c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

A01-16553AT A A

AIAA2001-0716A Parallel Multiblock Mesh Movement Schemefor Complex Aeroelastic ApplicationsM. A. PotsdamEloret Corp.Moffett Field, CAG. P. GuruswamyNASA Ames Research CenterMoffett Field, CA

39th AIAA Aerospace Sciences Meeting & Exhibit8-11 January 2001 /Reno, NV

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191

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AIAA-2001-0716

A PARALLEL MULTIBLOCK MESH MOVEMENT SCHEME FORCOMPLEX AEROELASTIC APPLICATIONS

Mark A. Potsdam*Eloret Corp.

Moffett Field, CA

Guru P. Guruswamy1

NASA Ames Research CenterMoffett Field, CA

ABSTRACT

A scheme has been developed for the movement of multiblock, structured grids due to surfacedeformation arising from aeroelastics, control surface movement, or design optimization. Elements of themethod include a blending of a surface spline approximation and nearest surface point movement forblock boundaries. Transfinite interpolation is employed for volume grid deformation. The scheme isdemonstrated on a range of simple and complex aeroelastic aircraft applications using Navier-Stokescomputational fluid dynamics and modal structural analyses on parallel processors. Results are robust andaccurate, requiring only minimal user input specification.

INTRODUCTION

Computational fluid dynamics (CFD) hasreached a state where complex geometries can beanalyzed in order to investigate complex flowfieldsand solve difficult engineering problems. CFD isalso being used more frequently withinmultidisciplinary applications for designoptimization, aeroelastics, control surface analysisand aeroservoelastics, and thermal analyses.While linear methods for these problems are wellunderstood and relatively inexpensive, theypresent limitations. Non-linear methods arerequired to model complex flows, including vortexinduced oscillations, transonic buffet, transonicflutter dip, and large control surface movements.One of the enabling technologies formultidisciplinary analyses using high fidelitymethods has been the advent of large scaleparallel computing platforms.

The combination of CFD with other disciplinesfrequently involves deforming geometries due todesign modifications, surface movement, orstructural loads. A scheme is required to deformthe volume mesh to accept the surfacemovement. For structured grid algorithms,particular difficulties are posed at the grid

interfaces in order to avoid repeated, expensivegrid recoupling.

Numerous grid movement schemes exist fordeforming block structured grids inmultidisciplinary applications. The problemrequires modifying a structured grid based onchanges to a subset of its boundary points. Thesimplest method is to completely regenerate thegrid based on the new surface [1,2], but this isonly feasible for the simplest block structuredgeometries or zones and can be time consuming.

The most common methods generateperturbations on existing grids. Algebraicshearing is the predominant method used forperturbing single block grids [3,4] and has founduse with overset grids as well [5,6]. In thismethod, surface point movement is projectedalong an index line emanating from the surface.The surface movement can be decayed to zero atthe outer or overset boundary. Rotationalmovement can be added to maintain orthogonalityat the surface. This scheme is simple toimplement and is quite fast. However, it cannot beeasily generalized to multiblock grids wherein theblock face opposite the surface is not an outerboundary. In this case, the abutting blocks willinfluence the face movement. Additionally, large

* Senior Research Scientist/Engineer, AIAA Senior Membert Senior Research Scientist, AIAA Associate FellowCopyright © 2001 American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the UnitedStates under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under thecopyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner.

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deflections can have adverse effects on gridquality.

Transfinite interpolation (TFI) is a more generalthree-dimensional method that is widely used[7,8,9,10] for cases involving multiple deformingboundary faces. TFI combines the speed andefficiency of an algebraic method with the ability tohandle fully 3D perturbations. Modifications canbe made to add robustness. Drawbacks relating tosubfaces are examined in this paper with the aimof eliminating them to create a more generalscheme.

More complex grid movement schemesinvolve a spring analogy [11,12,13]. Elasticitybased schemes which include both linear andtorsional springs have been shown to producegood quality meshes. However, they tend to becomputationally and memory intensive and havefound wider use on unstructured meshes wherestructured 3D interpolation methods are not asapplicable.

All of these schemes make use of gridconnectivity information. For multiblock gridinterfaces, this can be problematic since points arenot required to match at the interface. Even if apoint happens to match on the boundary, theconnectivity to other points can be different. Thismay result in different movements for points at thesame location in space. Point-by-point schemes[14,15,16] remove this problem by individuallymoving grid points based on their position inspace and their relation to the deforming surface.A drawback to this approach is that the lack of gridconnectivity information can produce grids that arenot smooth. Hartwich [14] presents a successfulpoint-by-point scheme that is assisted byoperating on grid interface subgrids. Takingadvantage of the fact that the grids in use aretypically multigridable, small subgrids (5x5), withinwhich TFI is still performed, maintain a smallamount of interconnectivity necessary forsmoothness. Chen [16] uses a 3D boundaryelement method solver to both interface the fluidand structures surface grids and deform the fluidsvolume grid, assuring that the surface and volumegrid distributions will be smooth and continuouswith each other. A two zone approach is used tomaintain grid quality near the surface. It remains toextend this methodology to general multiblockgrids.

Objectives

The objective of this work is to develop ageneralized multiblock moving grid scheme thatremoves some of the limitations present in currentstate-of-the-art methods.

The scheme used to deform the CFD gridsmust meet several requirements:

1) Robustness. The scheme must be robustenough to handle arbitrarily complexmultiblock grids, including the Navier-Stokes clustering and singularities (i.e.axes, C-cuts) frequently found in CFDgrids.

2) Accuracy. The grid deformation schememust produce grids of acceptable qualityto the flow solver. While positiveJacobians (volumes) are a minimumrequirement, maintaining smoothness,orthogonality, and the overall quality ofthe original grid is required. Additionally,at the grid interfaces, point matched gridsclearly must remain point matched. Adesirable characteristic for abutted grids isnot having to recalculate interpolationcoefficients, necessitating that points in aregion move in unison.

3) Ease of Use. Ideally the grid deformationscheme should be invisible to the user orrequire only minimal inputs. The usershould not be burdened with describingany particular motion of the gridboundaries or corner points.

4) Efficiency. In a tightly coupled analysis,both the fluids and structures modelsadvance every iteration. For dynamic,time accurate analyses, tight coupling isnecessary. Therefore, the griddeformation scheme must be efficientsince it may be required at every timestep.

5) Parallelizable. The scheme must integratewith parallel computational codes and notresult in excess communication costs orprocessor idle time.

The grid movement scheme developed herebuilds on and improves upon the grid movementimplementation in ENSAERO [7] and the schemeby Hartwich [14]. Byun [7] uses transfiniteinterpolation (TFI) exclusively to move grid blockcorners, edges, faces, and interior points in order.While this scheme offers the advantages of speed

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and efficiency, it also contains two majordrawbacks:

1) Subfaces. TFI is a global methodologywhich interpolates multidirectionally basedonly on block boundary values. By itselfTFI does not correctly handle subfacegrids, where two or more grids abutagainst one. This is due to the fact that, ingeneral, for two adjoining grid faces A andB which abut against a single face C=A+B

TFl(face( A)) + TFI(/a ce(B)) *TFI(/ao?(A + B)) (1)

because the adjoining AB boundaryvalues are ignored in the A+B solution. Asimple example of a 2D point matchedinterface where TFI breaks down withoutspecial treatment is shown in Figure 1,where the outer grid interfaces with 3inner grids. The separation of the gridboundary faces after TFI is shown andresults in the loss of point match.

2) Input Specification. User input to thescheme includes all grid block cornerpoints and their motion relative tostructural nodes. Additional input isnecessary to handle specialized gridtopologies. The extensive input can betime consuming and error prone.Requiring the user to specify the motionof the block boundaries relative to thestructures can produce unexpectedresults.

In order to remove the subface limitation of theTFI scheme, coding logic could be written todetermine subface connectivity in the pointmatched case and perform separate TFIs on thesubsections. This has the advantage of beingrelatively inexpensive. The drawbacks includecomplicated coding and required access tointerface blocking data. It is also not clear howgeneral patched or chimera grid interfaces couldbe handled. For example, the patched grid shownin Figure 2, where a single grid abuts againstnumerous others in a complex manner, might betoo difficult to handle correctly.

An alternate solution chosen in this work is todevelop a point-by-point methodology that doesnot require grid connectivity information on theboundary faces. By basing face point movementon 1) distance to the nearest structural surfaceand 2) a surface spline approximation to the

structural surface movement, the need for TFI onboundary faces or any connectivity information isremoved.

METHODS

The application focus in this work is onaeroelastic analysis, the multidisciplinary couplingof aerodynamic and structural modeling usingcomputational fluid dynamics (CFD) andcomputational structural dynamics (CSD). Due tothe complex nature of many aeroelastic problems,extensive computational resources may berequired. Throughout this work parallelprocessing strategies and parallel computers havebeen used to obtain efficient solutions.

CFD

The CFD code used in this work is ENSAERO(HiMAP) [17]. ENSAERO is a finite differenceNavier-Stokes solver employing either an ARC3Dcentral difference scheme or Goorjian-Obayashiupwinding. Recent improvements to the codeinclude a multiblock scheme using abutting oroverlapping grids, point matched or non-pointmatched at the interfaces. Both Baldwin-Lomaxand Spalart-Allmaras turbulence models areavailable. The code has been parallelized to runon parallel supercomputers such as the SGI Origin2000 or IBM SP2. Coarse grain parallelization isimplemented such that each processor performscalculations on one or more grid blocks. Blocksare distributed automatically by the load balancingalgorithm based solely on the number of points.Zonal interface data is communicated using MPImessage passing. The code has been optimizedfor the cache memory architectures typically foundon these machines, however, suitableperformance on Cray vector machines ismaintained.

CSD

A modal structural model [18] is coupled withthe ENSAERO flow solver. The modal structuralapproximation is similar to a Rayleigh-Ritz methodand uses a linear combination of mode shapes toapproximate structural response to a load. Modeshapes may be determined using experimentaldata or a finite element model. One and threedegree of freedom (DOF) per node models aresupported using unstructured triangular meshesto model the structural geometry.

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Fluid-Structure Interface

A fluid-structure interface is required totransfer surface loads from the CFD solution to thestructural model and to transfer surfacedeflections from the CSD solution to the CFDmodel. In general, the CFD surface grid andstructures mesh will not be similar, with eachdiscipline focusing on different critical areas. Alumped load point-to-cell projection method is•jsed in ENSAERO to link CFD grid points tomodal nodes [19].

The CFD and structures codes are not fullyintegrated, but remain as separate executables.This allows easier integration of alternate analysismethods such as unstructured CFD or full finiteelement analysis. The modules are runconcurrently under the MPIRUN multiple processmanager and communicate using MPI messagepassing.

The structures module only deforms the CFDgrid surfaces corresponding to the structuralsurface. The remaining piece to complete thefluid-structure interfacing is the deformation of theparts of the block faces not included in thestructural surface (flow through interfaces, wakes,planes of symmetry, axes) and the interior volumepoints.

CFD Grid Block Face Deformation

A moving grid scheme has been developedthat does not use TFI for block boundary faces.This means that the movement of a face pointdoes not depend on the movement ofneighboring points, a condition necessary toremove dependency on grid topology (subfaces).This condition is satisfied if the face pointmovement is based on location in space (x,y,z)and distance to the deforming surface [14]. Thescheme combines several elements to computeface point movement.

1) Nearest Surface Point. Points near adeforming surface follow the movement ofthe nearest surface point.

2) Surface Spline. Away from the deformingsurface, points move smoothly based on asurface spline approximation of thedeforming surface movement.

3) Blending Function. A blending functionsmoothly overlaps the (1) near- and (2) far-surface movement regions.

4) Decay Function. A decay function is usedto decrease point movement away fromthe body.

Nearest Surface Point

The most logical means of computing themovement of a block face point is to base it on themovement of the nearest structural surface point.This creates a shearing movement for pointsassociated with a surface point. It is a relativelygood strategy for treating tightly clustered Navier-Stokes grids and for avoiding local grid linecrossing in the near-body region. While notincluded here, modifications can be made tomaintain grid orthogonality at the surface byaccounting for surface point rotation in addition totranslation [5].

The nearest point strategy, however, may notresult in a smooth deformation of the grid. Pointsadjacent to each other may slave off differentsurface points with different deformations,resulting in a jagged appearance of the grid. Toimprove smoothness, the nearest surface pointshould be an interpolated point on the structuredsurface as determined by the shortestperpendicular distance, not necessarily a gridpoint.

A further difficulty arises when neighboringgrid points do not reference surface points inclose proximity to each other. An example of asupercritical airfoil is shown in Figure 3. The airfoilhas been rotated about the leading edge, andfield points follow the movement of only thenearest interpolated surface point. Two pointsnear the center of a circular arc approximating thelower surface cove are highlighted. They slave offsurface points which are not in close proximity,and mesh discontinuity results. Similar topologiesoccur in internal ducts. In such regions analternate, smoothly varying grid movementscheme is required.

Surface Spline

A surface spline [20] is a mathematicalequation for interpolating a multivariate function. Itcontains structural behavior by basing itsderivation on the small deflection equation of aninfinite plate. Modifications for scaling, symmetry,and smoothing are employed. Using a set ofarbitrarily placed points with defineddisplacements, functions are devised to compute

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displacements (Ax,Ay,Az) everywhere as afunction of location in space (x,y,z). for example,

(2)

This meets the same conditions as the nearestsurface point strategy, except that the function issmooth and differentiable. Its accuracy, however,is dependent on the number of points used togenerate the function.

Surface spline generation requires thesolution of a system of linear equations, and itsevaluation contains natural logarithms. Currently,subsets of the fluid-structure interface points arespecified to be used in the spline. The number ofinput points should be limited from the completefluids and/or structures point sets to keep the costof the surface spline evaluation reasonable. Whileprevious works have frequently employed thesurface spline as a method for fluid-structureinterfacing [21], it is used here in a novel mannerto compute the movement of the off-body blockboundary face points.

The lumped load point-to-cell methodology isretained for transferring deflections from thestructural mesh to the CFD surface grid. Becausethe spline may lack the fidelity and accuracy of theactual surface movement, it cannot be usedconfidently in the Navier-Stokes clustered regionsnear the surface. Here it is replaced by thenearest surface point movement strategy. Thesurface spline is employed where the nearestpoint movement scheme may fail due to having"closest" points not in close proximity or in areaswhere high fidelity is not a concern.

Blending Function

A blending function is required to smoothlytransition between the nearest (interpolated)surface point movement and the surface splineapproximation methods. Because the nearestpoint movement fails when the field of view of apoint becomes too large, a reasonable flag forblending can be based on a ratio between thedistance to the nearest surface grid point and thedistance to the next nearest distinct surface gridpoint. Near the surface the inverse of this ratio, d,approaches infinity as the nearest distanceapproaches zero and/or the next nearest is largein comparison. In the field away from the surfacesd will be order 1. The blending weight factor,determined by experimentation, is defined as

j _ n ext_n ea rest_po in t

nearest_point

m = 0.5 - 2.0

(3)

This function is still under development.Near the surface the weighting function is

one, decaying to zero in the field. It is applied to acorrection term for the surface point movement,Azcorr, which is the difference between the actualinterpolated surface point movement, Az5,rMf,, ascalculated by the structural model and theinterpolated surface point movement as predictedby the surface spline, tespline,

(4)

The tilde signifies values computed at the nearestinterpolated surface point.

Decay Function

To keep the movement of the grid away fromthe body to a minimum, changes are decayedusing an overall weighting function,

(5)— _ nearest_pomt

d,ref

The decay function is based on distance to thenearest surface and, with (3 = 1/4, decays toessentially zero at dnearestj)oint = 4dref However,there is no requirement for using the decayfunction as there are no difficulties associated withmovement of the outer boundaries which can beincluded in the surface spline definition.

Grid Block Face Point Displacement

The final displacement of the grid boundaryface point can be calculated as,

, y, z) = wtd • [ &zspline (x, y, z) + wtcorr &zcorr ] (6)

Similar equations can be written for Ax and Aywhen using a 3D structural model.

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CFD Volume Grid Deformation

The structural model and the grid movementscheme outlined above define the movement ofthe six block faces. Although the scheme wouldbe well suited for deformation of interior gridpoints, in particular chimera grid boundaries, fringepoints, and holes, it is more costly in comparisonwith algebraic methods. Transfinite interpolation[22] is used to compute the interior volumedeformation due to its low cost and efficiency.The mesh movement increment (Ax,Ay,Az) isinterpolated, not the actual point locations (x,y,z).For poor initial quality grids, modification to the TFIblending functions may be required. Typical TFIschemes use blending functions that are linear inarc length, S. Exponential blending functions [23]in the non-viscous directions work well for regionsof poor grid quality,

(7)

where K = 0 reverts to the linear case, andK = 2.5 is used for increased robustness of theTFI scheme.

Implementation

The face movement scheme is applied to allpoints on the block faces not prescribed bystructural motion. Additionally, it is applied tointerior points that are donors for overlappedinterfaces. Because of the inherent properties ofthe scheme, point matched points are guaranteedto have the same movement regardless of theirconnectivity in their respective block topologies.Non-point matched regions will move together in asmooth manner. Plane of symmetry points can beflagged in order to zero out their movement in thesymmetry direction. Although the spline andstructural models maintain symmetry, the nearestsurface point to a symmetry plane point may not lieon the plane of symmetry and may result inmovement in the symmetry direction.

The nearest and next nearest point distancescan be calculated in a preprocessing step. Theuse of an efficient alternating digital tree (ADT)[24] significantly speeds this process. A furtherenhancement to the ADT is to begin with areasonable starting guess and only back up in thetree as far as necessary, rather than starting at theroot for each point. This modification works

especially well for face points that are tightlyclustered and for next nearest neighbor searches.Once a nearest surface point is found, searchingthe surrounding quadrilaterals determines thenearest interpolated surface point and itsinterpolation coefficients.

In a parallel environment, each processorperforms the deformation of its own blockboundaries and volumes. The only global dataneeded is the movement of the completestructural surface. The structures modulebroadcasts this to all fluids modules using MPI andMPIRUN. With this data available, each fluidsmodule is able to independently generate thesurface spline and deform the boundaries of itsblocks. No grid interface information need becommunicated between blocks.

User input to the scheme is fairly simple. Themain input is the CFD surface definition specifyingthe structural surface, data required for any fluid-structure interaction problem. Surface patchescan be specified as structurally deforming, fixed,or undergoing rigid body motion. Additionally, theuser is required to specify a subset of eachsurface patch for use in defining the surfacespline. The input consists of the numbers Ns andN| for each patch where NjXNj equal arc lengthspaced points on the four boundary edges areautomatically generated. For edges that undergosignificant deformation in the edge direction,higher resolution by the spline is required, andmore points in that direction are used in thesubset. For example, a wing patch may requireseveral spline points in the spanwise direction butonly a few in the chordwise direction, whichundergoes smaller deflections. Surface splinesubset points for a wing/fuselage geometry areshown in Figure 4. Also shown are the structuralsurface patch boundaries which coincide with gridblock boundaries. Points on the fuselage arefixed. It may not be necessary to subset both theupper and lower wing surfaces, and some surfacepatches need not contribute to the spline. Aquick check of surface deflection when sampledeformations are applied can assist in determiningappropriate surface spline points. The number ofsurface spline points used results in a trade-offbetween cost and grid quality.

RESULTS

The current mesh movement scheme wasimplemented in ENSAERO. Several applicationsare shown to illustrate the flexibility of the method

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on a range of multiblock configurations, from a2Dairfoil to a full aircraft configuration. All CFD Navier-Stokes grids are clustered for a y+ of order one atthe viscous surface. Convergence of steady stateresults was determined by force/moment outputand wing pressures. CFD solutions use theupwind option.

Two-Dimensional Airfoil

A single block two-dimensional airfoil test caseis shown in Figure 5 in its original and deformedposition. The C-mesh airfoil grid with open trailingedge and wake has been translated and rotatedfrom an initial zero degrees angle of attackposition. Original grid quality and smoothness aremaintained throughout a large range of motion.No deficiencies are seen where the grid motiontransitions between nearest surface pointmovement and the surface spline approximationmethods.

Arrow Wing-Body

Aeroelastic results for a low aspect ratioBoeing arrow wing-body (BAWB) configurationwere calculated at transonic conditions(M = 0.85, a = 7.93°) using the Baldwin-Lomaxturbulence model with Degani-Schiff cut-off.Figure 6 shows a comparison of rigid andaeroelastic wing pressures with experimental data.It should be noted that the 1 DOF mode shapesare artificial. In actuality, the model is quite stiff, asindicated by the good agreement between thetest data and the rigid solution. The CFD solutionscapture the leading edge vortex equally well,indicating sufficient quality in the deformed gridhas been maintained with no added discrepanciesat the grid block interfaces. The grid contains 1.2million points (2x 155 streamwise x 67 spanwise x59 normal). The spline points shown in Figure 6are chosen to adequately model expectedaeroelastic motion, with clustering in regions ofhigher deflection towards the wing tip. In Figure 7wing pressures and wing tip trailing edgedeflections using the current grid movementscheme are compared with aeroelastic resultscalculated using the full TFI scheme [7]. Resultsare on a coarse grid (2x 110x58x40) but are ingood agreement with each other.

The BAWB grids are H-H topology, abuttedahead of and behind the leading and trailingedges in the normal (boundary layer) direction.Splits in both the streamwise and spanwise

direction result in 8 blocks. The original anddeformed faces of a streamwise block interfaceplane in the midchord region are shown inFigure 8 for the coarse grid. Both the interfaceand a wing tip close-up are seen to have deformedsmoothly. The coarse grid also serves to illustratethe robustness of the modified TFI scheme withthe exponential blending functions. Regions inthe grid with poor grid quality are deformedwithout further degradation (Figure 8 inset right).For the full TFI scheme, it was previouslynecessary to move the Navier-Stokes near-bodyregion by shearing. Coding logic was required toidentify and extract the viscous region which isnow handled seamlessly with one methodology.

The coarse grid solution was run on 9processors of an SGI Origin 2000 - one block perprocessor and one processor for the structuresmodule. A breakdown of the time spentdeforming the grids as a percentage of the totaltime per iteration on each fluids processor isshown in Table 1 in the BAWB column. The griddeformation scheme requires 26% of the totaltime per iteration. The spline uses 87 points, andits evaluation cost labeled 'Deform boundaries' isseen to be the largest. Spline generation time isminimal, and the algebraic TFI volume deformationis quite efficient.

DAST ARW-2 Wing/Fuselage

A high aspect ratio high wing AeroelasticResearch Wing (ARW-2) was tested extensively inthe NASA LaRC Transonic Dynamics Tunnelunder the Drones for Aerodynamic and StructuralTesting (DAST) Program [25]. The model wasbuilt to replicate full-scale wing structure and isrealistically flexible. Rigid and aeroelasticENSAERO Navier-Stokes calculations using theSpalart-Allmaras turbulence model wereperformed at transonic buffet conditions (M = 0.8,a = 3.0°) with air as the test gas. Wing pressurecomparisons in Figure 9 show rigid (jig), modal andbeam structural models, and experimental data.Good agreement is seen between the two griddeformation/aeroelastic schemes. The modalstructural model uses the current grid movementscheme on a 1.7 million point multizone grid. Thefirst five mode shapes (1 DOF) are included. Asingle block wing/fuselage C-O grid (289streamwise x 86 spanwise x 67 normal) was splitresulting in 10 blocks. The beam modelcalculations were performed on a single zone C-Hgrid (289 streamwise x 76 spanwise x 70 normal)

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using the wing version of ENSAERO. Eachspanwise constant Y grid plane independentlyundergoes rigid body translation and rotation inorder to model the aeroelastic motion. The beamresults do not include a fuselage, which has beendetermined to have minimal effect on the outerportion of the wing.

Aeroelastic wing pressure comparisons withexperimental data are reasonable given thesignificant amount of separation present at thiscondition. Calculated wing tip deflection at therear spar is 4.83 inches up compared with theexperimental deflection of 5.18 inches. Themodel wing semispan is 113.92 inches.

Results used 11 processors of an SGI Origin2000. A timing breakdown as a percentage of aflow solver step is shown in Table 1. The splineuses 109 points (Figure 4). The performance ofthe ARW computations are consistent with BAWBfigures.

Table 1. Timing Breakdown for Grid Deformation

Operation

GeneratesplineDeformboundariesDeformvolumeTotal griddeformation

Time (% of flow solver step)BAWB(N-S)1.7

19.0

5.7

26.4

ARW(N-S)0.6

17.6

6.3

24.5

L1011(Eulerl

2.4

25.9

6.2

34.5

Lockheed L-1011

A final test case is a full configurationLockheed L-1011-500 transport aircraft [26]. Theconfiguration represents a .02 scale wind tunnelmodel which was used extensively for fluttertesting. The model includes the wing, fuselage,underwing nacelle, pylon and core cowl, verticaland horizontal tails, and sting. The aft engine isnot present. Inviscid rigid and forced motionaeroelastic analyses were performed at Mach 0.88and a = 0.0°. The grid system contains 36blocks and 9 million points. Although the surfacenormal spacings are appropriate for inviscidanalyses, the grids were generated with theeventual aim of Navier-Stokes flutter calculations.For viscous analysis the points would be

reclustered towards the surfaces, but the numberof points would not increase. All block interfacesare point matched. Of particular note, the gridsystem is quite complicated, containing numerousdegeneracies and blocks with multiple solidsurface faces. The complex multiblock gridstructure in the nacelle/pylon region is shown inFigure 10. Five structural modes are used: 1) firstwing bending, 2) nacelle/pylon vertical, 3)nacelle/pylon lateral, 4) second wing bending, and5) first wing torsion. They include significantinteraction between the wing and thenacelle/pylon. The fuselage, sting, andempennage are rigid. The first 4 mode shapes (3DOF) imposed on the unstructured modal meshare shown in Figure 11.

Forced motion calculations using modeshapes 1 and 3 are shown in Figure 12. Testdeflections were also performed with all modesactive. This confirms the ability of the scheme toperturb the volume grids based on complexsurface movement of an arbitrary multiblockconfiguration. No negative Jacobians areproduced, and point matched block interfaces aremaintained.

For the L-1011 the CFD flow solver runs mostefficiently on 28 processors of an SGI Origin 2000.Timing breakdowns for the grid motion are shownin Table 1. The spline uses 214 points (Figure10). Due to the complexity of the grids, it wasnecessary to use additional spline points in thewing/pylon junction region so that the spline moreaccurately modeled the motion. The increasedpercentage cost of the grid deformation scheme isdue to the inviscid analysis. Including viscousterms would increase the cost per step andreduce the percentage costs of grid deformationto be more in line with the other viscous testcases. Additionally, since the boundarydeformation scheme scales with the number ofboundary points and the flow solver scales withthe number of volume points, improved efficiencyon larger numbers of processors could have beengained by considering both quantities in the loadbalancing.

CONCLUSIONS

A grid movement scheme has beendeveloped for general multiblock configurations.It includes improvements over previous schemesthat have limitations on grid block interfacetopology and robustness in Navier-Stokesclustered regions. The current method handles

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point matched and non-point matched,overlapped and abutted interfaces. This isaccomplished by basing block face pointmovement only on location of the point in spaceusing a combination of nearest surface point andsurface spline approximation. Volume gridmovement is performed efficiently usingtransfinite interpolation. The scheme is appliedeffectively to a range of complex, multiblockaeroelastic configurations. A computationalpenalty is paid for generality and ease of use butcan be reduced by judicious inputs.

ACKNOWLEDGMENTS

The work of the first author was completedunder NASA Ames Fluid Dynamics Analysiscontract NAS2-14109. Calculations wereperformed using the resources of the HighPerformance Computing and CommunicationProgram (HPCCP) and Numerical AerodynamicSimulation (NAS) facility at the NASA AmesResearch Center. Continued support from CathySchulbach, program manager of the HPCCPComputational Aerosciences (GAS) Program, isgratefully acknowledged.

REFERENCES1. Farhangnia, M. Guruswamy, G. P., and

Biringen, S., 'Transonic Buffet AssociatedAeroelasticity of a Supercritical Wing," AIAAPaper 96-0286, January 1996.

2. Slater, J. W., "A Moving Grid Capability forNPARC," AIAA Paper 98-0955, January1998.

3. Steger, J. L. and Bailey, E., "Calculation ofTransonic Aileron Buzz," AIAA Journal, Vol.18, No. 3, 1980, pp. 249-255.

4. Campbell, R. L. and Smith, L. A., "A HybridAlgorithm for Transonic Airfoil and WingDesign," AIAA Paper 87-2552, August1987.

5. Morton, S. A., Melville, R. B., and Visbal, M.R., "Accuracy and Coupling Issues ofAeroelastic Navier-Stokes Solutions onDeforming Meshes," Journal of Aircraft, Vol.25, No. 5, September-October 1999, pp.798 -805.

6. Gee, K. and Rizk, Y. M. "OVERAERO-MPI:Parallel Overset Aeroelasticity Code,"HPCCP/CAS Workshop 1998, August 24-26 1998, NASA CP-1999-208757, January1999.

7. Byun, C., and Guruswamy, G. P., "A Parallel,Multi-block, Moving Grid Method forAeroelastic Applications on Full Aircraft,"AIAA Paper 98-4782, September 1998.

8. Reuther, J., Jameson, A., Farmer, J.,Martinelli, L., and Saunders, D.,"Aerodynamics Shape Optimization ofComplex Aircraft Configurations via anAdjoint Formulation," AIAA Paper 96-0094,January 1996.

9. Wang, Z. J. and Przekwas, A. J. "UnsteadyFlow Computation Using Moving Grid withMesh Enrichment," AIAA Paper 94-0285,January 1994.

10. Jones, W. T. and Samareh-Abolhassani, J.,"A Grid Generation System for Multi-Disciplinary Design Optimization," AIAAPaper 95-1689, June 1995.

11. Batina, J. T., "Unsteady Euler Algorithm withUnstructured Dynamic Mesh for Complex-Aircraft Aeroelastic Analysis," AIAA Paper89-1189.

12. Bartels, R. E., "An Elasticity-based MeshScheme Applied to the Computation ofUnsteady Three-Dimensional Spoiler andAeroelastic Problems," AIAA Paper 99-3301, June 1999.

13. Farhat, C., Degand, B., Koobus, B., andLesoinne, M., "An Improved Method ofSpring Analogy for Dynamic UnstructuredFluid Meshes," AIAA 98-2070, April 1998.

14. Hartwich, P. M., and Agrawal, S., "Methodsfor Perturbing Multiblock Patched Grids inAeroelastic and Design OptimizationApplications," AIAA Paper 97-2038, June1997.

15. Anderson, W. K. and Venkatakrishnan, V.,"Aerodynamic Optimization on UnstructuredGrids with a Continuous Adjoint

9

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Formulation," AIAA Paper 97-0643, January1997.

16. Chen, P. C. and Hill, L. R., "A Three-Dimensional Boundary Element Method for 22.CFD/CSD Grid Interfacing," AIAA Paper 99-1213, April 1999.

17. Guruswamy, G. P., Byun, C., Farhangnia,M., and Potsdam, M. A., "User's Manual forHiMAP: A Portable Super Modular 3-Level 23.Parallel Multidisciplinary Analysis Process,"NASA TM-1999-209578, September 1999.

18. Guruswamy, G. P., "Unsteady Aerodynamicand Aeroelastic Calculations for WingsUsing Euler Equations," AIAA Journal, Vol. 24.28, No. 9, March 1990, pp. 461-469.

19. Guruswamy, G. P. and Byun, C., "Fluid-Structural Interactions Using Navier-StokesFlow Equations Coupled with Shell Finite 25.Element Structures," AIAA Paper 93-3087,July 1993.

20. Harder, H. L., and Desmarais, R. N.,"Interpolation Using Surface Splines,"Journal of Aircraft, Vol. 9, No. 2, February 26.1972, pp. 189-191.

21. Smith, M. J., Hodges, D. H., and Cesnik, C.E. S., "An Evaluation of Computational

Algorithms to Interface Between CFD andCSD Methodologies," Report WL-TR-96-3055, Nov. 1995.

Thompson, J. F., Warzi, Z. U. A., and Mastin,C. W., Numerical Grid Generation,Foundations and Applications, ElsevierScience Publishing Company, New York,NY, 1985.

Eriksson, L.-E., "Practical Three-Dimen-sional Mesh Generation Using TransfiniteInterpolation/' SIAM Journal of Sci. Stat.Comput, Vol. 6, No. 3, July 1985, pp. 712-741.

Aftosmis, M., "Lecture Notes on 'SolutionAdaptive Cartesian Grid Methods,'" VonKarman Institute for Fluid Dynamics, LectureSeries 1997-02, March 1997.

Seidel, D. A, Eckstrom, C. V., and Sandford,M. C., "Transonic Region of High DynamicResponse Encountered on an ElasticSupercritical Wing," Journal of Aircraft, Vol.26, No. 9, September 1989, pp. 870-875.

Goodwin, S.A., Byun, C., and Farhangnia,M., "Aeroelastic Computations Using AParallel Computing System," AIAA Paper99-0795, January 1999.

separation atgrid block interface

after TFI

Figure 1 TFI Grid Interface Separation with Subfaces

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Figure 2 Abutted Non-Point Matched Subfaces in Complex Multiblock Configurations

Figure 3 Errors in Grid Deformation Based on Nearest Surface Point Movement

spline points

Figure 4 Point Subset for Surface Spline

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f

Figure 5 Deformation of 2D Airfoil C-mesh

Figure 6 Arrow Wing-Body Navier-Stokes Aeroelastic Solution,M = 0.85, a = 7.93°, Re = 9.4 million, Baldwin-Lomax, Fine Grid

x/c x/c x/c ITERATION

Figure 7 Arrow Wing-Body Comparison of Grid Deformation Schemes,Wing Pressures and Wing Tip Trailing Edge Deflection, Coarse Grid

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wing tip poor grid quality

Original Deformed

Figure 8 Arrow-Wing Body Grid Block Face Movement,Wing Tip Close-up and Poor Grid Quality

o

- current (mooai)- aigebmie (beam)

Figure 9 DAST ARW Navier-Stokes Aeroelastic Solution,M = 0.80, a = 2.98°, Re = 1.3 million, q = .72 psi, Spalart-Allmaras

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Figure 10 Lockheed L-1011 Nacelle/Pylon Multiblock Grid System

wing modes 1 & 4

nacelle/pylon modes 2 & 3

Figure 11 Lockheed L-1011 Structural Mode Shapes

rigidgeometry

Figure 12 Lockheed L-1011 Forced Modal Motion Inviscid Aeroelastic Solution,M = 0.88, a = 0.0°

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