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NASA NTRS1990

Grid generation for computational CFD of full aerodynamic configurations

It is now possible to compute flow about very complex three-dimensional aerodynamic configurations. Grid generation is an essential part of such computations and a basic capability has been demonstrated. The present problems are: (1) choosing among the competing approaches (structured, unstructured or rectangular); (2) automating and packaging software for grid generation; (3) assessing and assuring grid quality; (4) solid boundary-surface representation and grid generation on solid boundaries; (5) automated domain decomposition (structured grids); (6) grid adaption during the flow solution process. This paper discusses some of the capabilities in the computation of complex three-dimensional grids and addresses some of he current challenges.

Smith, Robert E.↗

NASA NTRS1995

Tuned grid generation with ICEM CFD

ICEM CFD is a CAD based grid generation package that supports multiblock structured, unstructured tetrahedral and unstructured hexahedral grids. Major development efforts have been spent to extend ICEM CFD's multiblock structured and hexahedral unstructured grid generation capabilities. The modules added are: a parametric grid generation module and a semi-automatic hexahedral grid generation module. A fully automatic version of the hexahedral grid generation module for around a set of predefined objects in rectilinear enclosures has been developed. These modules will be presented and the procedures used will be described, and examples will be discussed.

Wulf, Armin↗

NASA NTRS1995

Grid generation on trimmed Bezier and NURBS quilted surfaces

This paper presents some recently added capabilities to RAGGS, Rockwell Automated Grid Generation System. Included are the trimmed surface handling and display capability and structures and unstructured grid generation on trimmed Bezier and NURBS (non-uniform rational B-spline surfaces) quilted surfaces. Samples are given to demonstrate the new capabilities.

Woan, Chung-Jin↗

NASA NTRS1992

Conservative Grid-Interface Algorithm For Computing Flows

Best features of structured- and unstructured-grid methods combined. Gaps and overlaps between zonal grids eliminated by grid-interface algorithm, which generates single interfacial grid and corrects fluxes of flow quantities accordingly. Incorporated into two three-dimensional Navier-Stokes finite-volume codes and tested in computations of incompressible and compressible flows about simple bodies. Good numerical results obtained. General enough to be incorporated into other finite-volume codes without restrictions on complexities of shapes of bodies and zonal interfaces.

Klopfer, G. H.↗

NASA NTRS2002

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Liu, Yen↗

NASA NTRS2011

Summary of the First AIAA CFD High Lift Prediction Workshop (invited)

The 1st AIAA CFD High Lift Prediction Workshop was held in Chicago in June 2010. The goals of the workshop included an assessment of the numerical prediction capability of current-generation CFD technology/ codes for swept, medium/high-aspect ratio wings in landing/take-off (high lift) configurations. 21 participants from 8 countries and 18 organizations, submitted a total of 39 datasets of CFD results. A variety of grid systems (both structured and unstructured) were used. Trends due to flap angle were analyzed, and effects of grid family, grid density, solver, and turbulence model were addressed. Some participants also assessed the effects of support brackets used to attach the flap and slat to the main wing. This invited paper describes the combined results from all workshop participants. Comparisons with experimental data are made. A statistical summary of the CFD results is also included.

Rumsey, C. L.↗

NASA NTRS1977

Splines under tension in integral transfer problems

Splines under tension are used to develop an interpolatory representation of integral radiation operators. A quantitative measure of the stability of this representation is derived and approximated in terms of local grid lengths and the tension parameter. Cubic splines (zero tension parameter) are shown to be approximately stable when the ratio of successive grid lengths lies within a specific range. Scaling procedures for determining the tension constant from the structure of the grids and the characteristics of the problem are discussed, and the utility of these procedures is illustrated by application to the formation of resonance lines in two-dimensional media with exponential height variation of opacity.

Jones, H. P.↗

NASA NTRS2003

Effects of Wing Leading Edge Penetration with Venting and Exhaust Flow from Wheel Well at Mach 24 in Flight

A baseline solution for CFD Point 1 (Mach 24) in the STS-107 accident investigation was modified to include effects of: (1) holes through the leading edge into a vented cavity; and (2) a scarfed, conical nozzle directed toward the centerline of the vehicle from the forward, inboard corner of the landing gear door. The simulations were generated relatively quickly and early in the investigation because simplifications were made to the leading edge cavity geometry and an existing utility to merge scarfed nozzle grid domains with structured baseline external domains was implemented. These simplifications in the breach simulations enabled: (1) a very quick grid generation procedure; and (2) high fidelity corroboration of jet physics with internal surface impingements ensuing from a breach through the leading edge, fully coupled to the external shock layer flow at flight conditions. These simulations provided early evidence that the flow through a two-inch diameter (or larger) breach enters the cavity with significant retention of external flow directionality. A normal jet directed into the cavity was not an appropriate model for these conditions at CFD Point 1 (Mach 24). The breach diameters were of the same order or larger than the local, external boundary-layer thickness. High impingement heating and pressures on the downstream lip of the breach were computed. It is likely that hole shape would evolve as a slot cut in the direction of the external streamlines. In the case of the six-inch diameter breach the boundary layer is fully ingested. The intent of externally directed jet simulations in the second scenario was to approximately model aerodynamic effects of a relatively large internal wing pressure, fueled by combusting aluminum, which deforms the corner of the landing gear door and directs a jet across the windside surface. These jet interactions, in and of themselves, were not sufficiently large to explain observed aerodynamic behavior.

Gnoffo, Peter A.↗

NASA NTRS2009

Simulation of an Isolated Tiltrotor in Hover with an Unstructured Overset-Grid RANS Solver

An unstructured overset-grid Reynolds Averaged Navier-Stokes (RANS) solver, FUN3D, is used to simulate an isolated tiltrotor in hover. An overview of the computational method is presented as well as the details of the overset-grid systems. Steady-state computations within a noninertial reference frame define the performance trends of the rotor across a range of the experimental collective settings. Results are presented to show the effects of off-body grid refinement and blade grid refinement. The computed performance and blade loading trends show good agreement with experimental results and previously published structured overset-grid computations. Off-body flow features indicate a significant improvement in the resolution of the first perpendicular blade vortex interaction with background grid refinement across the collective range. Considering experimental data uncertainty and effects of transition, the prediction of figure of merit on the baseline and refined grid is reasonable at the higher collective range- within 3 percent of the measured values. At the lower collective settings, the computed figure of merit is approximately 6 percent lower than the experimental data. A comparison of steady and unsteady results show that with temporal refinement, the dynamic results closely match the steady-state noninertial results which gives confidence in the accuracy of the dynamic overset-grid approach.

Lee-Rausch, Elizabeth M.↗

NASA NTRS2012

Improved Finite-Volume Method for Radiative Hydrodynamics

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy for such simulations on structured and unstructured grids compared to more conventional approaches. Results will be shown for shock radiation during hypersonic reentry. Issues of parallelization within a radiation sweep will also be discussed.

Wray, Alan↗

NASA NTRS1993

A gridless Euler/Navier-Stokes solution algorithm for complex-aircraft applications

The development of a gridless computational fluid dynamics (CFD) method for the solution of the two- and three-dimensional Euler and Navier-Stokes equations is described. The method uses only clouds of points and does not require that the points be connected to form a grid as is necessary in conventional CFD algorithms. The gridless CFD approach appears to resolve the inefficiencies encountered with structured or unstructured grid methods, and consequently offers great potential for accurately and efficiently solving viscous flows about complex aircraft configurations. The method is described in detail and calculations are presented for standard Euler and Navier-Stokes cases to assess the accuracy and efficiency of the capability.

Batina, John T.↗

NASA NTRS1993

A gridless Euler/Navier-Stokes solution algorithm for complex-aircraft applications

The development of a gridless computational fluid dynamics (CFD) method for the solution of the two- and three-dimensional Euler and Navier-Stokes equations is described. The method uses only clouds of points and does not require that the points be connected to form a grid as a necessary in conventional CFD algorithms. The gridless CFD approach appears to resolve the inefficiencies encountered with structured or unstructured grid methods, and consequently offers great potential for accurately and efficiently solving viscous flows about complex aircraft configurations. The method is described in detail and calculations are presented for standard Euler and Navier-Stokes cases to assess the accuracy and efficiency of the capability.

Batina, John T.↗

NASA NTRS2022

The Effects of Surface Fossil Magnetic Fields on Massive Star Evolution: IV. Grids of Models at Solar, LMC, and SMC Metallicities

Magnetic fields can drastically change predictions of evolutionary models of massive stars via mass-loss quenching, magnetic braking, and efficient angular momentum transport, which we aim to quantify in this work. We use the MESA software instrument to compute an e xtensiv e main-sequence grid of stellar structure and evolution models, as well as isochrones, accounting for the effects attributed to a surface fossil magnetic field. The grid is densely populated in initial mass (3–60 M ), surface equatorial magnetic field strength (0–50 kG), and metallicity (representative of the Solar neighbourhood and the Magellanic Clouds). We use two magnetic braking and two chemical mixing schemes and compare the model predictions for slowly rotating, nitrogen- enriched (‘Group 2’) stars with observations in the Large Magellanic Cloud. We quantify a range of initial field strengths that allow for producing Group 2 stars and find that typical values (up to a few kG) lead to solutions. Between the subgrids, we find notable departures in surface abundances and evolutionary paths. In our magnetic models, chemical mixing is al w ays less efficient compared to non-magnetic models due to the rapid spin-down. We identify that quasi-chemically homogeneous main sequence evolution by efficient mixing could be prevented by fossil magnetic fields. We recommend comparing this grid of evolutionary models with spectropolarimetric and spectroscopic observations with the goals of (i) revisiting the derived stellar parameters of known magnetic stars, and (ii) observationally constraining the uncertain magnetic braking and chemical mixing schemes.

stars: abundances↗

NASA NTRS1978

Graphite/epoxy orthogrid panel fabrication

The structural concept considered for a spacecraft body structure is a grid stiffened skin with a skin laminate configuration and the stiffener grid geometry selected to best suit the design requirements. The orthogrid panel developed weighs 0.55 lb/sq ft and resisted an ultimate in-plane shear load of 545 lbf/in. The basic concept of a grid stiffener composite panel is that a relatively thin skin is reinforced with a gridwork of stiffeners so that the overall panel can resist design loads without becoming structurally unstable or being overstressed. The main feature of the orthogrid panel design is that it provides the potential for low cost structural panels when advanced to the production phase. The most innovative part of the fabrication method is the foam/fiberglass stiffener web grid billet fabrication and machining to size.

Lager, J. R.↗

NASA NTRS1992

A gridless Euler/Navier-Stokes solution algorithm for complex two-dimensional applications

The development of a gridless computational fluid dynamics (CFD) method for the solution of the two-dimensional Euler and Navier-Stokes equations is described. The method uses only clouds of points and does not require that the points be connected to form a grid as is necessary in conventional CFD algorithms. The gridless CFD approach appears to resolve the problems and inefficiencies encountered with structured or unstructured grid methods. As a result, the method offers the greatest potential for accurately and efficiently solving viscous flows about complex aircraft configurations. The method is described in detail, and calculations are presented for standard Euler and Navier-Stokes cases to assess the accuracy and efficiency of the capability.

Batina, John T.↗

NASA NTRS1993

Unstructured Grids on NURBS Surfaces

A simple and efficient computational method is presented for unstructured surface grid generation. This method is built upon an advancing front technique combined with grid projection. The projection technique is based on a Newton-Raphson method. This combined approach has been successfully implemented for structured and unstructured grids. In this paper, the implementation for unstructured grid is discussed.

Samareh-Abolhassani, Jamshid↗

NASA NTRS1999

Parallel Grid Manipulations in Earth Science Calculations

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center is moving its data assimilation system to massively parallel computing platforms. This parallel implementation of GEOS DAS will be used in the DAO's normal activities, which include reanalysis of data, and operational support for flight missions. Key components of GEOS DAS, including the gridpoint-based general circulation model and a data analysis system, are currently being parallelized. The parallelization of GEOS DAS is also one of the HPCC Grand Challenge Projects. The GEOS-DAS software employs several distinct grids. Some examples are: an observation grid- an unstructured grid of points at which observed or measured physical quantities from instruments or satellites are associated- a highly-structured latitude-longitude grid of points spanning the earth at given latitude-longitude coordinates at which prognostic quantities are determined, and a computational lat-lon grid in which the pole has been moved to a different location to avoid computational instabilities. Each of these grids has a different structure and number of constituent points. In spite of that, there are numerous interactions between the grids, e.g., values on one grid must be interpolated to another, or, in other cases, grids need to be redistributed on the underlying parallel platform. The DAO has designed a parallel integrated library for grid manipulations (PILGRIM) to support the needed grid interactions with maximum efficiency. It offers a flexible interface to generate new grids, define transformations between grids and apply them. Basic communication is currently MPI, however the interfaces defined here could conceivably be implemented with other message-passing libraries, e.g., Cray SHMEM, or with shared-memory constructs. The library is written in Fortran 90. First performance results indicate that even difficult problems, such as above-mentioned pole rotation- a sparse interpolation with little data locality between the physical lat-lon grid and a pole rotated computational grid- can be solved efficiently and at the GFlop/s rates needed to solve tomorrow's high resolution earth science models. In the subsequent presentation we will discuss the design and implementation of PILGRIM as well as a number of the problems it is required to solve. Some conclusions will be drawn about the potential performance of the overall earth science models on the supercomputer platforms foreseen for these problems.

Sawyer, W.↗

NASA NTRS1985

Testing of a failure accommodation system on a highly flexible grid

This paper presents a scheme for on-line failure detection in systems with appreciable structural dynamics. The design is suboptimal because of extensive computational requirements of optimal schemes. To accomplish failure detection, the innovations sequence of a finite order Kalman filter is examined. Because of the heavy dependence of the system on the zero-mean character of the innovations sequence of the filter much attention has been given to the design and evaluation of the Kalman filters used. The filter designs are based on modal models of the structural dynamics. Two modal models were considered, one based on an analytic finite element model and the other based on empirically derived frequency and damping. Experiments using a grid structure are presented which illustrate operation and performance of the filter designs based on these models. The general character of the results presented is that appreciable errors exist in the filter design based on the finite element model. Substantial improvement results if the design model is modified to include empirically derived frequency and damping.

Montgomery, R. C.↗