Jörg Schumacher Theoretical Fluid Mechanics

Department of Mechanical Engineering

Technische Universität Ilmenau

Germany

How can numerical simulations contribute?

EuTuCHe Workshop Geneva, 23.–25.04.2007

Supercomputing More and more organized on European scale (Petaflop Project Pace)

DEep Computing Initiative within DEISA → 2 turbulence projects (2006/2007)

Resolution of the most intensive gradients in turbulence at R~100 on a 20483

800,000 CPUh on 512 CPUs (1.9Tbyte RAM) 1 velocity snapshot = 68 Gbyte Quasi-Lagrangian analysis in 513 around 100 Lagrangian tracers (700

Gbytes) UNICORE platform for Grid computing Parallel NetCDF for I/O

Case 1: Cartesian Cell

Cartesian geometry (x,y,z) Ra=107–109 Pr=0.7 (later Pr > 1) Aspect ratio: =L/H=2-32

Free-slip boundaries in z Equidistant grid Periodic side walls

Geometry and Parameters

H

L

Temperature Profile

Pr=0.7Ra=1.1×107

=2

R=80Nu=27.85 0.56

32Nu

HδT

1Δ

ηK

228 TE

129256256NNN zyx

Case 2: Cylindrical Cell

Cylindrical geometry (r,,z) Ra=107–1012 Pr=0.7 (later Pr > 1) Aspect ratio: =L/H=1

No-slip boundaries for flow Non-equidistant grid Temperature fixed at bottom/top Adiabatic side walls

(Verzicco & Orlandi, JCP 1996)

H

L

Geometry and Parameters

Nusselt Number Convergence

03.0Nu2

HδT

128165257NNN zrθ

4

3~K

Pr=0.7Ra=107

=3

R=(Ra/Pr)1/4 ~100Nu=16.06 0.05

3zθr ΔmaxRΔΔmaxΔ

~

151 TE

Towards Large

1ΓR 2ΓR

θ2Γ ΔR θ1Γ ΔR

Example:

Sustain resolution & Double

3z

θ1r2 ΔmaxΔ

RΔmaxΔ~

2R

zrθ12 NΓNΓN~~

2Γθ,Δ

Number of lateral grid points grows with if the strong resolution constraints are sustained!

Contributions (I)

Experiment

Parallel data processing Database for later use

Associated suprcomputing projects on classical/quantum turbulence

Direct participation

Indirect participation

Contributions (II)

Resolution of high-Ra boundary layers Transition from laminar to turbulent boundary layer at Ra>1011

What are the differences to „classical“ boundary layers? Detailed Lagrangian study of breakdown of wind for aspect

ratios >1 Ultimate regime of convection?

M. Emran (Ilmenau) R. Verzicco (Bari)