HOPR - High Order Preprocessor

HOPR - High Order Preprocessor

Florian Hindenlang1,

Thomas Bolemann2, Malte Hoffmann2, Claus-Dieter Munz2

1Max-Planck Institute for Plasma Physics, Garching2Institute for Aero- and Gasdynamics, University of Stuttgart

High-Order Computational Fluid Dynamics Technologies WebinarSeptember 21, 2015

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Curved Meshes: HOPR

I DG is high order accurate on unstructured grids

I Curved elements to maintain accuracy at curved wall boundaries

I DG for industrial applications:I Wall-bounded flowsI 3D curved geometries, intersecting surfaces, sharp cornersI Unstructured and coarse grids

⇒ HOPR (High Order Preprocessor)released Open-Source: www.hopr-project.org

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Facts on HOPR

I Open-source under GPL v2: www.hopr-project.org

I Mesh preprocessor for parallel high order simulations(DG, FR, SEM, pFEM...)

I Written in FORTRAN

I Generate simple meshes for testing, directly in HOPR

I HOPR Input:I Unstructured hybrid meshes from any grid generatorI Several formats supported (CGNS mostly used)

⇒ Different strategies to produce high order meshes from the initiallinear mesh

I HOPR Output: HDF5 mesh file

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HOPR output: HDF5 mesh file

I Idea: Direct parallel readinI HOPR sorts elements along a Space-Filling Curve

⇒ 1D element list, can be split into arbitrary number of domainsI Element-per-element datablocks:

high order node coordinates, side info (BC, connectivity)

⇒ Split global arrays into non-overlapping blocks during parallel readin!

HDF5 mesh file

globalattributes

BCNames

BCTypes

ElemInfo SideInfoNodeCoordselem1elem2elem3

elem4elem5elem6

globalattributes

BCNames

BCTypes

globalattributes

BCNames

BCTypes

globalattributes

BCNames

BCTypes

computenLocElemsoffsetElem



elem1elem2elem3

elem4elem5elem6

elem7elem8

elem7elem8

offset/sizeSidesNodes

offset/SizeSidesNodes

offset/SizeSidesNodes

buildelement

connectivity

buildelement

connectivity

buildelement

connectivity

rank

#0

rank

#1

rank

#2

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HOPR Mesh Curving Flowchart

commercial mesher: ICEM, ANSA,... (cgns unstruct. format) linear unstructured hybrid mesh

curved boundary faces

Normal vector(s) at surface nodes

point-normalsICEM

spectral elementssurface

subdivision

ICEM Cheb.-Lobattonodes on edges

curved boundary edges

blend curved edges to face

blend curved edgesto inner faces

blend curved facesto volumes

subdividedsurface mesh

curved high order mesh

block-structured mesh(cgns struct. format)

Agglomerationof subblocks to

curved hexahedra

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point-normalsICEM


subdivision










curved hexahedra

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Curved edges from normal vectors

Get normal vectors at linear surface mesh points:

1. In HOPR without additional data:a) Reconstruction via linear surface meshb) Analytic functions (sphere ,cylinder ...)

2. Additional point-normal file(from CAD,...)

⇒ Generate curved edges

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Curved edges from normal vectors

Get normal vectors at linear surface mesh points:

1. In HOPR without additional data:a) Reconstruction via linear surface meshb) Analytic functions (sphere ,cylinder ...)

2. Additional point-normal file(from CAD,...)

⇒ Generate curved edges

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Multiple normal vectors to recover sharp edges & corners

p1

p2

n1

t 1

e p1

p2

n1

t 1

en2

(a) (b)

(a) 1 normal vector, tangential vector by projection

(b) 2 normal vectors, tangential vector by cross product

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Blending curved edges to curved faces

=12 { X

a X

b X

c− X

t }

= X a X b − X t

Superposition of linear blended pairs of curved edges (Coons patches)

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point-normalsICEM


subdivision










curved hexahedra

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High Order Surface by Subdivision

linear surface mesh

I Mesh generator: subdivision of the initial mesh while keeping newpoints on the CAD surfaces

⇒ Polynomial surface patches by interpolation

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after one subdivision



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after two subdivisions



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Blending curved faces to curved volume

1. Curved face on boundary

2. Blend adjacent faces with linear edges

3. Blending of all element faces → volume mapping

4. Generalized for all element types (tets,pyramids,prisms,hexas)

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Example: DLR-F6 Wing-Body-Nacelle Configuration

I Test case of an idealized passenger jetliner

I CAD geometry provided as STEP file

I Element layer on geometry ∼ 3600 hexa∼ 400 prism

I Volume grid : ∼ 225000 tetrahedra∼ 2900 pyramids

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⇒ Visualization of polynomial patches shows smooth boundary surfaceelements

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point-normalsICEM


subdivision










curved hexahedra

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Hexa-meshes: Agglomeration

I Start from fine block-structured meshes

⇒ Coarsen by a fixed factor

⇒ Use inner points to generate high order element mapping

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Agglomeration Example: Serrated nozzle I

I Test case provided by Andrei Cimpoeru, Imperial College

I 85 blocks, 20.6M linear elements, 21.8M points, 0.5 GB CGNS file

I Agglomeration of 4x4x4 elements ⇒ 322,110 P4-elements

I HOPR used ≈ 6 GB RAM, run for ≈ 2 minutes(1 min eliminate duplicate nodes, 40s Jacobian checker)

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Agglomeration Example: Serrated nozzle II

all elements curvedinvalid elements inside the volume

only curved at wall BCinvalid elements at the boundary

#elems with Jscaled < 0 0− 0.1 0.1− 0.2 0.2− 0.3 ≥ 0.3

all linear 0 0 65 204 321,841all curved 10 737 896 1,684 318,783curved BC 61 6 70 216 321,757

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1st layer curvedinvalid elements

2 layers curved⇒ all elements valid



1st layer 10 50 104 376 321,5702 layers 0 0 197 520 321,393

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1st layer 10 50 104 376 321,5702 layers 0 0 197 520 321,393

3 layers 0 0 178 667 321,2654 layers 0 0 160 746 321,204

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Ongoing Work on Boundary Layer Meshes

I Structured grids:

⇒ Agglomeration (works in current HOPR release)

I Unstructured grids: Only curving the first element at the surfaceleads to inverted elements

⇒ For prismatic layers of linear elements:Blending of element stack with curved boundary face (not released)

⇒ Insert boundary layers afterwards (not released)

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Boundary layer Insertion

I Valid curved mesh with prismatic elements (hex, prism)I Split the first element layer

⇒ into a given number boundary layer elements (input parameter)

⇒ with a given stretching (input parameter)

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Boundary layer Insertion

I Valid curved mesh with prismatic elements (hex, prism)I Split the first element layer

⇒ into a given number boundary layer elements (input parameter)

⇒ with a given stretching (input parameter)

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Conclusion

I HOPR provides unstructured high order meshes

I Different curving strategies, depending on provided data

I HDF5 mesh file, designed for parallel IO

I Software is open-source

⇒ Announcement for next ICOSAHOM:David Kopriva wants to organize a mini-symposium todiscuss a standard for a high order mesh format

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Thanks to E. Sonnendrucker, C.-D. Munz, G. Gassner, T. Bolemann, H.Frank, and

Thank you for your attention!

www.hopr-project.org

HOPR Homepage (with Mailing List, Tutorials, Documentation...)

Contact: [email protected], [email protected]

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Appendix:

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Mesh Format: Element Node Connectivity

I All element mappings in the mesh have the same order (watertight)I Element node connectivity defined for all orders (i , j , k loops)I Full order elements only

XI, i

ETA, j

ZETA, k

1 3

6

13 15

18

2

14

4

16

5

17

7 9

12

8

10 11

1 3

6

10

2

4 5

7 8

9

1 3

97

19 21

2725

2

8

20

26

4 6

22 24

5

23

10 12

1816

11

17

13 1514

1 3

97

14

2

8

4 65

10 11

12 13

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SFC Domain Decomposition

I 3D unstructured simulation (N = 4) of a turbulent flow past asphere (Re = 1000)

I Domain decomposition based on a space filling curve element sorting

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I SFC-DD allows arbitrary number of domains, given a-posteriori

#Domains #Elements/core #MPIneighbors (mean)128 165-166 5-23 (11.75)

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1024 20-21 5-21 (11.99)

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1024 20-21 5-21 (11.99)4096 5-6 5-20 (10.37)

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HOPR - High Order Preprocessor