh terrain otherwise inaccessible to wheeled robots. A team of Spiderbots can network and can exhibit collaborative efforts to SUCCeSSfUlly complete a set of tasks. The Spiderbot is designed and developed to demonstrate hexapods that can walk on flat surfaces, crawl on meshes, and assemble simple structures. The robot has six legs consisting of two spring-compliant joints and a gripping actuator. A hard-coded set of gaits allows the robot to move smoothly in a zero-gravity environment along the mesh. The primary objective of this project is to create a Spiderbot that traverses a flexible, deployable mesh, for use in space repair. Verification of this task will take place aboard a zero-gravity test flight. The secondary objective of this project is to adapt feedback from the joints to allow the robot to test each arm for a successful grip of the mesh. The end result of this research lends itself to a fault-tolerant robot suitable for a wide variety of space applications.

Foor, David C.↗

NASA NTRS2006

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

Nielsen, Eric J.↗

NASA NTRS2009

Recent Enhancements To The FUN3D Flow Solver For Moving-Mesh Applications

An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been extended to handle general mesh movement involving rigid, deforming, and overset meshes. Mesh deformation is achieved through analogy to elastic media by solving the linear elasticity equations. A general method for specifying the motion of moving bodies within the mesh has been implemented that allows for inherited motion through parent-child relationships, enabling simulations involving multiple moving bodies. Several example calculations are shown to illustrate the range of potential applications. For problems in which an isolated body is rotating with a fixed rate, a noninertial reference-frame formulation is available. An example calculation for a tilt-wing rotor is used to demonstrate that the time-dependent moving grid and noninertial formulations produce the same results in the limit of zero time-step size.

Biedron, Robert T,↗

NASA NTRS2010

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

Baxes, Gregory A.↗

NASA NTRS2011

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

Baxes, Gregory A.↗

NASA NTRS2005

Parallel Adaptive Mesh Refinement Library

Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.

Mac-Neice, Peter↗

NASA NTRS2011

Loft: An Automated Mesh Generator for Stiffened Shell Aerospace Vehicles

Loft is an automated mesh generation code that is designed for aerospace vehicle structures. From user input, Loft generates meshes for wings, noses, tanks, fuselage sections, thrust structures, and so on. As a mesh is generated, each element is assigned properties to mark the part of the vehicle with which it is associated. This property assignment is an extremely powerful feature that enables detailed analysis tasks, such as load application and structural sizing. This report is presented in two parts. The first part is an overview of the code and its applications. The modeling approach that was used to create the finite element meshes is described. Several applications of the code are demonstrated, including a Next Generation Launch Technology (NGLT) wing-sizing study, a lunar lander stage study, a launch vehicle shroud shape study, and a two-stage-to-orbit (TSTO) orbiter. Part two of the report is the program user manual. The manual includes in-depth tutorials and a complete command reference.

Eldred, Lloyd B.↗

NASA NTRS2003

Meshed-Pumpkin Super-Pressure Balloon Design

An improved, lightweight design has been proposed for super-pressure balloons used to carry scientific instruments at high altitudes in the atmosphere of Earth for times as long as 100 days. [A super-pressure balloon is one in which the pressure of the buoyant gas (typically, helium) is kept somewhat above ambient pressure in order to maintain approximately constant density and thereby regulate the altitude.] The proposed design, called "meshed pumpkin," incorporates the basic concept of the pumpkin design, which is so named because of its appearance. The pumpkin design entails less weight than does a spherical design, and the meshed-pumpkin design would reduce weight further. The basic idea of the meshed-pumpkin design is to reinforce the membrane of a pumpkin balloon by attaching a strong, lightweight fabric mesh to its outer surface. The reinforcement would make it possible to reduce the membrane mass to one-third or less of that of the basic pumpkin design while retaining sufficient strength to enable the balloon to remain at approximately constant altitude for months.

Jones, Jack↗

NASA NTRS2013

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗