TestCase C3.5 - DNS of the transition of the Taylor-Green ...
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PROD-F-015-01 TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 Introduction and result summary Koen Hillewaert Argo team leader Contact: koen.hillewaert@cenaero.be Doc. ref.:
Transcript of 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: [email protected]
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 ′
w = 0
p = p0 + ρ0 V20 (cos 2x ′ + cos 2y ′) (cos 2z ′ + 2) /16
T = T0
with
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 ′
w = 0
p = p0 + ρ0 V20 (cos 2x ′ + cos 2y ′) (cos 2z ′ + 2) /16
T = T0
with
Re = ρ0V0L/µ = 1600
M = V0/√γRT0 = 0.1
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Testcase descriptionReference : pseudo-spectral 512 modes
Kinetic energy
Ek =1
ρ0∫
Ωρ
u ⋅ u
2dΩ ,
Dissipation rate and relation to enstrophy
ε = −dEk
dt=2
µ
ρ0∫
ΩSd
∶ Sd dΩ
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ε1=2νE
+µv
ρ0∫
Ω(∇ ⋅ v)2 dΩ
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ε2≈0
−1
ρ0∫
Ωp∇ ⋅ v dΩ
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ε3≈0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Testcase descriptionError definitions
Errors with respect to pseudo spectral solution
∆ε1 = ∣∣dEk
dt− (
dEk
dt)
∗∣∣
t,∞∆ε2 = ∣∣2νE − 2νE∗∣∣
t,∞
Independent error
∆ε3 = ∣∣dEk
dt+ 2νE∣∣
t,∞
with
∣∣a∣∣t,∞ = maxt∈[0,10]
∣a∣
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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)
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsError on measured dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
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
Giangaspero SBP-SAT(8)-RK4, o=8
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Spiering DG(5)-RK4-GPU, o=6
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-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Boom SBP-SATc(3,3)-ESDIRK2, o=3
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(1)-RK4, o=2
Diosady DG(3)-RK4, o=4
Diosady DG(7)-RK4, o=8
Diosady DG(15)-RK4, o=16
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
10-3
10-2
10-1
100
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
Giangaspero SBP-SAT(8)-RK4, o=8
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Spiering DG(5)-RK4-GPU, o=6
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-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Boom SBP-SATc(3,3)-ESDIRK2, o=3
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(1)-RK4, o=2
Diosady DG(3)-RK4, o=4
Diosady DG(7)-RK4, o=8
Diosady DG(15)-RK4, o=16
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsError on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
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
Giangaspero SBP-SAT(8)-RK4, o=8
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Spiering DG(5)-RK4-GPU, o=6
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-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Boom SBP-SATc(3,3)-ESDIRK2, o=3
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(1)-RK4, o=2
Diosady DG(3)-RK4, o=4
Diosady DG(7)-RK4, o=8
Diosady DG(15)-RK4, o=16
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsError on enstrophy dissipation : cpu time
1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1e1010-4
10-3
10-2
10-1
100
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
Giangaspero SBP-SAT(8)-RK4, o=8
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Spiering DG(5)-RK4-GPU, o=6
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-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Boom SBP-SATc(3,3)-ESDIRK2, o=3
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(1)-RK4, o=2
Diosady DG(3)-RK4, o=4
Diosady DG(7)-RK4, o=8
Diosady DG(15)-RK4, o=16
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsDifference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-5
10-4
10-3
10-2
10-1
100
101
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
Giangaspero SBP-SAT(8)-RK4, o=8
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Spiering DG(5)-RK4-GPU, o=6
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-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Boom SBP-SATc(3,3)-ESDIRK2, o=3
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(1)-RK4, o=2
Diosady DG(3)-RK4, o=4
Diosady DG(7)-RK4, o=8
Diosady DG(15)-RK4, o=16
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsDifference between measured and theoretical dissipation : cpu time
1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1e1010-5
10-4
10-3
10-2
10-1
100
101
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
Giangaspero SBP-SAT(8)-RK4, o=8
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Spiering DG(5)-RK4-GPU, o=6
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-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Boom SBP-SATc(3,3)-ESDIRK2, o=3
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(1)-RK4, o=2
Diosady DG(3)-RK4, o=4
Diosady DG(7)-RK4, o=8
Diosady DG(15)-RK4, o=16
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results : measured dissipation ∆ε1
Results from HOW1 : measured dissipation
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsResults from HOW1 : theoretical dissipation ∆ε2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global resultsResults from HOW1 : difference ∆ε3
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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)
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order -1Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
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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
10-3
10-2
10-1
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order -1Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
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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
10-3
10-2
10-1
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
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Global results for order -1Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-5
10-4
10-3
10-2
10-1
100
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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
10-4
Muite Spectral-IMR, o=-1
Muite Spectral-NSCK, o=-1
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order 16Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-6
10-5
10-4
10-3
10-2
10-1
Diosady DG(15)-RK4, o=16
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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
10-2
10-1
Diosady DG(15)-RK4, o=16
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order 16Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-6
10-5
10-4
10-3
10-2
10-1
Diosady DG(15)-RK4, o=16
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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
10-2
10-1
Diosady DG(15)-RK4, o=16
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order 16Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-6
10-5
10-4
10-3
10-2
10-1
Diosady DG(15)-RK4, o=16
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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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
10-2
10-1
Diosady DG(15)-RK4, o=16
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order 3Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-2
10-1
100
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SATc(3,3)-ESDIRK2, o=3
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
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Global results for order 3Error on measured dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2
10-1
100
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SATc(3,3)-ESDIRK2, o=3
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Global results for order 3Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-2
10-1
100
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SATc(3,3)-ESDIRK2, o=3
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 3Error on enstrophy dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1
100
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SATc(3,3)-ESDIRK2, o=3
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 3Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-2
10-1
100
101
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SATc(3,3)-ESDIRK2, o=3
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 3Difference between measured and theoretical dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1
100
101
Boom SBP-SAT(3,3)-ESDIRK2, o=3
Boom SBP-SATc(3,3)-ESDIRK2, o=3
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 2Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-2
10-1
100
Giangaspero SBP-SAT(2)-RK4, o=2
Boom SBP-SAT(2,2)-ESDIRK2, o=2
Boom SBP-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Diosady DG(1)-RK4, o=2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 2Error on measured dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2
10-1
100
Giangaspero SBP-SAT(2)-RK4, o=2
Boom SBP-SAT(2,2)-ESDIRK2, o=2
Boom SBP-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Diosady DG(1)-RK4, o=2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 2Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-2
10-1
100
Giangaspero SBP-SAT(2)-RK4, o=2
Boom SBP-SAT(2,2)-ESDIRK2, o=2
Boom SBP-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Diosady DG(1)-RK4, o=2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 2Error on enstrophy dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1
100
Giangaspero SBP-SAT(2)-RK4, o=2
Boom SBP-SAT(2,2)-ESDIRK2, o=2
Boom SBP-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Diosady DG(1)-RK4, o=2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 2Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-2
10-1
100
Giangaspero SBP-SAT(2)-RK4, o=2
Boom SBP-SAT(2,2)-ESDIRK2, o=2
Boom SBP-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Diosady DG(1)-RK4, o=2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 2Difference between measured and theoretical dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1
100
Giangaspero SBP-SAT(2)-RK4, o=2
Boom SBP-SAT(2,2)-ESDIRK2, o=2
Boom SBP-SAT(2,3)-ESDIRK2, o=2
Boom SBP-SATc(2,2)-ESDIRK2, o=2
Boom SBP-SATc(2,3)-ESDIRK2, o=2
Diosady DG(1)-RK4, o=2
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 5Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Grimich RBC(5), o=5
Marin-Perez DNC5filter-RK4, o=5
Marin-Perez DNC5Matrix-RK4, o=5
Marin-Perez DNC5Scalar-RK4, o=5
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 5Error on measured dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2
10-1
100
Grimich RBC(5), o=5
Marin-Perez DNC5filter-RK4, o=5
Marin-Perez DNC5Matrix-RK4, o=5
Marin-Perez DNC5Scalar-RK4, o=5
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 5Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Grimich RBC(5), o=5
Marin-Perez DNC5filter-RK4, o=5
Marin-Perez DNC5Matrix-RK4, o=5
Marin-Perez DNC5Scalar-RK4, o=5
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 5Error on enstrophy dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1
100
Grimich RBC(5), o=5
Marin-Perez DNC5filter-RK4, o=5
Marin-Perez DNC5Matrix-RK4, o=5
Marin-Perez DNC5Scalar-RK4, o=5
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 5Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Grimich RBC(5), o=5
Marin-Perez DNC5filter-RK4, o=5
Marin-Perez DNC5Matrix-RK4, o=5
Marin-Perez DNC5Scalar-RK4, o=5
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 5Difference between measured and theoretical dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-1
100
Grimich RBC(5), o=5
Marin-Perez DNC5filter-RK4, o=5
Marin-Perez DNC5Matrix-RK4, o=5
Marin-Perez DNC5Scalar-RK4, o=5
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 4Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Carton DG(3,prism)-RK4, o=4
Carton DG(3,tetra)-RK4, o=4
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(3)-RK4, o=4
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 4Error on measured dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3
10-2
10-1
100
Carton DG(3,prism)-RK4, o=4
Carton DG(3,tetra)-RK4, o=4
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(3)-RK4, o=4
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 4Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Carton DG(3,prism)-RK4, o=4
Carton DG(3,tetra)-RK4, o=4
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(3)-RK4, o=4
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 4Error on enstrophy dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3
10-2
10-1
100
Carton DG(3,prism)-RK4, o=4
Carton DG(3,tetra)-RK4, o=4
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(3)-RK4, o=4
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 4Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
101
Carton DG(3,prism)-RK4, o=4
Carton DG(3,tetra)-RK4, o=4
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(3)-RK4, o=4
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 4Difference between measured and theoretical dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3
10-2
10-1
100
101
Carton DG(3,prism)-RK4, o=4
Carton DG(3,tetra)-RK4, o=4
Luedeke Pade4-RK3, o=4
Spiering DG(3)-RK4-GPU, o=4
Boom SBP-SAT(4,3)-ESDIRK2, o=4
Boom SBP-SAT(4,4)-ESDIRK2, o=4
Boom SBP-SATc(4,3)-ESDIRK2, o=4
Boom SBP-SATc(4,4)-ESDIRK2, o=4
Diosady DG(3)-RK4, o=4
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 6Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Spiering DG(5)-RK4-GPU, o=6
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 6Error on measured dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2
10-1
100
Spiering DG(5)-RK4-GPU, o=6
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 6Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Spiering DG(5)-RK4-GPU, o=6
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 6Error on enstrophy dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2
10-1
100
Spiering DG(5)-RK4-GPU, o=6
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 6Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-3
10-2
10-1
100
Spiering DG(5)-RK4-GPU, o=6
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 6Difference between measured and theoretical dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-2
10-1
100
Spiering DG(5)-RK4-GPU, o=6
Garmann FDL3DI-RK4, o=6
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 8Error on measured dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
Giangaspero SBP-SAT(8)-RK4, o=8
Diosady DG(7)-RK4, o=8
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 8Error on measured dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3
10-2
10-1
100
Giangaspero SBP-SAT(8)-RK4, o=8
Diosady DG(7)-RK4, o=8
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 8Error on enstrophy dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
Giangaspero SBP-SAT(8)-RK4, o=8
Diosady DG(7)-RK4, o=8
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 8Error on enstrophy dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3
10-2
10-1
100
Giangaspero SBP-SAT(8)-RK4, o=8
Diosady DG(7)-RK4, o=8
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 8Difference between measured and theoretical dissipation : resolution
1e-3 1e-2 1e-1 110-4
10-3
10-2
10-1
100
Giangaspero SBP-SAT(8)-RK4, o=8
Diosady DG(7)-RK4, o=8
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Global results for order 8Difference between measured and theoretical dissipation : cpu time
0.1 1 1e1 1e2 1e3 1e4 1e5 1e6 1e710-3
10-2
10-1
100
Giangaspero SBP-SAT(8)-RK4, o=8
Diosady DG(7)-RK4, o=8
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGrimich RBC(5) : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGrimich RBC(5) : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGrimich RBC(5) : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGrimich RBC(5) : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,prism)-RK4 : energy
0 2 4 6 8 10 12 14
0.04
0.06
0.08
0.10
0.12
reference
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,prism)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,prism)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,prism)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,tetra)-RK4 : energy
0 2 4 6 8 10 12 14
0.04
0.06
0.08
0.10
0.12
reference
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,tetra)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,tetra)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeCarton DG(3,tetra)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
288.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(2)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : energy
0 2 4 6 8 10 12 140.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
64.0
128.0
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
64.0
128.0
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
64.0
128.0
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGiangaspero SBP-SAT(8)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
64.0
128.0
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeLuedeke Pade4-RK3 : energy
0 2 4 6 8 10 12 140.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeLuedeke Pade4-RK3 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeLuedeke Pade4-RK3 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeLuedeke Pade4-RK3 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(3)-RK4-GPU : energy
0 2 4 6 8 10 12 140.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
144.0
192.0
216.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(3)-RK4-GPU : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
144.0
192.0
216.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(3)-RK4-GPU : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
144.0
192.0
216.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(3)-RK4-GPU : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
144.0
192.0
216.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(5)-RK4-GPU : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
160.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(5)-RK4-GPU : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
160.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(5)-RK4-GPU : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
160.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeSpiering DG(5)-RK4-GPU : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
160.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5filter-RK4 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5filter-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5filter-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5filter-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : energy
0 2 4 6 8 10 12 14
0.04
0.06
0.08
0.10
0.12
reference
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Matrix-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : energy
0 2 4 6 8 10 12 14
0.04
0.06
0.08
0.10
0.12
reference
128.0
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
128.0
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
128.0
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMarin-Perez DNC5Scalar-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
128.0
64.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,2)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,3)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,3)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,3)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(2,3)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(3,3)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(3,3)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(3,3)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(3,3)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,3)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,3)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,3)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,3)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,4)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,4)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,4)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SAT(4,4)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,2)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,3)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,3)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,3)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(2,3)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(3,3)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(3,3)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(3,3)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(3,3)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,3)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,3)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,3)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,3)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,4)-ESDIRK2 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,4)-ESDIRK2 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,4)-ESDIRK2 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeBoom SBP-SATc(4,4)-ESDIRK2 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
32.0
64.0
128.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(1)-RK4 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(1)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(1)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(1)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(3)-RK4 : energy
0 2 4 6 8 10 12 140.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(3)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(3)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(3)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
128.0
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(7)-RK4 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(7)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(7)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(7)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
192.0
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(15)-RK4 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(15)-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(15)-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeDiosady DG(15)-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
256.0
384.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-IMR : energy
0 2 4 6 8 10 12 14
0.04
0.06
0.08
0.10
0.12
reference
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-IMR : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-IMR : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-IMR : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
256.0
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-NSCK : energy
0 2 4 6 8 10 12 14
0.04
0.06
0.08
0.10
0.12
reference
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-NSCK : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-NSCK : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeMuite Spectral-NSCK : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
512.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGarmann FDL3DI-RK4 : energy
0 2 4 6 8 10 12 140.02
0.04
0.06
0.08
0.10
0.12
0.14
reference
64.0
128.0
192.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGarmann FDL3DI-RK4 : dissipation
0 2 4 6 8 10 12 140.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
reference
64.0
128.0
192.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGarmann FDL3DI-RK4 : enstrophy
0 2 4 6 8 10 12 140
2
4
6
8
10
12
reference
64.0
128.0
192.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
PRO
D-F
-015-0
1
Detail per author and schemeGarmann FDL3DI-RK4 : difference
0 2 4 6 8 10 12 1410-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
64.0
128.0
192.0
256.0
TestCase C3.5 - Taylor-Green vortex © 2013 Cenaero - All rights reserved
PR
OD
-F-0
15
-01
