TestCase C3.5 - DNS of the transition of the Taylor-Green ...

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TestCase C3.5 - DNS of the transition of theTaylor-Green vortex, Re=1600

Introduction and result summary

Koen HillewaertArgo team leader

Contact: koen.hillewaert@cenaero.be

Doc. ref.:

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Testcase descriptionProblem definition

Periodic domain

(x , y , z) ∈ Ω = [−πL, πL]3

(x ′, y ′, z ′) = (x , y , z)/L

At t=0

u = V0 sin x ′ cos y ′ cos z ′

v = −V0 cos x ′ sin y ′ cos z ′

p = p0 + ρ0 V20 (cos 2x ′ + cos 2y ′) (cos 2z ′ + 2) /16

T = T0

Re = ρ0V0L/µ = 1600

M = V0/√γRT0 = 0.1

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Testcase descriptionProblem definition

Periodic domain

(x , y , z) ∈ Ω = [−πL, πL]3

(x ′, y ′, z ′) = (x , y , z)/L

At t=0

u = V0 sin x ′ cos y ′ cos z ′

v = −V0 cos x ′ sin y ′ cos z ′

p = p0 + ρ0 V20 (cos 2x ′ + cos 2y ′) (cos 2z ′ + 2) /16

T = T0

Re = ρ0V0L/µ = 1600

M = V0/√γRT0 = 0.1

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Testcase descriptionReference : pseudo-spectral 512 modes

Kinetic energy

ρ0∫

u ⋅ u

2dΩ ,

Dissipation rate and relation to enstrophy

ε = −dEk

ρ0∫

∶ Sd dΩ

´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ε1=2νE

ρ0∫

Ω(∇ ⋅ v)2 dΩ

´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ε2≈0

ρ0∫

Ωp∇ ⋅ v dΩ

´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ε3≈0

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Testcase descriptionError definitions

Errors with respect to pseudo spectral solution

∆ε1 = ∣∣dEk

dt− (

∗∣∣

t,∞∆ε2 = ∣∣2νE − 2νE∗∣∣

Independent error

∆ε3 = ∣∣dEk

dt+ 2νE∣∣

∣∣a∣∣t,∞ = maxt∈[0,10]

∣a∣

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Summary of contributions

10 contributors D. C. Del Rey-Fernandez, P. D. Boom and D. W. Zingg - University of Toronto

SBP-SATc(2,3)-ESDIRK2 SBP-SAT(4,3)-ESDIRK2 SBP-SATc(4,4)-ESDIRK2SBP-SAT(3,3)-ESDIRK2 SBP-SAT(2,2)-ESDIRK2 SBP-SATc(4,3)-ESDIRK2SBP-SAT(2,3)-ESDIRK2 SBP-SAT(4,4)-ESDIRK2 SBP-SATc(2,2)-ESDIRK2SBP-SATc(3,3)-ESDIRK2

L. T. Diosady and S. M. Murman - NASA DG(7)-RK4 DG(1)-RK4 DG(3)-RK4DG(15)-RK4

D. J. Garmann and M. R. Visbal - AFRL FDL3DI-RK4 E. van der Weide, M. Svard and G. Giangaspero - University of Twente

SBP-SAT(2)-RK4 SBP-SAT(8)-RK4 K. Grimich and P. Cinnella - ENSAM Paris RBC(5) H. Luedeke - DLR Pade4-RK3 F. Spiering - DLR DG(3)-RK4-GPU DG(5)-RK4-GPU B. Muite, B. Cloutier and M. Parsani - KAUST Spectral-IMR Spectral-NSCK R. Marin-Perez and P. Cinnella - ENSAM DNC5Matrix-RK4 DNC5Scalar-RK4

DNC5filter-RK4 C. Carton de Wiart and K. Hillewaert - Cenaero DG(3,tetra)-RK4

DG(3,prism)-RK4 83 data sets 145358923.706990 total computing time (units)

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Global resultsError on measured dissipation : resolution

1e-3 1e-2 1e-1 110-4

Grimich RBC(5), o=5

Carton DG(3,prism)-RK4, o=4

Carton DG(3,tetra)-RK4, o=4

Giangaspero SBP-SAT(2)-RK4, o=2

Luedeke Pade4-RK3, o=4

Spiering DG(3)-RK4-GPU, o=4

Marin-Perez DNC5filter-RK4, o=5

Marin-Perez DNC5Matrix-RK4, o=5

Marin-Perez DNC5Scalar-RK4, o=5

Boom SBP-SAT(2,2)-ESDIRK2, o=2

Boom SBP-SATc(2,2)-ESDIRK2, o=2

Diosady DG(1)-RK4, o=2

Muite Spectral-IMR, o=-1

Muite Spectral-NSCK, o=-1

Garmann FDL3DI-RK4, o=6

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Global resultsError on measured dissipation : cpu time

1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1e1010-4

Grimich RBC(5), o=5

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Global resultsError on enstrophy dissipation : resolution

1e-3 1e-2 1e-1 110-4

Grimich RBC(5), o=5

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Global resultsError on enstrophy dissipation : cpu time

1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1e1010-4

Grimich RBC(5), o=5

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Global resultsDifference between measured and theoretical dissipation : resolution

1e-3 1e-2 1e-1 110-5

Grimich RBC(5), o=5

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Global resultsDifference between measured and theoretical dissipation : cpu time

1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1e1010-5

Grimich RBC(5), o=5

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Global results : measured dissipation ∆ε1

Results from HOW1 : measured dissipation

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Global resultsResults from HOW1 : theoretical dissipation ∆ε2

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Global resultsResults from HOW1 : difference ∆ε3

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Conclusions

Results

error evolution dependent on error type : measured dissipation converges earlier than enstrophy, difference diminishes

with order convergence of pressure-strain term (NASA, AFRL)

resolution no clear winner in case of error vs resolution at similar order ↔ central FD

(HOW1) minor impact of element type

structured methods only marginally faster then unstructured ↔ central FD (HOW1)

globally order of convergence satisfied - exceptions DG(7)and DG(15) schemes : aliasing issues DG(3)/DLR : single precision

overlay of vorticity plots needed (dispersion vs. dissipation)

Interesting approach for measuring GPU performance (DLR)

Check for time discretisation (cfr. Kaust)

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ConclusionsRemarks

Further work

overlays of vorticity contours

consolidation with previous results

Evolution of the testcase

fully unstructured / perturbed meshes standard ?

how to ensure correct WU comparison (∆t) ?

other dissipation terms

higher Re ? LES ?

strong scaling tests

Thanks to

all participants

Cenaero : Corentin Carton de Wiart

UCL : G. Winckelmans and M. Duponcheel : reference results

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Global results for order -1Error on measured dissipation : resolution

1e-3 1e-2 1e-1 110-4

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Global results for order -1Error on measured dissipation : cpu time

0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-4

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Global results for order -1Error on enstrophy dissipation : resolution

1e-3 1e-2 1e-1 110-4

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Global results for order -1Error on enstrophy dissipation : cpu time

0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-4

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Global results for order -1Difference between measured and theoretical dissipation : resolution

1e-3 1e-2 1e-1 110-5

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Global results for order -1Difference between measured and theoretical dissipation : cpu time

0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-5

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Global results for order 16Error on measured dissipation : resolution

1e-3 1e-2 1e-1 110-6

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Global results for order 16Error on measured dissipation : cpu time

0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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Global results for order 16Error on enstrophy dissipation : resolution

1e-3 1e-2 1e-1 110-6

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Global results for order 16Error on enstrophy dissipation : cpu time

0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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Global results for order 16Difference between measured and theoretical dissipation : resolution

1e-3 1e-2 1e-1 110-6

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Global results for order 16Difference between measured and theoretical dissipation : cpu time

0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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1e-3 1e-2 1e-1 110-2

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2

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1e-3 1e-2 1e-1 110-2

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1

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1e-3 1e-2 1e-1 110-2

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1

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1e-3 1e-2 1e-1 110-2

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2

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1e-3 1e-2 1e-1 110-2

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1

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1e-3 1e-2 1e-1 110-2

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1

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1e-3 1e-2 1e-1 110-3

Grimich RBC(5), o=5

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2

Grimich RBC(5), o=5

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1e-3 1e-2 1e-1 110-3

Grimich RBC(5), o=5

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1

Grimich RBC(5), o=5

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1e-3 1e-2 1e-1 110-3

Grimich RBC(5), o=5

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1

Grimich RBC(5), o=5

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1e-3 1e-2 1e-1 110-3

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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1e-3 1e-2 1e-1 110-3

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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1e-3 1e-2 1e-1 110-3

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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1e-3 1e-2 1e-1 110-3

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2

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1e-3 1e-2 1e-1 110-3

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2

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1e-3 1e-2 1e-1 110-3

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2

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1e-3 1e-2 1e-1 110-4

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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1e-3 1e-2 1e-1 110-4

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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1e-3 1e-2 1e-1 110-4

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0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3

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Detail per author and schemeGrimich RBC(5) : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeGrimich RBC(5) : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeGrimich RBC(5) : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeGrimich RBC(5) : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeCarton DG(3,prism)-RK4 : energy

0 2 4 6 8 10 12 14

reference

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Detail per author and schemeCarton DG(3,prism)-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeCarton DG(3,prism)-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeCarton DG(3,prism)-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeCarton DG(3,tetra)-RK4 : energy

0 2 4 6 8 10 12 14

reference

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Detail per author and schemeCarton DG(3,tetra)-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeCarton DG(3,tetra)-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeCarton DG(3,tetra)-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : energy

0 2 4 6 8 10 12 140.00

reference

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Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeLuedeke Pade4-RK3 : energy

0 2 4 6 8 10 12 140.00

reference

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Detail per author and schemeLuedeke Pade4-RK3 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeLuedeke Pade4-RK3 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeLuedeke Pade4-RK3 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeSpiering DG(3)-RK4-GPU : energy

0 2 4 6 8 10 12 140.00

reference

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Detail per author and schemeSpiering DG(3)-RK4-GPU : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeSpiering DG(3)-RK4-GPU : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeSpiering DG(3)-RK4-GPU : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeSpiering DG(5)-RK4-GPU : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeSpiering DG(5)-RK4-GPU : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeSpiering DG(5)-RK4-GPU : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeSpiering DG(5)-RK4-GPU : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeMarin-Perez DNC5filter-RK4 : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeMarin-Perez DNC5filter-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeMarin-Perez DNC5filter-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeMarin-Perez DNC5filter-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : energy

0 2 4 6 8 10 12 14

reference

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Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : energy

0 2 4 6 8 10 12 14

reference

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Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : difference

0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.00

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : difference

0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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Detail per author and schemeDiosady DG(1)-RK4 : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeDiosady DG(1)-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeDiosady DG(1)-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeDiosady DG(1)-RK4 : difference

0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.00

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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0 2 4 6 8 10 12 140.02

reference

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0 2 4 6 8 10 12 140.000

reference

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0 2 4 6 8 10 12 140

reference

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0 2 4 6 8 10 12 1410-12

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Detail per author and schemeMuite Spectral-IMR : energy

0 2 4 6 8 10 12 14

reference

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Detail per author and schemeMuite Spectral-IMR : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeMuite Spectral-IMR : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeMuite Spectral-IMR : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeMuite Spectral-NSCK : energy

0 2 4 6 8 10 12 14

reference

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Detail per author and schemeMuite Spectral-NSCK : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeMuite Spectral-NSCK : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeMuite Spectral-NSCK : difference

0 2 4 6 8 10 12 1410-12

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Detail per author and schemeGarmann FDL3DI-RK4 : energy

0 2 4 6 8 10 12 140.02

reference

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Detail per author and schemeGarmann FDL3DI-RK4 : dissipation

0 2 4 6 8 10 12 140.000

reference

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Detail per author and schemeGarmann FDL3DI-RK4 : enstrophy

0 2 4 6 8 10 12 140

reference

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Detail per author and schemeGarmann FDL3DI-RK4 : difference

0 2 4 6 8 10 12 1410-12

TestCase C3.5 - DNS of the transition of the Taylor-Green ...

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Calibrating the γγγ-Reθθθθ Transition Model for Commercial CFDcfd.mace.manchester.ac.uk/.../P-Malan-AIAA2009-gamma-re-theta.pdf · Calibrating the γγγ-Reθθθθ Transition

Transition-Metal-Catalyzed Reactions in Heterocyclic Synthesisaether.cmi.ua.ac.be/artikels/Artikels Gitte/Artikels/Reviews/Trans... · Transition-Metal-Catalyzed Reactions in Heterocyclic

Information-Centric Networks Section # 3.2: DNS Issues Instructor: George Xylomenos Department: Informatics.

DNS Study on Three Vortex Identification Methods · 1 American Institute of Aeronautics and Astronautics. DNS Study on Three Vortex Identification Methods . Yinlin Dong. 1, Yong Yang.

Decoherence by Quantum Phase Transition

Information-Centric Networks Section # 3.3: DNS Issues Instructor: George Xylomenos Department: Informatics.

The Transition Metals - University of Massachusettsalpha.chem.umb.edu/.../Lec3-TheTransitionMetalsIIelectroncounting.pdf · The Transition Metals ... subtract the oxidation state