Microscopic Simulations of Complex Hydrodynamic Phenomena

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Microscopic Simulations of Complex Hydrodynamic Phenomena Edited by

Michel Mareschal Free University of Brussels Brussels, Belgium

and

Brad Lee Holian Los Alamos National Laboratory Los Alamos, New Mexico

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Proceedings of a NATO Advanced Study Institute on Microscopic Simulations of Complex Hydrodynamic Phenomena, held July 15-17, 1991, in Alghero, Sardinia

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NATO Advanced Study Institute on Microscopic Simulations of Complex Hydrodynamic Phenomena (1991: Alghero, Italy)

Microscopic simulations of complex hydrodynamic phenomena / edited by Michel Mareschal and Brad Lee Holian.

p. cm.—(NATO ASI series. Series B, Physics; vol. 292) "Proceedings of a NATO Advanced Study Institute on Microscopic Simulations

of Complex Hydrodynamic Phenomena, in Alghero, Sardinia"—T.p. verso. "Published in cooperation with NATO Scientific Affairs Division." Includes bibliographical references and index.

1. Fluid dynamics—Data processing—Congresses. 2. Molecular dynamics-Data processing—Congresses. I. Mareschal, Michel. II. Holian, Brad Lee. III. Title. IV. Series: NATO ASI series. Series B, Physics; v. 292. TA357.5.D37N38 1991 92-13378 532 /.5-dc20 CIIP^

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PREFACE

This volume contains the proceedings of a NATO Advanced Study Institute which was held in Alghero, Sardinia, in July 1991.

The development of computers in the recent years has lead to the emergence of unconventional ideas aiming at solving old problems. Among these, the possibility of computing directly fluid flows from the trajectories of constituent particles has been much exploited in the last few years: lattice gases cellular automata and more generally Molecular Dynamics have been used to reproduce and study complex flows. Whether or not these methods may someday compete with more traditional approaches is a question which cannot be answered at the present time: it will depend on the new computer architectures as well as on the possibility to develop very simple models to reproduce the most complex phenomena taking place in the approach of fully developed turbulence or plastic flows. In any event, these molecular methods are already used, and sometimes in an applied engineering context, to study strong shock waves, chemistry induced shocks or motion of dislocations in plastic flows, that is in domains where a fully continuum description appears insufficient. The main topic of our Institute was the molecular simulations of fluid flows.

The project to hold this Institute was made three years ago, in the summer of 1989 during a NATO workshop in Brussels on the same subject. It was felt by the participants that it would be profitable to have a longer and more tutorial meeting. We decided to organize it in the form of a summer school where all methods for computing flows from molecular modelling could be taught and, to some extent, confronted. However, we did not want to restrict ourselves to the technique's aspects and we enlarged the spectrum of the lectures by including the study of fundamental problems as well as of physical applications. It is a pleasure to acknowledge the encouragement we received from all members of the scientific committee. A non-negligible part of this encouragement is certainly due to the quality of the Parisian restaurant "Le Petit Zinc" where this project has been discussed.

The division and presentation of the articles of these proceedings has been made a posteriori by us. The first part is devoted to the Non-Equilibrium Molecular Dynamics studies. This contains articles which either discuss the theoretical foundation of the method or apply the method to specific non-equilibrium flows. Besides, Bill Hoover provided us with a personal view of the history of Non-Equilibrium Molecular Dynamics: this might give an opportunity to young researchers to realize that progress in Physics is often the result of controversies Applications to rheology (Ciccotti, Ryckaert, Pierieoni, Michopoulos), Shock waves (Holian, Carter), strong temperature gradients (Mansour) and convective instabilities (Rapaport) are the main subjects treated.

Lattice gas papers are th~ most numerous and this is an evidence of the excitement this technique has brought to the community of computational physicists. Theoretical foundations are explained in the basic introduction given by Ernst. Quite interesting also was the study by Levermore of the rigorous limits which lead to the hydrodynamic Navier-Stokes equations. Two articles deal with lattice-Boltzmann simulations (Mc Namara and Succi): the ability of

vii

lattice-Boltzmann to reach high Reynolds number flow simulation has been also discussed during the (second) round-table discussion which is presented in the next chapter, after presentation of the DSMC method by its main author (Bird) and of the Brownian Dynamical simulation technique (Bossis).

Applications in lattice-gas simulations are numerous and they range from the study of diffusion in various lattice models (Cohen) to the flows in porous media (Rothman). Colloidal systems have been treated by a method which combines lattice-gas efficiency for the fluid motion and dynamics of the colloidal particles (van der Hoef): there is little doubt that the ability to mix different approaches on different time and spatial scales will be a key point in the success of the future methods proposed (see also Hoover). It is worth mentioning that a (more research oriented) workshop was held in Nice in June 91, just before our school, and that many papers were also presented at this conference: the proceedings of the Nice meeting are to be published as a special issue of the Journal of Statistical Physics: they are complementary to ours.

In the fourth part, a few fundamental problems are reviewed. The paper by Frisch is on a modern view of the Kolmogorov theory. Besides its historical interest, it also introduces into the delights of turbulence as seen from a modern point of view. Two other papers follow, which discuss the relation between Lyapunov exponents, characteristic of the chaotic behavior in phase space, and transport coefficients, expressions of the dissipative nature of fluids. This relation was also discussed in a round-table and we have tried to keep the lively character of the exchanges in the report. The discussions of this round-table as well as of the other one, were taperecorded, written down by Brigitte Herpigny (thank you Brigitte) and then sent to the authors for corrections.

Other applications describe the parallel between the statistical approach to turbulence and to fractures in solids (Chudnovsky), the simulation of membranes by phenomenological lattice models (Abraham) and the use of cellular automata-like models for the plastic flows in crystals (Pontikis) and of NEMD on granular flows (Thompson).

At the IUPAP meeting organized in Brussels in 1956, Berni Alder presented his fIrst Molecular Dynamics studies of assemblies of hard spheres. As can be read in the proceedings of this meeting, Berni was then asked whether his new method could lead to a derivation of hydrodynamics from fIrst principles: Berni replied that one could imagine computations of fluid flow in high-speed aerodynamics based on MD with the development of larger computing facilities. It is therefore quite natural that this Institute was held to honor Berni's 65th birthday: not only did his work set a high standard for subsequent work in the fIeld of non-equilibrium fluids, but also it has been very important in the understanding of the connection between hydrodynamic modeling and microscopic motion. This book ends with the long-time tails story as it was told to us by its discoverer.

Our only hope is that the reports made accessible in these proceedings can give readers a little bit of the pleasure we had in participating to this school.

Michel Mareschal, CECAM (Orsay), and Brad Holian, Los Alamos

November 1991

viii

ACKNOWLEDGEMENTS

The main financial contribution to the Institute expenses has come from the NATO special programme on "Chaos, Order and Patterns". The European Economic Community has also awarded a fellowship to cover part of our expenses. The Sardinian region, the Italian C.N.R. (parallel computing programme), Belgian government (Poles d'Attraction Interuniversitaires and Services de la Programmation de la Politique Scientifique), IBM-Italy and Apple Computers have provided financial and material support.

The Secretariat of the Institute was made by Sonia Wellens in Brussels: warm thanks for the work achieved. Locally, in Aighero, we received a very important support from the department of Chemistry of the University of Sassari: the organization committee made of Piero Demontis and Pino Suffritti, has quite efficiently solved an incredible amount of problems: these were due in part to the fact that we were inaugurating the CORISA, a new research Center capable of housing conferences. Last, but not least, Brigitte Herpigny, the scientific secretary, has been essential in the friendly atmosphere which prevailed during the entire meeting.

ix

SCIENTIFIC COMMITIEE

Berni J. Alder, Livermore, Honorary Chairman

Jean-Pierre Boon, Universite Libre de Bruxelles

Giovanni Ciccotti, Universita "La Sapienza" di Rorna and CECAM (Orsay)

Eddy G. D. Cohen, Rockefeller University

Brad Lee Holian, Los Alamos National Laboratory, director

Michel Mareschal, Universite Libre de Bruxelles and CEA (Saclay), director

Gregoire Nicolis, Universite Libre de Bruxelles

Ilya Prigogine, Solvay Institutes (Brussels) and University of Texas at Austin

Farid F. Abraham Berni J. Alder Roberto Benzi Graeme A. Bird Jean-Pierre Boon George Bossis Alexander Chudnovsky, Giovanni Ciccotti, Eddy G. D. Cohen Gary D. Doolen Matthieu T. Ernst Denis 1. Evans Mitchell J. Feigenbaum Uriel Frisch Pierre Gaspard

LECTURERS

Brad Lee Holian William Graham Hoover Joel L. Lebowitz Henk N. W. Lekkerkerker David Levermore Mohammed Malek Mansour Gregoire Nicolis Harald A. Posch Daniel H. Rothman Jean-Paul Ryckaert John Somers Sauro Succi Martin van der Hoef Carter White

CONTENTS

I. INTRODUCTION

From Fluid Particles to Physical Particles: Computing Hydrodynamics M. Mareschal and B.L. Holian .................................................................................. 1

From Global, ala Kolmogorov 1941, Scaling to Local Multifractal Scaling in Fully Developed Turbulence

U. Frisch ................................................................................................................. 13

II. NON-EQUILIBRIUM MOLECULAR DYNAMICS

Theoretical Foundation and Rheological Application of Non-equilibrium Molecular Dynamics

O. Ciccotti, C. Pierleoni and J-P. Ryckaert ............................................................ 25

Nonequilibrium Molecular Dynamics at Livermore and Los Alamos W.O. Hoover .......................................................................................................... .47

Shock Waves and Spallation by Molecular Dynamics B.L. Holian ............................................................................................................. 75

Molecular Dynamic Study of Density Fluctuation in a Non-Equilibrium System M. Malek Mansour, M. Mareschal, O. Sonnino

and E. Kestemont.. .................................................................................. 87

Temporal Periodicity in Microscopic Simulation of Rayleigh-Benard Convection D.C. Rapaport. ...................................................................................................... 101

NEMD Simulations and the Rheology of Liquid Hydrocarbons A. Berker, S. Chynoweth and Y. Michopoulos .................................................... 105

Molecular Dynamics Simulations of Shock-Induced Chemistry: Application to Chemically Sustained Shock Waves

C.T. White, D.H. Robertson, M.L. Elert and D.W. Brenner ................................ 111

III. LATTICE GASES

Lattice Boltzmann Simulation of High Reynolds Number Fluid Flow in Two Dimensions

G. Mc Namara and B.1 Alder .............................................................................. 125

xi

New Types of Diffusion in Lattice Gas Cellular Automata E.G.D. Cohen ........................................................................................................ 137

Statistical Mechanics and Kinetic Theory of Lattice Gas Cellular Automata M. H. Ernst ........................................................................................................... 153

A Mean Field Theory for Biased Lattice Gas Models H.J. Bussemaker and M.H. Ernst. ......................................................................... 169

Fluid Dynamical Limits of Discrete Kinetic Theories D. Levennore ....................................................................................................... 173

The Lattice Boltzmann Equation: Theory and Application S. Succi, R. Benzi, A. Cali and M. Vergassola .................................................... 187

Study of Diffusion in Lattice-Gas Fluids and Colloids M.A. van der Hoef and D. Frenkel ...................................................................... 205

Simple Models of Complex Fluids D. H. Rothman ...................................................................................................... 221

IV. OTHER SIMULATION METHODS

A Contemporary Implementation of the Direct Simulation Monte Carlo Method G.A. Bird ............................................................................................................... 239

Brownian and Stokesian Dynamics G. Bossis and 1. F. Brady ...................................................................................... 255

Round Table Discussions (I): Issues in Hydrodynamic Simulations ................................. 271

V. CHAOS, TURBULENCE AND IRREVERSIBILITY

Lyapunov Exponents and Bulk Transport Coefficients DJ. Evans, S. Sarman, A. Baranyai, E.G.D. Cohen

and G. P. Morriss ................................................................................... .285

Dynamical Chaos Underlying Diffusion in the Lorentz Gas P. Gaspard and F. Baras ....................................................................................... .301

Generalized Gaussian Dynamics, Phase-Space Reduction and Irreversibility: A Comment

G. Eyink and J.L. Lebowitz ................................................................................. .323

Round Table Discussions (II) : Irreversibility and Lyapunov Spectra .............................. .327

VL RELATED TOPICS

Statistical Fracture Mechanics A. Chudnovsky and B. Kunin .............................................................................. .345

Computational Statistical Mechanics of Tethered Membranes F.F. Abraham ....................................................................................................... .361

Granular Flow at Low Shear Rates P.A. Thompson and G.S. Grest. ............................................................................ 403

xii

Three-Dimensional Simulations of Plastic Flow in Crystals B. Devincre, V. Pontikis, Y. Brechet, G. Canova,

M. Condat and L. Kubin ....................................................................... .413

VIT. RECOLLECTIONS

Concluding Remarks: The Long-Time Tails Story BJ. Alder .............................................................................................................. 425

Participants ........................................................................................................................ .431

Index .................................................................................................................................... 437

xiII