Table Of ContentMultiblock Grid
Generation
Results of the EC/BRITE-
EURAM Project
EUROMESH, 1990-1992
Edited by
Nigel P. Weatherill,
Michael J. Marchant,
and D. A. King
Notes on Numerical Fluid Mechanics (NNFM) Volume 44
Series Editors: Ernst Heinrich Hirschel, Munchen
Kozo Fujii, Tokyo
Bram van Leer, Ann Arbor
Keith William Morton, Oxford
Maurizio Pandolfi, Torino
Arthur Rizzi, Stockholm
Bernard Roux, Marseille
Volume 26 Numerical Solution of Compressible Euler Flows (A. Dervieux I B. van Leer I
J. Periaux I A. Rizzi, Eds.)
Volume 27 Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (B. Roux, Ed.)
Volume 28 Vortical Solution of the Conical Euler Equations (K. G. Powell)
Volume 29 Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid
Mechanics (P. Wesseling, Ed.)
Volume 30 Numerical Treatment of the Navier-Stokes Equations (w. Hackbusch I
R. Rannacher, Eds.)
Volume 31 Parallel Algorithms for Partial Differential Equations (w. Hackbusch, Ed.)
Volume 32 Adaptive Finite Element Solution Algorithm for the Euler Equations
(R. A. Shapiro)
Volume 33 Numerical Techniques for Boundary Element Methods (w. Hackbusch. Ed.)
Volume 34 Numerical Solutions of the Euler Equations for Steady Flow Problems
(A. Eberle I A. Rizzi I H. E. Hirschel)
Volume 35 Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics
(J. B. Vos I A. Rizzi II. L. Ryhming, Eds.)
Volume 36 Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows
(M. Deville I T.-H. La I Y. Morchoisne, Eds.)
Volume 37 Supercomputers and Their Performance in Computational Fluid Mechanics
(K. Fujii, Ed.)
Volume 38 Flow Simulation on High-Performance Computers I (E. H. Hirschel, Ed.)
Volume 39 3-D Computation of Incompressible Internal Flows (G. Sottas II. L. Ryhming. Eds.)
Volume 40 Physics of Separated Flow - Numerical, Experimental, and Theoretical Aspects
(K. Gersten, Ed.)
Volume 41 Incomplete Decompositions (ILU) - Algorithms, Theory and Applications
(W. Hackbusch I G. Wittum, Eds.)
Volume 42 EUROVAL - An European Initiative on Validation of CFD Codes (w. Haase I
F. Brandsma I E. Elsholz I M. Leschziner I D. Schwamborn, Eds.)
Volume 43 Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects
Proceedings of the Fourth International Conference on Hyperbolic Problems,
Taormina, Italy, April 3 to 8,1992 (A. Donato I F. Oliveri, Eds.)
Volume 44 Multiblock Grid Generation - Results of the ECIBRITE-EURAM Project EUROMESH,
1990-1992 (N. P. Weatherilll M. J. Marchant I D. A. King, Eds.)
Volume 45 Numerical Methods for Advection - Diffusion Problems (c. B. Vreugdenhil I B. Koren,
Eds.)
Volumes 1 to 25 are out of print.
The addresses of the Editors and further titles of the series are listed at the end of the book.
Multiblock Grid
Generation
Results of the ECIBRlTE-EURAM
Project EUROMESH, 1990-1992
Edited by
Nigel P. Weatherill,
Michael J. Marchant,
and D. A. King
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Multiblock grid generation: results of the Ec/BRlTE-EURAM
project EUROMESH, 1990-19921 ed. by Nigel P. Weatherill ... -
Braunschweig; Wiesbaden: Vieweg, 1993
(Notes on numerical fluid mechanics; 44)
ISBN-J3: 978-3-528-07644-3 e-ISBN-J3: 978-3-322-87881-6
DOl: 10.1007/978-3-322-87881-6
NE: Weatherill, Nigel P. [Hrsg.]; Europaische Gemeinschaften; GT
All rights reserved
© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweiglWiesbaden, 1993
Softcover reprint of the hardcover 1st edition 1993
Vieweg ist a subsidiary company of the Bertelsmann Publishing Group International.
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.
Printed on acid-free paper
ISSN 0179-9614
ISBN-J3: 978-3-528-07644-3
Foreword
Computational Fluid Dynamics research, especially for aeronautics, continues to be a
rewarding and industrially relevant field of applied science in which to work. An
enthusiastic international community of expert CFD workers continue to push forward
the frontiers of knowledge in increasing number. Applications of CFD technology in
many other sectors of industry are being successfully tackled. The aerospace industry
has made significant investments and enjoys considerable benefits from the application
of CFD to its products for the last two decades. This era began with the pioneering work
ofMurman and others that took us into the transonic (potential flow) regime for the first
time in the early 1970's. We have also seen momentous developments of the digital
computer in this period into vector and parallel supercomputing. Very significant
advances in all aspects of the methodology have been made to the point where we are on
the threshold of calculating solutions for the Reynolds-averaged Navier-Stokes
equations for complete aircraft configurations.
However, significant problems and challenges remain in the areas of physical
modelling, numerics and computing technology. The long term industrial requirements
are captured in the U. S. Governments 'Grand Challenge' for 'Aerospace Vehicle
Design' for the 1990's: 'Massively parallel computing systems and advanced parallel
software technology and algorithms will enable the development and validation of
multidisciplinary, coupled methods. These methods will allow the numerical simulation
and design optimisation of complete aerospace vehicle systems throughout the flight
envelope'.
This volume contains a set of papers describing work carried out during the EuroMesh
project on 'Multi-Block Mesh Generation for Computational Fluid Dynamics'. The
work was performed under a cost shared research contract (AERO 0018) within the
programme BRITFJEURAM Area 5 Aeronautics of the Commission of the European
Communities (CEC). EuroMesh was a pre-competitive research project lead by British
Aerospace Regional Aircraft Ltd under the umbrella of the Aeronautics initiative
managed and administered by the CEC DGXIIF. The project ran for two years with
fourteen partners (6 from the aeronautics industry, 3 universities and 5 research
institutes) from seven countries from the European Community and EFTA.
I would like to thank all those involved with EuroMesh for their enthusiasm and
cooperation. In particular I would like to thank the Task Managers and Working Group
Coordinators for their efforts. I would also like to offer my gratitude to Nigel Weatherill
and Michael Marchant (University College of Swansea) for their assistance in the
preparation of this publication and to Drietrich Knoerzer (CEC-DGXIIh) for his
guidance on the running of the project.
D. A. King, BAe Woodford, February 1993.
v
Contents
Page
I. Introduction
The EUROMESH Project 3
D. A. King
An introduction to grid generation using the multiblock approach 6
N. P. Weatherill
II. Topology Generation. 19
Topology generation within CAD systems 21
V. Treguer-Katossky, D. Bertin and E. Chaput
A topological mOOeller 27
R. Scateni
Advancing front technique used to generate block quadrilaterals 32
T. Schbhfeld
III. Surface Grid Generation and Geometry Modelling 35
Surface mesh generation using projections 37
J. M. de la Viuda
Generation of surface grids using elliptic PDEs 45
P. Weinerfelt
Generation of structured meshes over complex surfaces 48
B. Morin and V. Treguer-Katossky
Surface modelling using Coons multipatch and non-uniform rational surface 55
E. Chaput
Reparametrization of block boundary surface grids 63
S. Farestam
Ain:raft surface generation 71
H. Sobieczky
VII
Contents (continued)
Page
IV. Volume Grid Generation 17
Use ofONERA grid optimization method at CASA 79
J. M. de Ia Viuda, J. J. Guerra and A. Abbas
Multi-block mesh generation for complete aircraft configurations 86
K. Becker and S. Rill
Development of 3D multi-block mesh generation tools 117
J. Oppelstrup, o. Runborg, P. Mineau, P. Weinerfelt, R. Lehtimi'ki and B. Arlinger
Multi-block mesh optimization 130
T. Fol and V. Treguer-Katossky
Smoothing of grid discontinuities across block boundaries 139
P. Mineau
V. Grid Optimization and Adaption Methods 149
Grid adaption in computational aerodynamics 151
R. Hagmeijer and K. M. J. de Cock
Embedding within structured multi-block computational fluid dynamics
simulation 169
S. N. Sheard and M. C. Fraisse
Adaptive mesh generation within a 2D CFD environment using optimisation
techniques 179
A.F.E.Home
Two dimensional multi-block grid optimisation by variational techniques 189
M. R. Morris
Local mesh enrichment for a block structured 3D Euler solver 199
T. Schomeld
The adaptation of two-dimensional multiblock structured grids using a
PDE-based method 207
D. Catherall
Contribution to the development of a multiblock grid optimization and
adaption code . 224
O-P. Jacquotte, G. Coussement, F. Desbois and C. Gaillet
General grid adaptivity for flow simulation 263
M. J. Marchant, N. P. Weatherill and J. Szmelter
Error estimates and mesh adaption for a cell vertex finite volume scheme 290
J. A. Mackenzie, D. F. Mayers and A. J. Mayfield
Multigrid methods for the acceleration and the adaptation of the transonic
flow problems 311
A. E. Kanarachos, N. G. Pantelelis and I. P. Voumas
VIII
I. INTRODUCTION
1
The EUROMESH Project
D.A. King
Research Department
British Aerospace RAL
Woodford Aerodrome,Woodford,Cheshire,SK7 lQR - UK
Computational Fluid Dynamics (CFD) methods are now well established as an integral
part of the aerodynamic design process throughout the civil aerospace industry. They
have been successfully employed in the wing design for modern civil transport aircraft
and executive jets over the last two decades. Some significant increments in wing per-
formance have been associated with the introduction of new CFD methods. The design
of the Airbus A310 saw the introduction of double curvature wings into the Airbus fam-
ily in part through the introduction of transonic small perturbation (TSP) methods.
The A330/340 wing was primarily designed with viscous-coupled full potential tech-
niques. The next generation civil transports will be designed using methods both well
established and those capable of modelling full aircraft configurations with Euler and
Navier-Stokes flow solvers. These new methods will enable adverse aerodynamic inter-
ference effects to be designed out from an early stage in the product development through
an integrated total aircraft approach. CFD techniques continue to underpin our ability
to design aircraft with ever decreasing drag, emitting less pollution and consuming less
fuel. In addition, the introduction of various new aerodynamic technologies and design
concepts (eg laminar flow for lower drag, low cost for manufacture etc) will rely heav-
ily on CFD to minimise high cost testing or prototyping. For high speed cruise design
the traditional approach of designing in the wind tunnel has largely been replaced by
design on the supercomputer with checking in the tunnel. This has yealded significant
cost and performance benefits. However 3D CFD is not yet able to predict Clmax and
so low speed design and optimisation is still carried out experimentaly. Advanced CFD
methods have yet to make the same impact on dynamic design issues such as aeroelastic
flutter and buffet.
The major European airframe manufacturers have made substantial investment in the
development and calibration of state-of-the-art computational aerodynamics codes. Most
companies have specialised teams dedicated to the development, integration and appli-
cation of CFD to the design and analysis of their products. However, industry has
traditionally relied on the support of universities and research establishments to carry
out innovative basic research into new improved methods through both national gov-
ernmental and direct industrial support. The success of CFD in Europe is due in no
3
small part to the success of that partnership. The commercial sector has been slow to
offer suitable proprietary CFD systems to the aerospace industry in part because of its
unique transonic modelling requirements but also because of the relatively high accuracy
and consistancy levels demanded for aircraft design. The development and marketing
of commercial codes tends to have been concentrated on those industries whoose most
basic requirement involves complex physical modelling (eg of combustion, radiation or
two-phase flows).
Alongside transition, turbulence modelling and high performance computing one of the
key pacing items for industrial CFD is the development of fast user friendly techniques
for the generation of a suitable computational mesh for aircraft components or entire
configurations. Aerodynamic designers generally require very high standards of flow
prediction from CFD to enable them to progress the evolution of a design without regular
recourse to the wind tunnel. This means that meshes should be of a high quality to
facilitate accurate modelling of the complex air flows accross a wide speed range around
the various configurations of interest. In addition the grid generation systems should
be very flexible and easy to use to enable key geometric features to be modelled within
realistic design time-frames. Effective interfaces are required between company CFD
and CAD systems to ensure accurate geometrical representation and rapid model set-
up times. Where geometric compromises are necessitated appropriate tools should be in
place. A key design aim for a grid generation system should be to remove the need for the
user to interact with the field (off surface) mesh. This has not generaly been a feature of
current industrial (or any other) systems for modelling whole aircraft shapes. The need
for use during an intensive design cycle rather than post design analysis yields distinct
requirements for a system. Very rapid model set-up times for incremental adjustments
to configurations are essential where daily or hourly turnaround is required.
Over the last 15 years a number of grid generation approaches have been proposed to
meet these requirements. The use of irregular (unstructured) grids of tetrahedra with
finite element solvers or non-aligned meshes with finite volume or difference solvers have
been popular with some groups. In addition over the last 7-8 years considerable interest
has evolved in regular (structured) grid multi-block methods. Many different imple-
mentations of multi-block grid generation systems have been developed across Europe.
Subtley different block topology concepts have been adopted with a wide variation to the
degree of automation to the generation. A number of approaches for grid node specifica-
tion from simple algebraic teechniques to direct solution of partial differential equations
or optimisation formulations have been implemented. Further work is required to bring
these industrial systems up to a fully acceptable standard and there is considerable scope
for benefits to be accrued from collaboration on development and assesment.
With an increasing focus of the aerospace business towards European companies and con-
sortia competing with large North American companies and perhaps with the Japanese
in the next century the time is right for coordinated European wide collaboration on
CFD development. A framework for pre-competative industrial collaborative research
4
