Unstructured Grid Generation for Aerospace Applications (1999)

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ICASE/LaRC/ARO/NSF Workshop on Computational Aerosciences in the 21st Century

Unstructured Grid Generation For Aerospace Applications

David L. Marcum

and

J. Adam Gaither

NSF Engineering Research Center for Computational Field Simulation

P.O. Box 9627

Mississippi State University, MS 39759

email: [email protected]

1. Introduction

Unstructured grid technology has the potential to significantly reduce the overall user and CPU time

required for CFD analysis of realistic configurations. To realize this potential, improvements in

automation, anisotropic generation, adaptation, and integration within the solution process areneeded. Unstructured grid generation has advanced to the point where generation of a grid for most

any configuration requires only a couple of hours of user time. However, prior to grid generation,

the CAD geometry must be prepared. This process can take anywhere from hours to weeks. It is the

single most laborintensive task in the overall simulation process. Adherence to standards and

alternative procedures for surface grid generation which account for small gaps and overlaps and

generate across multiple surfaces can minimize and potentially eliminate much of the geometry

preparation. With improvements in the geometry preparation process the overall grid generation

task can be more fully automated. Anisotropic grid generation is another area in need of

improvement. Current techniques have not advanced to the level of robustness and generality as for

isotropic grid generation. Methodologies such as use of multiple normals or truly unstructured

placement of anisotropic points need to be developed into more robust procedures. Also,solutionadaptation is a potential advantage of an unstructured grid approach that has not been

developed into a feasible technology for highresolution threedimensional simulations. Highly

anisotropic adaptation is needed to improve feasibility. In addition, the grid generation, and in some

cases CAD geometry, should be fully integrated into the solution process for some applications. This

is essential for more automated design optimization or aeroelastic coupling applications as well as

those with moving bodies, control surface deflections, maneuvering vehicles, and/or unsteady flow.

Many of the grid and CAD tools in use today may require significant enhancement to be usable ina fully coupled and automatic mode within an overall simulation environment.

In this article, representative examples are presented to demonstrate the current status of

unstructured grid generation and describe areas for improvement. Also, the overall grid generation

process is reviewed to illustrate user operations that could be automated.

2. Unstructured Grid Generation Current Status

Unstructured grid generation for many engineering applications has advanced to the point where it

can be used routinely for very complex configurations. For example, isotropic element grids suitable

for inviscid CFD simulations can be generated for complete aircraft. In viscous cases, generation

ofhighaspectratio elements is more limited in usability as available procedures are not as robust

or consistent as those for isotropic elements. However, viscous simulations of relatively complex


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ICASE/LaRC/ARO/NSFWorkshop on Computational Aerosciences in the 21st Century

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configurations have been successfully performed using unstructured grids [Mavriplis and Pirzadeh,

1999 and Sheng, et al, 1999]. Currently, research and commercial systems are available with

unstructured grid generators integrated along with CAD/CAE tools. Many of these are suitable for

inviscid CFD applications and some have highaspectratio element capabilities for viscous cases.

Methods used are typically based on either an octree [Shepard and Georges, 1991], advancingfront

[Lohner and Parikh, 1988, Peraire et al, 1988, and Pirzadeh, 1996], Delaunay [Baker, 1987, George

et al, 1990, Holmes and Snyder, 1988, and Weatherill, 1985] or a combined approach [Marcum,

1995a, Mavriplis, 1993, Muller et al, 1993, and Rebay, 1993]. To demonstrate the current status of

unstructured grid generation, the advancingfront/localreconnection (AFLR) procedure

[Marcum, 1995a and 1995b] will be used. This procedure is integrated in research systems

(SolidMesh, MSU) and commercial systems (HyperMesh, Altair Computing).

2.1. AFLR Unstructured Grid Generation

The AFLR triangular/tetrahedral grid generation procedure is a combination of automatic point

creation, advancing type ideal point placement, and connectivity optimization schemes. A valid grid

is maintained throughout the grid generation process. This provides a framework for implementing

efficient local search operations using a simple data structure. It also provides a means for smoothlydistributing the desired point spacing in the field using a point distribution function. This functionis propagated through the field by interpolation from the boundary point spacing or by specified

growth normal to the boundaries. Points are generated using either advancingfront type point

placement for isotropic elements or advancingnormal type point placement for highaspectratio

elements. The connectivity for new points is initially obtained by direct subdivision of the elements

that contain them. Connectivity is then optimized by localreconnection with a minmax type

(minimize the maximum angle) type criterion. The overall procedure is applied repetitively until a

complete field grid is obtained. More complete details and results are presented in [Marcum, 1995a

and 1995b].

Procedures for both surface and volume grid generation based on AFLR have been integrated with

CAD tools in a research system called SolidMesh [Gaither, 1997 and Marcum, 1996]. This system

was used for geometry cleanup and preparation and grid generation for the example cases presented

later in this section.

For grid generation with the present methodology, the grid point distribution is automatically

propagated from specified control points to edge grids, from edge to surface grids, and finally from

surface grids to the volume grid. Surface patches, edges, and corner points for a fighter geometry

definition are shown in Fig. 1. The first step in the grid generation process is to initially set the desired

point spacing to a global value at all edge endpoints. Point spacings are then set to different values

at desired control points on edges in specific regions requiring further resolution. For example,

endpoints along leading edges and trailing edges would typically be set to a very fine point spacing.

Point spacings can be set anywhere along an edge. A point in the middle of a wing section wouldtypically be set to a larger point spacing than at the leading or trailing edges. As control point

spacings are set, a discretized edge grid is created for each edge. Specification of desired control

point spacings is typically the only user input required in the overall grid generation process.

Surface grid generation is an interactive process that requires only seconds for generation of a

hundred thousand faces on either a PC or workstation. High quality surface grids can be consistently

generated. For a typical surface grid, the maximum angle is 120 deg. or less, the standard deviation

is 7 deg. or less, and 99.5% or more of the elements have angles between 30 and 90 deg.


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Volume grid generation is driven directly from the surface grid. For a moderate size isotropic grid(500,000 elements) generation requires approximately 2 minutes on a workstation (Sun Ultra 60).A large isotropic grid (3,000,000 elements) requires approximately 20 minutes. Viscous grid cases

require considerably less time. For example, 23 minutes for 2,000,000 total elements or

approximately 30 minutes for 10,000,000 total elements. Generation times given include all I/O and

grid quality statistics. A workstation or server is usually used for volume generation due to memory

requirements, which are about 100 bytes per isotropic element generated. For grids with

highaspectratio elements the memory requirements are less. High quality volume grids can be

consistently generated if the surface grid is also of high quality. Typically, for an isotropic grid, the

maximum dihedral element angle is 160 deg. or less, the standard deviation is 17 deg. or less, and99.5% or more of the elements have dihedral angles between 30 and 120 deg. The minimum dihedral

angle is usually dictated by the geometry.

2.1. NASA Space Shuttle Orbiter

A grid suitable for inviscid CFD analysis was generated for the NASA Space Shuttle Orbiter. This

case demonstrates the level of geometric complexity that can be handled routinely using

unstructured grid technology. Geometry cleanup and preparation required approximately twentylaborhours to complete. In this case, the original geometry definition had extra surfaces, missingsurfaces, gaps, and overlaps. This is often the case in a research environment when a geometry has

been processed through different CAD/CAE systems and passed between researchers. Surface and

volume grid generation related work required approximately four laborhours. This time includedmodifications for grid quality optimization and resolution changes based upon multiple preliminary

CFD solutions. The surface grid on the orbiter surface is shown in Fig. 2. The total surface grid

contains 150,206 boundary faces. A tetrahedral field cut is shown in Fig. 3. Element size varies

smoothly in the field. The complete volume grid contains 547,741 points and 3,026,562 elements.Grid quality distributions for the surface and volume grids are shown in Figs. 4 and 5, respectively.

Element angle distributions, maximum values, and standard deviations verify that the surface and

volume grids are of very high quality. Computed density contours from an inviscid solution areshown in Fig. 6. The overall structure of the flow field is captured, especially near the body.

However, away from from the body, the resolution is not very accurate.

Solutionadaptive grid generation could be used to improve the flow field resolution considerably.

A suitable solutionadapted grid for this case would have to utilize anisotropic elements to

efficiently resolve the highly directional solution gradients. While techniques for adaptation have

been studied for some time, they have not been developed into a feasible technology for

highresolution threedimensional simulations. Highly anisotropic adaptation is needed to improve

feasibility. The anisotropic elements should be aligned in a structured type manner with each other

and the flow physics for optimal solution algorithm efficiency. The adaptation process must be

capable of resolving many types of features, such as shock waves, contact discontinuities,

expansions, compressions, detached viscous shear layers, vortices, etc. There are promisingapproaches, such as point movement with enrichment, feature decomposition, etc. However,

significant research work is required to develop a usable procedure.

2.2. EET HighLift Configuration

A grid suitable for high Reynolds Number viscous CFD analysis was generated for a highlift wing

body configuration of the Energy Efficient Transport (EET). This case demonstrates the level of

geometric complexity that can be handled for viscous flow cases using unstructured grid technology.


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Geometry cleanup and preparation required approximately seven laborhours to complete. In this

case, the original geometry definition was relatively clean and much of the time was spent on

tolerance issues and surface intersections. Surface and volume grid generation related work required

approximately two laborhours. This time included modifications for grid quality optimization and

resolution changes based upon a preliminary CFD solution. The surface grid on the upper and lower

surface of the wing are shown in Figs. 7a and 7b. The total surface grid contains 273,500 boundary

faces. Tetrahedral field cuts are shown in Figs. 8a and 8b. Element size varies smoothly in the field

and there is a smooth transition between highaspectratio and isotropic element regions. Also, inareas where there are small distances between surfaces, the merging highaspectratio regions

transition (locally) to isotropic generation. If these regions advance too close, without transition, the

element quality can be substantially degraded. For this case, increased grid resolution of the leading

and trailing edges of the main wing, flap, slat, and vane would improve the grid quality in merging

regions. The complete volume grid contains 2,215,470 points and 12,873,429 elements. Most of the

tetrahedral elements in the highaspectratio regions can be combined into pentahedral elements for

improved solver efficiency. With element combination, the complete volume grid contains

1,813,111 tetrahedrons, 61,366 fivenode pentahedrons (pyramids), and 3,645,862 sixnode

pentahedrons (prisms). Grid quality distributions for the surface and volume grids are shown in Figs.

4 and 5, respectively. Element angle distributions and maximum values verify that the surface and

volume grids are of very high quality. The distribution peaks are at the expected values of near 0,

70, and 90 deg. Computed streamlines from a viscous, turbulent, incompressible solution are shown

near the upper and lower surfaces of the wing in Figs. 9a and 9b. Comparison to experimental data

(not shown) is reasonable overall [Sheng, et al, 1999]. However, additional resolution is needed on

the flap, slat, and vane, particularly at the leading edges.

The EET configuration illustrates that unstructured grid technology can be used to simulate viscous

flow about relatively complex configurations. However, the unstructured grid generation process

is not as advanced as for isotropic elements. Improvements are needed in robustness and element

quality for cases with complex geometry and multiple components in close proximity. Several

techniques are listed below which could be used to improve the unstructured grid generation processfor viscous cases.

An anisotropic surface grid could be used to efficiently increase grid

density along leading and trailing edges of wing components.

Automatic surface refinement of close boundaries with merging boundary

layers (as is done in 2D) would improve grid quality.

Embedded surfaces in the field could be used to improve accuracy in

wake regions.

Multiple boundarylayer surface normals could be used to enhance grid

quality and resolution at points where the boundary surface isdiscontinuous. A tetrahedral field cut for an example case with multiple

normals is shown in Fig. 10.

3. Overall Unstructured Grid Generation Process

As demonstrated in the previous examples, user time required to generate an unstructured grid from

a properly prepared geometry definition is only a couple of hours. However, the process of preparing

the geometry can take anywhere from hours to weeks. It is the single most laborintensive task in


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the overall CFD simulation process. Much of this time is often spent on repair of gaps and overlaps,

which can be minimized through standards. Even with a geometry definition which is truly a solid

there can be significant CAD work required to prepare the geometry for CFD analysis. Elimination

of features or components not relevant to the analysis can require substantial effort. Geometry

preparation can also include further work in grouping of multiple surface definitions. Alternative

procedures for CAD preparation and surface grid generation are needed which account for small

gaps and overlaps, generate across multiple surfaces, and automatically detect and remove features

and components not relevant to the analysis. These procedures would minimize and potentially

eliminate much of the geometry preparation. With improvements in the geometry preparation

process the overall grid generation task can be more fully automated. This can include automatic

specification of appropriate element size, at least, for a given class of configurations. Examples ofuser steps that could be readily automated and use of multiple surface grouping are presented below.

With the procedure described in this article, volume element size and distribution is determined from

the boundary. A lowquality surface grid will produce lowquality volume elements near the

surface. In most cases, a highquality surface grid will produce a highquality volume grid.

Lowquality surface elements are usually the result of inappropriate edge spacing. With fast surface

grid generation and simple point spacing specification, optimizing the surface quality is a quickprocess. User input could be eliminated by automatically reducing point spacing in low quality

regions. An example of a surface mesh with a low quality triangle, that can be corrected by point

spacing placement or reduction, is shown in Fig. 11a. In this case, the surface patch has close edges

which can not be eliminated. In Fig. 11a, the initial choice of a uniform spacing at the edge

endpoints produces a single lowquality triangle. Specifying a single point spacing at the middle

of the edge near the close edges, eliminates the lowquality element, as shown in Fig. 11b.

Alternatively, the spacing near the close edges can be reduced to produce a more ideal grid, at the

expense of an increased number of elements, as shown in Fig. 11c.

Other conditions can affect volume quality even if the surface grid is of highquality. An example

is shown in Fig. 12. In this case, there are two nearby surfaces with large differences in element size.This results in distorted volume elements between the surfaces, as shown in Fig. 12. These elements

can be eliminated by increasing the spacing on the surface which has the smaller elements and/or

decreasing the spacing on the surfaces which have the larger elements. From a solution algorithm,

perspective, the spacings should probably be reduced. The region between the two objects can notbe resolved by the solver without additional grid points. Automatic detection and refinement of

close boundary surfaces could reduce or eliminate user input for these situations. This could be

even more beneficial for viscous cases. Volume grid quality can degrade if the boundarylayer

regions from opposing boundaries merge with highaspectratio elements.

Surface definition can also impact surface grid quality. This type of problem is usually due to a

surface patch with a width that is smaller than the desired element size. An example case with a

surface containing 11 surface definition patches is shown in Fig. 13a. The detail view shown in Fig

14a of the top center area reveals a very short edge due to the way the surface patches are defined.

Generating individual surface grids for each patch can result in an irregular and lowquality overall

surface grid, as shown in Fig. 13b. Very highaspectratio elements are generated in the region ofthe short edge, as shown in Fig. 14a. Combing the patches into one surface patch improves the

quality, as shown in Figs. 13c and 14b. This can be accomplished by replacing the multiple patches

with a new single definition. However, that process can require considerable user time and it

modifies the original geometry. An alternative is to topologically group the surface definition


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patches in an intermediate mapped space. This requires minimal user input (selection of patches to

be grouped) and preserves the original geometry definition. The surface grid shown in Figs. 13c and

14b was generated using a preliminary version of this procedure. Grouping of multiple surface

patches can also be used to remove unnecessary features from a geometry definition. For example,

the surface grid shown in Fig. 15a contains a slightly recessed circular region which is well resolved

with the point spacings shown. If a larger point spacing is desired, this feature may not be relevant.

Grouping the surface patches resolves this region only to the resolution of the selected point

spacings, as shown in Fig. 15b.

4. Summary

Representative examples were presented which demonstrated that unstructured grid generation has

advanced to the point where generation of a grid for most any configuration requires only a couple

ofhours of user time. However, the overall grid generation process can take anywhere from hoursto weeks. Automation and improvements in procedures for preparing the CAD surface definition

would substantially reduce the required user time. For viscous grid generation, enhanced methods

are needed to improve grid quality and robustness. Also, significant research work is required to

develop viable solutionadaptive procedures for highresolution of complex threedimensionalflow fields.

5. Acknowledgements

The authors would like to acknowledge support for this work from the Air Force Office of Scientific

Research, Dr. Leonidas Sakell, Program Manager, Ford Motor Company, University Research

Program, Dr. Thomas P. Gielda, Technical Monitor, Boeing Space Systems Division, Dan L.

Pavish, Technical Monitor, NASA Langley Research Center, Dr. W. Kyle Anderson, Technical

Monitor, and the National Science Foundation, ERC Program, Dr. George K. Lea, Program

Director. In addition, the author would like to acknowledge Reynaldo Gomez of NASA Johnson

Space Center for providing the Space Shuttle Orbiter geometry and Dr. W. Kyle Anderson of NASALangley Research Center for providing the Energy Efficient Transport geometry and experimental

data.

References

Baker, T. J., 1987, ThreeDimensional Mesh Generation by Triangulation of Arbitrary Point Sets,

AIAA Paper 871124.

Gaither, J. A., 1997. A Solid Modelling Topology Data Structure for General Grid Generation,

MS Thesis, Mississippi State University.

George, P. L., Hecht, F., and Saltel, E., 1990, Fully Automatic Mesh Generator for 3D Domains

of any Shape,Impact of Computing in Science and Engineering, 2, 187.

Holmes, D. G. and Snyder, D. D., 1988, The Generation of Unstructured Meshes Using Delaunay

Triangulation,Proceedings of the Second International Conference on Numerical Grid Generationin Computational Fluid Dynamics, Eds. Sengupta, S., Hauser, J., Eiseman, P. R., and Thompson,

J. F., Pineridge Press Ltd.

Lohner, R. and Parikh, P., 1988, ThreeDimensional Grid Generation by the AdvancingFront

Method,International Journal of Numerical Methods in Fluids, 8, 1135.


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Marcum, D. L. and Weatherill, N. P., 1995a, Unstructured Grid Generation Using Iterative Point

Insertion and Local Reconnection,AIAA Journal, 33, 1619.

Marcum, D. L., 1995b, Generation of Unstructured Grids for Viscous Flow Applications, AIAA

Paper 950212.

Marcum, D. L., 1996, Unstructured Grid Generation Components for Complete Systems, 5thInternational Conference on Grid Generation in Computational Fluid Simulations, Starkville, MS.

Mavriplis, D. J. and Pirzadeh, S., 1999, LargeScale Parallel Unstructured Mesh Computations for

3D HighLift Analysis, AIAA Paper 990537.

Mavriplis, D. J., 1993, An Advancing Front Delaunay Triangulation Algorithm Designed for

Robustness, AIAA Paper 930671.

Muller, J. D., Roe, P. L., and Deconinck, H., 1993, A Frontal Approach for Internal Node

Generation in Delaunay Triangulations,International Journal of Numerical Methods in Fluids, 17,

256.

Peraire, J., Peiro, J., Formaggia, L., Morgan, K., and Zienkiewicz, O. C., 1988, Finite ElementEuler Computations in ThreeDimensions, International Journal of Numerical Methods in

Engineering, 26, 2135.

Pirzadeh, S., 1996, ThreeDimensional Unstructured Viscous Grids by the AdvancingLayers

Method,AIAA Journal, 34, 43.

Rebay, S., 1993, Efficient Unstructured Mesh Generation by Means of Delaunay Triangulation and

BowyerWatson Algorithm, Journal of Computational Physics, 106, 125.

Sheng, C. Hyams, D., Sreenivas, K., Gaither, A., Marcum, D., Whitfield, D., and Anderson W.,

1999, ThreeDimensional Incompressible NavierStokes Flow Computations About Complete

Configurations Using a MultiBlock Unstructured Grid Approach, AIAA Paper 990778.

Shepard, M.S. and Georges, M. K., 1991, Automatic ThreeDimensional Mesh Generation by the

Finite Octree Technique,International Journal of Numerical Methods in Engineering, 32, 709.

Weatherill, N. P., 1985, A Method for Generation of Unstructured Grids Using Dirichlet

Tessellations, Princeton University,MAE Report No. 1715.


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Fig. 1 Surface patches, edges, and corner points for fighter geometry definition.

Fig. 2 NASA space shuttle orbiter surface grid.


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Fig. 3 Symmetry plane surface grid and tetrahedral field cut for NASA space shuttle orbiter

grid.

Fig. 4 NASA space shuttle orbiter and EET highlift wingbody surface grid quality.


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Fig. 5 NASA space shuttle orbiter and EET highlift wingbody volume grid quality.

Fig. 6 Computed density contours for NASA space shuttle orbiter.


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a) Top surface of wing.

b) Bottom surface of wing.

Fig. 7 EET highlift wingbody surface grid.


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a) Field cut with wing surface grid.

b) Field cut with wing removed.

Fig. 8 Tetrahedral field cuts for EET highlift wingbody grid.


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a) Top surface of wing.

b) Bottom surface of wing.

Fig. 9 Computed streamlines for EET highlift wingbody.


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Fig. 10 Tetrahedral field cut for highaspectratio element grid with multiple surface normals.


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a) Surface grid patch with distorted surface element.

b) Surface grid patch improved by applying a point spacing near problem edge.

c) Surface grid patch improved by applying a reduced point spacing near problem edge.

Fig. 11 Surface grid problem due to close edges.


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Fig. 12 Distorted tetrahedral elements between surface grids which are close and have large

differences in surface element size.


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a) Original surface definition patches, edges, and corner points.

b) Surface grid with multiple surface definition patches.

c) Surface grid with one topologically combined surface definition patch.

Fig. 13 Surface grid problem due to multiple surface definitions.


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a) Surface grid with multiple surface definition patches.

b) Surface grid with one topologically combined surface definition patch.

Fig. 14 Detail view of surface grid problem due to multiple surface definitions.


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a) Surface grid with detail feature resolved.

b) Surface grid at low resolution with feature unresolved.

Fig. 15 Use of combined surface definition patches to eliminate features at different resolutions.

Unstructured Grid Generation for Aerospace Applications (1999)

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