3D Navier3D Navier--Stokes Cutcell solver for Octree MeshesStokes Cutcell solver for Octree MeshesL. Bretonnet, Y. Li and C. HirschL. Bretonnet, Y. Li and C. Hirsch

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1Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

OutlineOutline

1. Mesh generation process

2. Flow solver

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3. Validation test cases

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2Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Octree Mesh GenerationOctree Mesh Generation

The initial Octree mesh is generatedi H TMusing Hexpress .

The mesh covers the entire domain.The refinement is based either on a cell

size objective or on the surface curvature

TM

size objective or on the surface curvature.

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3Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Cutcell computationCutcell computation

• Detect cells intersecting the surface and store list ofintersecting triangles

• Using a seed point and a painting algorithm, detect cellsthat are entirely in the solid/fluid part of the domain.

C t i t ti f C t i ll ith f t i l• Compute intersection of Cartesian cell with surface triangles using polygon clipping algorithm. (Sutherland, Hogdman,1974)

• Compute “fluid” faces of the cutcell.

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.com • Build cutcell by grouping connected polygons.

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agglomerated with one of their neighbor.• Link neighbor cutcell faces

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Link neighbor cutcell faces.

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Flow SolverFlow Solver

Spatial discretizationSolve compressible Navier-Stokes equationsCell-centered conservative finite-volume discretizationCell centered conservative finite volume discretizationInviscid fluxes discretized using JST or Roe schemeViscous fluxes purely centrally discretized

Time stepping and convergence accelerationExplicit 4-stage Runge-Kutta schemeLocal time-stepping

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pp gEfficient agglomeration multigrid, FMG (agglomeration)

Gradient computation

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pAt cell center using least-squareAt fluid face center as the average of neighboring cells gradientAt boundary face center using Green-Gauss.

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5Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Flow SolverFlow Solver

Cartesian solver optimizationCutcell faces are treated in an unstructured way using face-cell

connectivity, with optimization due to their x,y,z direction.connectivity, with optimization due to their x,y,z direction.Fluid cells are Cartesian. Finite difference formulas are used

whenever possible to accelerate the computation.Special treatment is needed for faces between cutcell and fluid p

cell to ensure conservation.

Pressure reconstruction

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The pressure at solid walls is reconstructed using the gradient in the cutcell center.

This is done to ensure correct pressure variation along the solid

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6Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Supersonic wedgeSupersonic wedge

15= oαInitial configuration :

318921

1000002

−

==

mkg

PaPM

ρ .1892.1= mkgρ

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2D wedge, Euler flow, Pressure field

Initial Cartesian mesh : 90x60

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7Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Supersonic wedgeSupersonic wedge

Pressure

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8Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Supersonic wedgeSupersonic wedge

Mach number

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9Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Subsonic cylinderSubsonic cylinderOUTLET

20=M

Initial configuration :

3. 1892.1

1000002.0

−=

==

mkg

PaPM

ρ

INLE

T

OU

TLET

OUTLET

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64 cells along the cylinder

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Subsonic cylinderSubsonic cylinder

Pressure coefficient along the surface

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Coarse mesh Fine mesh

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Coarse mesh64 cells along the cylinder 128 cells along the cylinder

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

NACA 0012 profileNACA 0012 profile

M=0.8, Roe scheme, Venkatakrishnan limiters

o3=α

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Coarse mesh Fine mesh

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12Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

NACA NACA 0012 0012 profileprofile

Mach number along the profile

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Coarse mesh Fine mesh

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Laminar flat plateLaminar flat plate

OUTLET

Initial configuration :

INLE

T

1000002.0

==

PaPM

Initial configuration :

8400Re. 1892.1

1000003

≈=

=−mkg

PaP

ρ

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MIRROR SOLID

Boundary layer resolution :

X=0 X=0.7

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Coarse mesh (3 level of refinement) : 5 pointsAverage mesh (4 level of refinement) : 10 points

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Average mesh (4 level of refinement) : 10 pointsFine mesh (5 level of refinement) : 15 points

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Laminar flat plateLaminar flat plate

Results for JST schemeResults for JST schemeFine mesh

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Laminar flat plateLaminar flat plate

Results for Roe schemeResults for Roe schemeAverage mesh

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Laminar flat plateLaminar flat plate

Skin frictionSkin friction

JST Roe

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17Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Laminar inclined plateLaminar inclined plate

OUTLET

LET

INL

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6 levels of refinement15829 cells

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Re = 728015 points inside the boundary layer

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Laminar inclined plateLaminar inclined plate

Results for JST schemeResults for JST scheme

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19Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Laminar inclined plateLaminar inclined plate

Results for Roe schemeResults for Roe scheme

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20Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009

Conclusion and perspectivesConclusion and perspectives

Conclusion A 3D Octree Cutcell mesh generator has been buildA 3D Octree Cutcell mesh generator has been buildA dedicated optimized solver has been implementedThe solver is validated for 2D Euler cases and the laminar flat plate

FutureNavier-Stokes validation on 2D cases

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Navier-Stokes validation on 2D casesValidation on 3D cases.Turbulence modelingImplicit residual smoothing

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PreconditioningLES

Example of 3D mesh : Pressure field for DLR F4

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Example of 3D mesh : Pressure field for DLR F4

Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009