Table Of ContentUlrich Schumann
Rainer Friedrich (Eds.)
Direct and Large
Eddy Simulation
of Turbulence
Notes on Numerical Fluid Mechanics
Volume 15
Series Editors: Ernst Heinrich Hirschel, MUnchen
Maurizio Pandolfi, Torino
Arthur Rizzi, Stockholm
Bernard Roux, Marseille
Volume 1 Boundary Algorithms for Multidimensional Inviscid Hyperbolic Flows
(Karl Forster, Ed.)
Volume 2 Proceedings of the Third GAMM-Conference on Numerical Methods
in Fluid Mechanics (Ernst Heinrich Hirschel, Ed.) (out of print)
Volume 3 Numerical Methods for the Computation of Inviscid Transonic Flows
with Shock Waves (Arthur Rizzi I Henri Viviand, Eds.)
Volume 4 Shear Flow in Surface-Oriented Coordinates (Ernst Heinrich Hirschel I
Wilhelm Kordulla)
Volume 5 Proceedings of the Fourth GAMM-Conference on Numerical Methods
in Fluid Mechanics (Henri Viviand, Ed.) (out of print)
Volume 6 Numerical Methods in Laminar Flame Propagation (Norbert Peters I
Jurgen Warnatz, Eds.)
Volume 7 Proceedings of the Fifth GAMM-Conference on Numerical Methods
in Fluid Mechanics (Maurizio Pandolfi I Renzo Piva, Eds.)
Volume 8 Vectorization of Computer Programs with Applications to Computational
Fluid Dynamics (Wolfgang Gentzsch)
Volume 9 Analysis of Laminar Flow over a Backward Facing Step (Ken Morgan I
Jaques Periaux I FranC!ois Thomasset, Eds.)
Volume 10 Efficient Solutions of Elliptic Systems (Wolfgang Hackbusch, Ed.)
Volume 11 Advances in Multi-Grid Methods (Dietrich Braess I Wolfgang Hackbusch I
Ulrich Trottenberg, Eds.)
Volume 12 The Efficient Use of Vector Computers with Emphasis on Computational
Fluid Dynamics (Willi Schonauer I Wolfgang Gentzsch, Eds.)
Volume 13 Proceedings of the Sixth GAMM-Conference on Numerical Methods
in Fluid Mechanics (Dietrich Rues I Wilhelm Kordulla, Eds.)
Volume 14 Finite Approximations in Fluid Mechanics (Ernst Heinrich Hirschel, Ed.)
Volume 15 Direct and Large Eddy Simulation of Turbulence (Ulrich Schumann I
Rainer Friedrich, Eds.)
Manuscripts should have well over 100 pages. As they will be reproduced photomechanically
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editor Prof. Dr. E. H. Hirschel, Herzog-Heinrich-Weg 6, D-8011 Zorneding.
Ulrich Schumann
Rainer Friedrich (Eds.)
Direct and Large
Eddy Simulation
of Turbulence
Proceedings of the EUROMECH Colloquium No. 199,
MUnchen, FRG, September 30 to October 2, 1985
Springer Fachmedien Wiesbaden GmbH
CIP-Kurztitelaufnahme der Deutschen Bibliothek
Direct and large eddy simulation of turbulence:
proceedings of the Euromech Colloquium No. 199,
Miinchen, FRG, September 30-0ctober 2, 1985 I
Ulrich Schumann; Rainer Friedrich (ed.l.
Braunschweig; Wiesbaden: Vieweg, 1986.
(Notes on numerical fluid mechanics;
Vol. 15)
NE: Schumann, Ulrich [Hrsg.]; Euromech
Colloquium (199, 1985, Miinchen>; GT
All rights reserved
© Springer Fachmedien Wiesbaden 1986
Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig in 1986
No part of this publication may be reproduced, stored in a retrieval
system or transmitted, mechanical, photocopying or otherwise,
without prior permission of the copyright holder.
Produced by Lengericher Handelsdruckerei, Lengerich
ISSN 0179-9614
ISBN 978-3-663-00048-8 ISBN 978-3-663-00197-3 (eBook)
DOI 10.1007/978-3-663-00197-3
PREFACE
This volume contains papers presented to a EUROMECH-Colloquium held in
Munich, September 30 to October 2, 1985. The Colloquium is number 199 in a
series of colloquia inaugurated by the European Mechanics Committee. The
meeting was jointly organized by the 'Lehrstuhl fur Stromungsmechanik' at the
'Technische Universitat Munchen' and the 'Institut fur Physik der
Atmosphare' of the 'Deutsche Forschungs- und Versuchsanstalt fur Luft- und
Raumfahrt' (DFVLR) in Oberpfaffenhofen.
'Direct' and 'large eddy simulation' are terms which denote two closely con
nected methods of turbulence research. In a 'direct simulation' (DS), turbu
lent motion is simulated by numerically integrating the Navier-Stokes
equations in three-dimensional space and as a function of time. Besides ini
tial and boundary conditions no physical simplifications are involved. Com
puter resources limit the resolution in time and space, though simulations
with an order of one million discrete points in space are feasible. The simu
lated flow fields can be considered as true realizations of turbulent flow
fields and analysed to answer questions on the basic behaviour of turbulence.
Direct simulations are valid as long as all the excited scales remain within
the band of resolved scales. This means that viscosity must be strong enough
to damp out the not resolved scales or the simulation is restricted to a lim
ited integration-time interval only. In summary, DS provides a tool to
investigate turbulent motions from first principles at least for a finite
band of scales.
Large eddy simulation (LES) is a combination of direct simulation with sta
tistical modelling. The large 'eddies' are the motion structures at scales
which remain after a certain filter has been applied to the turbulent field.
This filter is strongly related to the discrete numerical representation of
the flow field employed in the simulation algorithm. For a finite difference
simulation the large scales must be resolvable by the underlying grid. In
contrast, the 'subgrid-scales' are those which are too small for the grid. In
LES, these subgrid-scales are modelled by a subgrid-scale (SGS) model. The
SGS-model mainly provides the correct damping of those resolved scales which
lie at the border of resolution and- which are excited by the large scale
motions. Also, the SGS-model has to describe turbulent fluxes not represented
by the large scales. SGS-models are formally very similar to the models com
monly used to describe time- or ensemble-averaged turbulent fields. Thus
they have bas ically the same advantages and disadantages. Approximation
er,rors in SGS-models are of less importance, however, because the SGS-motion
v
carries only a fraction of total turbulent kinetic energy and fluxes. If the
grid (and the related filter) is fine enough, this fraction becomes very
small. In summary, LES serves as a tool to construct the large scale portion
of turbulent fields at high Reynolds numbers.
Direct turbulence simulations were pioneered by Orszag and co-workers since
1969. The first convincing large eddy simulations were reported by Deardorff
in 1970 for a turbulent channel flow and applied to atmospheric boundary lay
ers thereafter. His SGS-model employed a proposal by Smagorinsky (1963) for
parametrization of subgrid-scale motions in meteorology. Lilly (1966) showed
that this SGS-model is consistent with Kolmogorov's inertial-subrange
theory. The state of the art as of 1983 was reported by Rogallo & Moin
(1984).
The Colloquium was concerned with the discussion of new developments in the
field of DS and LES and its applications. The presentations included new
aspects on the numerical algorithms to integrate the basic equations, treat
ments of filtering, boundary and initial conditions, and subgrid-scale mod
els. Also new concepts based on fractals and helicity were outlined which
possibly are capable of influencing SGS-modelling in the future. The applica
tions included transition and established turbulence, homogeneous and
inhomogeneous turbulence. They were related to basic research as well as to
engineering problems and to atmospheric boundary layers.
We were glad to receive much response to our invitation. About fifty scien
tists attended the colloquium, among them we could welcome most of the active
researchers in the field, in particular from the USA and Japan, and about
thirty papers have been presented. This was the first meeting of experts from
all over the world on this special subject. As no collection of papers
exists, which summarizes the present state of the art in DS and LES, it was
decided to collect the contributions for the present volume. Each paper has
been revised after being reviewed by at least one reviewer. A few contrib
utions have the form of extended abstracts; they summarize results, which
were presented at the Colloquium and which are described in more detail in
papers under publication. Some contributions are not included because their
content has been published just recently. However, we include the contrib
ution of Dr. McComb who was not able to participate in the colloquium. The
papers are grouped into sections of related subjects: 1. Transition to turbu
lence, 2. Subgrid-scale models and basic concepts, 3. Large eddy simulations
of wall-bounded shear flows, 4. Direct and large eddy simulations of mixed
shear and buoyant flows, 5. Convective or stable atmospheric boundary
layers. The volume ends up with summarizing statements on results, trends and
recommendations.
VI
We are very grateful to all who supported the Colloquium and the resultant
proceedings. We thank the Volkswagen Foundation, the companies Cray
Research, Munich and Messerschmitt-Bolkow-Blohm, Munich for financial sup
port of the meeting. Last, but not least we are indebted to all colleagues
who contributed to the proceedings or took part in the reviewing process.
Ulrich Schumann Rainer Friedrich
April 1986 Oberpfaffenhofen Mlinchen
VII
CONTENTS
Page
1. TRANSITION TO TURBULENCE
N. GILBERT, L. KLEISER: Subcritical Transition to Turbulence in Channel
Flow ................................. .
T. HERBERT: Vortical Mechanisms in Shear Flow Transition. . . . . . .. 19
2. SUBGRID-SCALE MODELS AND BASIC CONCEPTS
B. AUPOIX: Subgrid Scale Models for Homogeneous Anisotropic Turbulence 37
W. D. McCOMB: Application of Renormalization Group eRG) Methods to the
Subgrid Modelling Problem. . 67
E. LEVICH~ Helical Fluctuations, Fractal Dimensions and Path Integral in
the Theory of Turbulence . . . . . . . . . . . . . . . 82
3. LARGE EDDY SIMULATIONS OF WALL-BOUNDED SHEAR FLOWS
S. GAVRILAKIS, H. M. TSAI, P. R. VOKE, D. C. LESLIE: Large-Eddy
Simulation of Low Reynolds Number Channel Flow by Spectral and Finite
Difference Methods . . . . . 105
K. HORIUTI, A. YOSHIZAWA: Large Eddy Simulation of Turbulent Channel
Flow by 1-Equation Model .... . . 119
T. KOBAYASHI, M. KANO: Numerical Prediction of Turbulent Plane Couette
Flow by Large Eddy Simulation . 135
D. LAURENCE: Advective Formulation of Large Eddy Simulation for
Engineering Type Flows . . . . 147
L. SCHMITT, K. RICHTER, R. FRIEDRICH: Large-Eddy Simulation of Turbulent
Boundary Layer and Channel Flow at High Reynolds Number 161
Short Contributions:
J. KIM: Numerical Investigation of a Vortical Structure in a Wall-
Bounded Shear Flow . . . . . . .. ........... . .. 177
VIII
Page
P. MOIN: Recent Results on the Structure of Turbulent Shear Flows using
Simulation Databases 181
4. DIRECT AND LARGE EDDY SIMULATIONS OF MIXED SHEAR AND BUOYANT FLOWS
T. M. EIDSON, M. Y. HUSSAINI, T. A. ZANG: Simulation of the Turbulent
Rayleigh-Benard Problem using a Spectral/Finite Difference Technique. 188
G. GROTZBACH: Application of the TURBIT-3 Subgrid Scale Model to Scales
Between Large Eddy and Direct Simulations 210
K. KUWAHARA, S. SHIRAYAMA: Direct Simulation of High-Reynolds-Number
Flows by Finite-Difference Methods . . . . . . 227
U. SCHUMANN, S. E. ELGHOBASHI, T. GERZ: Direct Simulation of Stably
Stratified Turbulent Homogeneous Shear Flows . . . 245
Short Contribution:
R. W. METCALFE, S. MENON, J.J. RILEY: The Effect of Coherent Modes on
the Evolution of a Turbulent Mixing Layer . 265
5. CONVECTIVE OR STABLE ATMOSPHERIC BOUNDARY LAYERS
D. J. CARRUTHERS, J. C. R. HUNT, C. J. TURFUS: Turbulent Flow near
Density Inversion Layers . . . . 271
C.-H. MOENG: A Large Eddy Simulation Model for the Stratus-Topped
Boundary Layer . . . 291
F. T. M. NIEUWSTADT, R. A. BROST, T. L. van STIJN: Decay of Convective
Turbulence, a Large Eddy Simulation . 304
6. SUMMARIZING STATEMENTS ON RESULTS, TRENDS AND RECOMMENDATIONS 318
List of Participants 336
List of Authors 340
IX
