Table Of ContentLecture Notes
ni scisyhP
Edited by .J Ehlers, M~nchen, .K Hepp, Zi3rich
.R Kippenhahn, MiJnchen, .H WeidenmiJller, A. Heidelberg
and .J Zittartz, n16K
Managing Editor: W. Beiglb6ck, Heidelberg
141
Seventh International
Conference
on Numerical Methods ni
Fluid Dynamics
Proceedings of the Conference, Stanford ,ytisrev!nU
,drofnatS California dna NASA/Ames ).A.S.U(
enuJ 23-27, 0891
Edited .W yb .C Reynolds dna .R .W MacCormack
¢
galreV-regnirpS
Berlin Heidelberg New York 1.891
srotidE
William Craig Reynolds
Mechanical Engineering Dept. Stanford University
Stanford, CA 94305, USA
Robert William MacCormack
Mail Stop 202A-1, NASA-Ames Research Center
Moffett Field, CA 94035, USA
ISBN 3-540-10694-4 Springer-Verlag Berlin Heidelberg New York
ISBN 0-38?-10694-4 Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part
of the material is concerned, specifically those of translation, reprinting, re-use of
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© by Springer-Verlag Berlin Heidelberg 1891
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2153/3140-543210
Contents
Invited Lectures
CHAPMAN, D.R.: Trends and Pacing Items in Computational Aerodynamics ......... 1
LONGUET-HIGGINS, M.S.: Polygon Transformations in Fluid Mechanics ............ 12
RUSANOV, V.V.: On the Computation of Discontinuous Multi-
Dimensional Gas Flows .................................................... 31
VlVIAND, H.: Pseudo-Unsteady Methods for Transonic Flow Computations ......... 44
Contributed Papers
ARLINGER, B.: Axisymmetric Transonic Flow Computations Using a
Multigrid Metho.d. ........................................................ 55
BAKER, G.R., and ISRAELI, M.: Numerical Techniques for Free Surface
Motion with Application to Drop Motion Caused by Variable
Surface Tension ........................................................... 61
BARTELS, F.: Viscous Flow Between Concentric Rotating Spheres ................ 68
BAUM, H.R., CIMENT, M., DAVIS, R.W., and MOORE, E.F.: Numerical
Solutions for a Moving Shear Layer in a Swirling Axisymmetric Flow ........ 74
BENQUE, J.P., COEFFE, Y., and HERLEDAN, R.: Flow Induced by a Jet in a
Cavity - Measurements and 3D Numerical Simulation ......................... 80
BOOK, D., BORIS, J., KUHL, A., ORAN, E., PICONE, M., and ZALESAK, S.:
Simulation of ComDlex Shock Reflections from Wedges in Inert and
Reactive Gaseous Mixtures ................................................... 84
BRILEY, W.R. and McDONALD, H.: Computation of Three-Dimensional
Horseshoe Vortex Flow Using ~he Navier-Stokes Equations ................... 91
BRUSHLINSKY, K.V., SAVEL'EV, V.V., and ZUEVA, N.M.: Numerical Analysis
of Stability in Magnetohydrodynamical Problems ............................ 99
BUNEMAN, O.: Compressible Flow Simulation Using Hamilton's Equations
and Clebsch-type Vortex Parameters ....................................... 103
CHATTOT, J.J., GUIU-ROUX, J. and LAMINIE, J.: Finite Element Calculation
of Steady Transonic Flow in Nozzles Using Primary Variables .............. 107
CHEN, H.: Improved Surface Velocity Method for Transonic Finite-
Volume Solutions ......................................................... 113
CLOUTMAN, L.D., DUKOWICZ, J.K., and RAMSHAW, J.D.: Numerical Simulation
of Reactive Flow in Internal Combustion Engines .......................... 119
COUET, B., and LEONARD, A.: Mixing Layer Simulation by an Improved
Three-Dimensional Vortex-in-Cell Algorithm ............................... 125
CUVELIER, C.: On the Numerical Solution of a Capillary Free Boundary
Problem Governed by the Navier-Stokes Equations .......................... 132
VI
DECONINCK, H., and HIRSCH, C.: Transonic Flow Calculations with
Higher Order Finite Elements ............................................ 138
DEMIRDZIC, I., GOSMAN, A.D., and ISSA, R.: A Finite-Volume Method for
the Prediction of Turbulent Flow in Arbitrary Geometries ................ 144
DENNIS, S.C.R., and INGHAM, D.B.: A Finite Difference Method for the
Slow Motion of a Sphere in a Rotating Fluid ............................. 151
DERVIEUX, A., and THOMASSET, F.: Multifluid Incompressible Flows by
a Finite Element Method ................................................. 158
DULIKRAVICH, D.S.: Numerical Calculation of Transonic Axial
Turbomachinery Flows .................................................... 164
DWYER, H.A., RAISZADEH, F., and OTEY, G.: A Study of Reactive Diffusion
Problems with Stiff Integrators and Adaptive Grids ...................... 170
EISEMAN, P.R.: Coordinate Generation with Precise Controls ................. 176
FLETCHER, C.A.J.: An Alternating Direction Implicit Finite Element
Method for Compressible, Viscous Flow ................................... 182
FROMM, J.: Finite Difference Computation of the Capillary Jet, Free
Surface Prob.l.e.m. ..................................................... 188
FUJII, K.: Simultaneous Solutions of Inviscid Flow and Boundary
Layer at Transonic Speeds ............................................... 194
HERBERT, T.: Numerical Studies on Nonlinear Hydrodynamic Stability by
Computer-Extended Perturbation Series ................................... 200
HIRSH, R.S., and FERGUSON, R.E.: Compact Differencing Schemes for
Advective Problems ................... ~ .................................. 206
HORIUTI, K., KUWAHARA, K., and Oshima, Y.: Study of Two-Dimenslonal
Flow Past an Elliptic Cylinder by Discrete-Vortex Approximation ......... 212
HUANG, D., LI, Y.F., HUANG, L.P., and LIU, Y.Z.: Two Analytical Solutions
for the Reflection of Unsteady Shock Wave and Relevant Numerical Tests.. 218
INOUE, O.: Separated Boundary Layer Flows with High Reynolds Numbers ....... 224
ISRAELI,-M., and UNGARISH, M.: Improvement of Numerical Schemes by
Incorporation of Approximate Solutions Applied to Rotating
Compressible Flows ...................................................... 230
JOHNSON, G.M.: An Alternative Approach to the Numerical Simulation
of Steady Inviscid Flow ..................... ............................. 236
KENTZER, C.P.: Reformulation of the Method of Characteristics for
Multidimensional Flows .................................................. 242
KHOSLA, P.K., and RUBIN, S.G.: A Conjugate Gradient Iterative Method ....... 248
KORVlNG, C.: A Numerical Method for the Wave Resistance of a Moving
Pressure Distribution on the Free Surface ............................... 254
LA HARGUE, J.P., and SOUBBARAMAYER: Numerical Methods for Solving Some
Fluid Mechanics Problems Met in a Strongly Rotating Gas Centrifuge ...... 260
LEE, K.D., and RUBBERT, P.E.: Transonic Flow Computations Using Grid
Systems with Block Structure ............................................ 266
LINDROOS, M.: On the Convergence of Iterative Methods for Solving the
Steady-State Navier-Stokes Equations by Finite Differences .............. 272
METCALFE, R.W., and RILEY, J.J.: Direct Numerical Simulations of
Turbulent Shear Flows ................................................... 279
MOL, W.J.A.: Numerical Solution of the Navier-Stekes
Equations by Means of a Multigrid Method and Newton-Iteration .......... 285
MORF, R.H., ORSZAG, S.A., MEIRON, D.I., FRISCH, U., and
MENEGUZZI, M.: Analytic Structure of High Reynolds Number Flows ....... 292
NEDELEC, J.C.: Incompressible Mixed Finite Elements for the
Stokes' Equation in IR ..... ~ 3 .................... ...................... 299
NICHOLS, B.D., HIRT, C.W., and HOTCHKISS, R.S.: A Fractional Volume
of Fluid Method for Free Boundary Dynamics ............................. 304
ONO, K., KUWAHARA, K., and OSRIMA, K.; ~Numerical Analysis of Dynamic
Stall Phenomena of an Oscillating Airfoil by the Discrete-
Vortex Approximation ................................................... 310
ORLANDI, P.: Implicit Non-lterative Scheme for Turbulent Unsteady
Boundary Layers ........................................................ 316
PANDOLFI, M., and ZANNETTI, L.: A Physical Approach to Solve
Numerically Complicated Hyperbolic Flow Problems ....................... 322
PATERA, A.T., and ORSZAG, S.A.: Transition and Turbulence in Planar
Channel Flows .......................................................... 329
PIRUMOV, U.G., PROKHOROV, M.B., and RYZHOV, Y.A.: Some Mathematical
Problems of the Air Basin Preservation ................................. 336
REDDY, K.C.: A Projection Method Based on Gaussian Quadratures with
Application to Compressible Navier-Stokes Equations .................... 342
RIZZI, A., and SK~LLERMO, G.: Semidirect Solution to Steady
Transonic Flow by Newton's Method ...................................... 349
ROE, P.L.: The Use of the Riemann Problem in Finite Difference
Schemes ................................................ ................ 354
RYZHOV, O.S., and ZHUK, V.I.: Stability and Separation of Freely
Interacting Boundary Layers ............................................ 360
SANKAR, N.L., and TASSA, Y.: An Algorithm for Unsteady Transonic
Potential Flow Past Airfoils .... ....................................... 367
SHIDLOVSKY, V.P.: Numerical Analysis of the Asymptotic Flow
Behavior about the Edge of a Rotating Disk ............................. 373
SHOKIN, Y.: Analysis of Conservative Properties of the Difference
Schemes by the Method of Differential Approximation .................... 383
SOD, G.A.: A Generalized Hybrid Random Choice Method with Application
to Internal Combustion Engines ......................................... 387
VI
STRANI, M., and PIVA, R.: Computational Models of Convective
Motions Induced at Fluid Interfaces .................................... 393
TIEM, D.H., and GATIGNOL, R.: Free Molecular Flows Past a Concave Body .... 399
VAN DYKE, M.: Successes and Surprises with Computer-Extended Series ....... 405
VELDMAN, A.E.P., and DIJKSTRA, D.: A Fast Method to Solve Incompressible
Boundary-Layer Interaction Problems ........ ............................ 411
WAI, J.C., and YOSHIHARA, H.: Viscous Transonic Flow Over Airfoils ........ 417
WANG, R.Q., JIAO, L.Q., and LIU, X.Z.: Numerical Methods for the
Solution of the Simplified Navier-Stokes Equations ..................... 423
WARMING, R.F., and BEAM, R.M.: Recent Advances in the Development of
Implicit Schemes for the Equations of Fluid Dynamics ................... 429
WOODWARD, P.R., and COLELLA, P.: High Resolution Difference Schemes
for Compressible Gas Dynamics .......................................... 434
WU, H.M., and YANG, M.L.: SOMS - A Second Order Monotone Scheme for
Shock Capturing and Its Application to the Solutions of
Compressible Navier-Stokes Equations ................................... 442
YANENKO, N.N., KOVENYA, V.M., TARNAVSKY, G.A., and CHERNY, S.G.:
Economical Methods for Solving the Problems of Gas Dynamics ............ 448
YANENKO, N.N., GRIGORYEV, Y.N., and IVANOV, M.S.: Numerical
Simulation of Rarefied Gas Flows ....................................... 454
ZANG, T.A., and HUSSAINI, M.Y.: Mixed Spectral/Finite Difference
Approximations for Slightly Viscous Flows .............................. 461
ZHU, Y.-I, and CHEN, B.-m.: An Accurate Method for Calculating the
Interactions between Discontinuities in Three Dimensional Flow ......... 467
LIST OF PARTICIPANTS ....................................................... 473
Editors' Preface
This volume of Lecture Notes in Physics contains papers presented at the
Seventh International Conference on Numerical Methods in Fluid Dynamics, held
at Stanford University and the NASA Ames Research Center in the U.S.A., June
23-27, 1980. The papers were selected from abstracts submitted from all over
the world by three papers selection groups, one based in the USA, another in
Europe, and the third in the USSR. Briefs of the papers were distributed at
the Conference. This volume provides the full paper.
The book includes invited papers by D.R. Chapman, M.S. Longuet-Higgins,
".V.V Rusanov and H. ~iviand, plus 68 contributed papers. The invited papers
appear first, followed by the contributed papers in alphabetical order by
first author.
The Conference was attended by over 280 scientists. In addition to the
strong representation from the USA, there were several delegations from the
USSR, France, Germany, China, and many other countries. A list of the partici-
pants is given at the end of the volume.
The editors served as the general Conference Co-chalrmen.We are indebted
to our many colleagues who helped with the details of the meeting, but especially
to Mamoru Inouye'of the Ames Research Center, who supervised all of the local
arrangements, and to Dianne Sinn, the Conference Secretary.
Financial support for the Conference was provided by the National Science
Foundation, Air Force Office of Scientific Research and the Office of Naval
Research through a grant arranged by the last. In addition, the National
Aeronautics and Space Administration's Ames Research Center contributed through
provision of facilities and transportation.
We are indebted to Dr. .W BeiglbSck and the editorial staff of Springer-
Verlag for valuable assistance in preparing these proceedings.
December II, 1980 W.C. Reynolds
R.W. MacCormack
(Editors)
Papers Selection Committee Chairmen
U.S.A. R.W. MacCormack
U.S.S.R. O.M. Belotserkovskii
European R. Temam
INTERNATIONAL CONFERENCE ON
NUMERICAL METHODS INFLUID DYNAMICS
First Conference: Novosibirsk, USSR, 1969
Second Conference: Berkeley, California, USA, 1970
Third Conference: Paris, France, 1972
Fourth Conference: Boulder, Colorado, USA, 1974
Fifth Conference: Enschede, the Netherlands, 1976
Sixth Conference: Tbilisi, USSR, 1978
Seventh Conference: Stanford University and NASA/Ames, USA, 1980
TRENDS AND PACING ITEMS IN COMPUTATIONAL AERODYNAMICS
Dean .R Chapman
Stanford University
ABSTRACT
A perspective is presented of trends in computational aerodynamics, and of
important technology development items that pace future advanced applications.
From a survey of AIAA Journal papers published during the past two decades, the
growth trends and the progressively increasing emphasis on code development for
viscous, compressible, turbulentflow are illustrated. These trends are reflected
in the chronology of introduction by the aerospace industry of new computational
methods in aircraft design. Key pacing items outlined are: automatic grid genera-
tion for nonlinear inviscid computations; advanced computers, improved efficiency
of numerical methods, and improved turbulence models for Reynolds-averaged Navier-
Stokes computations; advanced computers, time-dependent three-dimensional law-of-
the-wall, code development, improved efficiency of numerical methods, andimproved
subgrid-scale turbulence modeling for large eddy simulations.
.I INTRODUCTION
The evolution of computational aerodynamics in recent years has provided a
major new technological capability of recognized practical importance to the aircraft
industry. This new capability can substantially increase airplane performance while
reducing risk, design time, and testing requirements (Dillner and Koper, 1979).
Moreover, it is evident that much more evolution of capability still lies ahead.
Of central concern to this paper is the circumstance that some quite diverse
items of technology pace the overall advances in computational aerodynamics. These
"pacing items" represent key technology developments which will primarily determine
when a new and advanced level of computational capability may become feasible to use
in future aerodynamic applications. The objectives of this paper are to provide a
synoptic look at underlying trends in computational aerodynamics and at various pacing
items relevant to further advances. These pacing items refer to developments required
to reach a level at which industry could begin to apply advanced codes. The actual ex
tent of use in engineering design thereafter can involve other important factors not
Considered herein.
II. TRENDS
To obtain a perspective of the growth trends in computational aerodynamics, a
survey was made of the papers published in the AIAA Journal during the past 20 years.
Over this period the annual number of papers and synoptics did not vary widely,
usually ranging from 200 to 300 per year. These were classified into the following
categories: "linearized inviscid," mainly papers on panel methods; "nonlinear in-
viscid," e.g., transonic flow, supersonic blunt body flow, etc,; "boundary layers,"
including viscous shock-layer papers and papers coupling external flow codes to
boundary layer codes; "Navler-Stokes," including the parabolized and thln-layer
versions; "vortex dynamics;" and "large eddy simulations" Results of the survey
are presented in Fig. .i The fraction of yearly AIAA papers involving computational
aerodynamics has grown from about 1% in the early 1960's to 22% in 1979. The small
peak in 1966 reflects blunt-body papers relevant to the Apollo program, whereas the
strong growth trend beginning in 1971 reflects papers relevant to aircraft design.
While linearized inviscld computations have remained a small part of the total and
nonlinear Inviscid methods have enjoyed a modest growth, the papers on viscous-flow
computation have contributed most of the pronounced growth. This is to be expected
for papers relevantto aircraft aerodynamics. Since practical computations of
/
viscous turbulent flow nec-
7 essarily involve some type
of turbulence modeling, e.g.
gJ
..J Reynolds-averaged or sub-
p- LINEARIZED INVISClD. M grid scale, it is antici-
o" pated that future turbulence
< NONLINEAR INVISClD ,~/
modeling for compressible
.< J J !. /LAYERS BOUNDARY flow will become a pervasive
¢z ¢ part of computational aero-
dynamics.
O
I-- 1. A perspective of this
<
< growth trend can be grasped
< NAVIER by reference to the other
M. disciplines covered in the
O \\\~ XETRovSEKOTS/ AIAA Journal. Roughly one-
Z
half of the publications
O • 'i!;, ~!N~' ' /DYNAMICS are devoted to aerodynamics,
J¢< j ~'/ ~ " LARGE EDDY and one-half to the combined
,/ SIMULATION disciplines of propulsion,
" 0 structural mechanics, thermo-
1960 1970 1980 physics, and aircraft tech-
YEAR nology. Thus, computational
aerodynamics, in growing to
nearly one-fourth of the
Figure i. Growth of computational aerodynamics
AIAA articles, has grown to
about one-half of the over-
all aerodynamics papers.
COMPUTATIONAL BOUNDARY LAYERS The growth trend over
the past two decades has
been reflected at various
times throughout this period
LINEARIZED INVISClD by the introduction in air-
craft design of new and
advanced computational aero-
dynamics methods. The years
NONLINEAR INVISClD
during which successively
advanced computational tech-
niques were introduced are
Re-AVE. NAVIER-STOKES depicted in the bar graph
of Fig. 2. These data are
based partly on publication
dates of key papers, and
LARGE EDDY SIMULATION partly on information ob-
tained from colleagues in
i I i I I the aircraft industry. In
each case, the use of a new
1960 1970 1980
advanced stage begins with
YEAR
limited application to 2D
airfoils, and later evolves
to 3D as both computers and
Figure .2 Chronology of introduction of compu-
codes become further ad-
tational aerodynamic techniques in aircraft
vanced. It is noted that
design.
for both the linearized and
the nonlinear inviscid
stages, the 3D external flow
codes were coupled to 3D boundary-layer codes shortly after both types of code were
developed.
Although the Reynolds-averaged Navier-Stokes codes apparently have not yet been
applied in practical design, the bar graph indicates that thls is anticipated In the
early 1980's. Navler-Stokes codes developed for transonic aileron buzz, afterbody
