European Conference on Computational Fluid Dynamics
ECCOMAS CDF 2006
P. Wesseling, E. Oñate, J. Périaux (Eds)
TU Delft, Delft The Netherland, 2006
ADIGMA
–
A EUROPEAN PROJECT O
N THE DEVELOPMENT
OF ADAPTIVE HIGHER O
RDER
VARIATIONAL
METHODS FOR
AEROSPACE APPLICATIO
NS
Norbert Kroll
German Aerospace Center (DLR)
Institute of Aerodynamics and Flow Technology
Lilienthalplatz 7
,
38108 Braunschweig
,
Germany
e

mail:
norbert.kroll@dlr.de
Key words:
H
igher order
CFD
methods, adaptive schemes, efficient solver
Abstract.
Computational Fluid Dynamics is a key enabler for meeting the strategic goals of
future air transportation. However, the limitations of today’s
numerical tools
reduce the
scope of innovation in aircraft development, keeping aircraft design at a conservative
l
e
vel
.
Within the 3
rd
Call of the 6
th
European Research Framework Programme,
the
strategic target
research project ADIGMA has been initiated.
The goal of
ADIGMA
is the development and
utilization of innovative adaptive higher

order methods for the compressible flow equations
enabling reliable, mesh independent numerical solutions for large

scale aerodynamic
applications in aircraft design. A cr
itical assessment of the newly developed methods for
industrial aerodynamic applications
will allow
the identification of the best numerical
strategies for integration as major building blocks for the next generation of industrial flow
solvers.
In order to
meet the ambitious objectives, a
partnership of 22 organizations from
universities, research organizations and aerospace industry
from
10 countries with well
proven expertise in CFD
has been set up
guaranteeing high level research work with a clear
path t
o industri
al exploitation. This paper gives on overview of the goals
and
the planned
activities of the 3

years project
.
1
INTRODUCTION
Computational Fluid Dynamics (CFD) has become a key technology in the development of
new products in the aeronautical
industry. During the last years the aerodynamic design
engineers have progressively adapted their way

of

working to take advantage of the
possibilities offered by new CFD capabilities based on the solution of the Euler and Reynolds
averaged Navier

Stokes (
RANS) equations. Significant improvements in physical modelling
and solution algorithms have been as important as the enormous increase of computer power
to enable numerical simulations in all stages of aircraft development. In particular, better
automatio
n of mesh generation techniques due to unstructured mesh technology and a
generalized block

structured grid approach with non

matching and overlapping grids resulted
in the ability to predict the flow physics and aerodynamic data of highly complex
configur
ations.
However, despite the progress made in CFD, in terms of user time and computational
resources, large aerodynamic simulations of viscous high Reynolds number flows around
N. Kroll
2
complex aircraft configurations are still very expensive. The requirement to r
eliably achieve
results at a sufficient level of accuracy within short turn

around times places severe
constraints on the application of CFD for aerodynamic data production, and the integration of
high

fidelity methods in multidisciplinary simulation and o
ptimization procedures.
Consequently, enhanced CFD capabilities for reducing design cycle and cost are
indispensable for industry. Finally on a longer term, advanced physical models like DES and
VLES will be used for evaluating the envelope of the final de
sign, but it becomes clear that
the results with second order methods too often depend on the mesh which cannot be tuned
sufficiently well, once more stressing the need for higher accuracy.
In order to add a major step towards the development of next gener
ation CFD tools with
significant improvements in accuracy and efficiency
the specific target research project
ADIGMA was initiated w
ithin the 3
rd
Call of the 6
th
Europea
n Research Framework
Programme.
ADIGMA is
dedicated
to further develop
ment and extensi
on of
promising
algorithms to real world applications by overcoming curre
nt limitations and bottlenecks.
A
number of innovative activities will be undertaken associated with the development of higher

order discretizations in combination with reliable advan
ced
adaptation strategies.
With the
help of a highly skilled consortium
well balanced between upstream r
esea
rch, applied
research and aerospace industry
, the ADIGMA project is aiming at scientific results and
algorithms/methods which are completely novel i
n an
industrial environment.
The project will
start the second half of 2006 and will last three years.
This paper describes the
background of
this research activity and
it gives a
n overview of the objectives, the planned activities and the
expected results
.
2 AERODYNAMIC SIMU
LATION TOOLS
–
STATE OF THE ART FOR
AIRCRAFT DESIGN
The majority of the aerodynamic simulation tools currently used in the aeronautical
industry for routine applications
are
based on second

order finite volume methods
[1]
. In the
case when complex configurations are considered very often the accuracy of these methods
ranges between first and second

order due to irregular and highly stretched meshes. The
results of the AIAA Drag Prediction Workshop DPW I
[2]
(wing/body configuration of a
transport aircraft) and DPW II
[3]
(wing/body/pylon/nacelle configuration) indicate that CFD
technology currently in use may not produce sufficiently accurate results
on meshes with
typical grid sizes that are used in an industrial environment. Reliable aerodynamic force
predictions and accurate simulation of complex flow phenomena require advances in physical
modelling, adaptive gridding (using goal

oriented error est
imation) and higher

order accurate
solution techniques for the governing RANS equations. For meeting these objectives with
second

order methods, very fine meshes with a large number of grid points are required
which, in the case of complex applications, le
ad to enormous computing times. Table
1
indicates typical mesh sizes for complex configurations based on unstructured second

order
finite volume methods. The estimations already take into account state

of

the

art feature

based grid adaptation.
N. Kroll
3
Nearly mesh
independent solutions are required to achieve confidence in numerical
simulations, since only based on such knowledge systematic statements concerning the
correctness or deficits of the physical modelling (turbulence and transition) for the flow
problem un
der consideration can be made. It is of utmost importance to achieve mesh
independent solutions with minimal effort in order to separate numerical and modelling
errors. Higher

order methods and reliable adaptation techniques are the appropriate strategies
to significantly reduce computational effort while maintaining accuracy. The advantage of
higher

order methods are expected to become even more profound for DES/LES simulations
due to the very high mesh resolution demands required for this type of simulati
on.
configuration
complete
aircraft
high lift, half
conf.
complete aircraft
complete fighter;
full configuration
complete
helicopter
objective
aerodynamic
forces
wake vortex,
(2 half spans)
vortical flow at
high
angle of
attack
helicop
ter wake
interactions
,
noise&vibration
problem size
(mesh
points)
15

20 m
illion
40 m
illion
> 30 m
illion
40

45 m
illion
Ta
ble 1:
Required
mesh siz
e densities for second

order methods
2.1
Higher

order discretization methods
One possibility to relieve the resolution requirement is the use of higher

order
discretization methods. On a given mesh they allow an improved prediction of crucial flow
phenom
ena, such as boundary layers including transition, drag forces, wakes, vortical flows
and interaction phenomena like blade/vortex interaction. They also support the use of
advanced turbulence models like Detached and Large Eddy Simulation. Figure
1
demonst
rates the effect of employing a higher

order discretization in the case of the
calculation of the laminar airfoil flow. It is obvious that higher

order methods outperform
classical second

order s
chemes. Significant less degree
s
of freedom are required for
higher

order methods than for classical schemes to reach the same level of accuracy.
However, in
order to be competitive, these methods have to be designed in such a way that the associated
increased computational complexity is more than balanced. Traditio
nal finite volume methods
rely on extended stencils to achieve higher

order approximations. This may lead to difficulties
in achieving stable iterative algorithms and higher

order algorithms on unstructured meshes,
and in fact these so

called ENO and WENO
reconstruction methods have not l
ead to
N. Kroll
4
industrial applications. A recent review of the state of the art concerning high

order accurate
methods for aerodynamics is given in
[4]
.
Recently, higher

order
Residual

Based Compact
(RB
C) finite volume schemes have been
developed
[5]
taking advantage of the residual vanishing at steady

state. While conventional
high

order schemes rely on separate higher

order approximation of each space deriva
tive
when approximating convective equations, RBC schemes have been originally built on lower
order approximation of each space derivative, combined so as to form a higher

order
approximation of the steady residual. The scheme is formally designed for any
order of
accuracy. A third order formulation has been successfully applied to 2D

and 3D aerodynamic
problems on structured meshes
[6]
.
The
extension of this promising strategy to unstructured
grids
requires fur
ther research work
.
Figure
1:
Effect of higher

order methods, laminar flow around airfo
il using DG
method,
pressure drag (left) and
error in pressure drag (right)
versus
number of degrees of freedom
[7]
In structural mechanics it has been demonstrated that standard Galerkin finite element
methods using classical continuous finite elements are very attractive for achieving higher

order accuracy for smooth problems. However, it is well kn
own that they do not give
reasonable results for convection

dominated problems. Additional stabilization terms are
required for the solution of the compressible Euler and Navier

Stokes equations
[8]
.
Stabilized finite element P
etrov Galerkin methods currently used in industry are limited to
second

order accuracy
.
Further research work is required to extend
the finite element Petrov
Galerkin method to higher

order accuracy.
Also based on the finite element framework, two other pr
omising solution strategies for the
compressible flow equations with high potential for successful extension to higher

order
approximations have been developed in the last few years. These are the
Discontinuous
Galerkin (DG) methods and the Continuous Resi
dual

Based (CRB) schemes.
N. Kroll
5
The development of
Discontinuous Galerkin methods
for the Euler and Navier

Stokes
equations is currently a hot rese
arch topic all over the world [9

26
]. Indeed, DG methods have
several important advantages over well established
finite volume methods. The concept of
higher

order discretization is inherent to the DG method. The stencil is minimal in the sense
that each cell communicates only with its direct neighbours. In particular, in contrast to the
increasing stencil size neede
d to increase the accuracy of classical finite volume methods the
stencil of DG methods is the same for any order of accuracy which has important advantages
for the implementation of boundary conditions and for the parallel efficiency of the method.
Moreov
er, due to this simple communication at cell interfaces, cells with so

called ‘hanging
nodes’ can be inherently treated, a fact that simplifies local mesh refinement (
h

refinement).
Additionally, the communication at cell interfaces is identical for any or
der of the method
which simplifies the use of methods with different polynomial orders p in adjacent cells. This
allows for the variation of the order of the polynomials over the computational domain (
p

refinement), which in combination with
h

refinement l
eads to the so

called ‘
hp

refinement’.
Being a finite element method, the DG approach takes advantage of the powerful
mathematical theory with respect to the derivation of
a posteriori
error estimates and the
derivation of residual

based indicators for loc
al mesh refinement or adjoint

based indicators
which are used for goal

oriented mesh refinement.
Despite the advantages and capabilities of the DG method mentioned above, the method is
not yet mature and current implementations are subject to strong limita
tions for its
applications to large scale industrial problems. This situation is clearly reflected by the variety
of research directions and the increasing number of scientific p
apers concerning the DG
methods.
With respect to compressible flows the main d
evelopment activities were devoted to
the solution of the Euler or laminar Navier

Stokes equations. First calculations have been
performed for turbulent flows using two

equation turbulence models, but the application of
the Discontinuous Galerkin method to
advanced turbulence models is far from being mature.
Significant research activity is necessary to investigate efficient and robust procedures which
can be used in industry on a routine basis. Another major shortcoming of the DG method is its
computationa
l costs. Second

order approximations already require the solution of four times
as many discrete equations as classical finite volume methods. For higher

order
discretizations this number increases significantly. Apart from the memory requirements
induced
by the storage of these additional unknowns, the efficient solution of the system of
equations still requires significant research effort.
Finally, another promising strategy to reach higher order accuracy is the
Continuous
Residual

Based
(CRB) method, co
mbining ideas from both finite elements and finite
volumes. It is based on a continuous finite element representation but it also includes
upwinding ideas and limiting, thus allowing satisfaction of a maximum principle (borrowed
from Godunov Finite Volume
methods). Discrete equations are derived by splitting
(distributing) in each element of the grid an approximation of the integral of the equations
over the element (cell residual). This approach has two important consequences: It naturally
lends itself to
the use of unstructured meshes, and its accuracy is entirely determined by the
accuracy with which the cell residual is evaluated, which is ultimately determined by the
N. Kroll
6
choice of the degree of the finite element interpolation space of the unknowns. For sec
ond
order accuracy (linear elements) the method has demonstrated improved accuracy compared
to standard finite volume schemes (
[27]
,
[28]
) while preserving monotone shock capturing.
The comp
actness
of the method allows to
devise very efficient parallel solution strategies.
Over the last years the method has been extended to time accurate problems based on a space

time formulation
[29]
.
Extension to higher order elements h
as started only recently and is
limited to scalar convection

diffusion problems, for which third and fourth order schemes
have been developed
[30]
.
Future activities need to be dedicated to the extension of
this
technology to t
he compressible Navier

Stokes equations. As for the DG method, achieving
efficient integration procedures is crucial for industrial applicability.
A key problem in higher

order methods is the preservation of monotonicity across
discontinuities such as shoc
ks. Many of the available stabilization or limiting procedures
include strong consistent stabilization terms which must be chosen in a problem

dependent
manner. Significant improvements in shock capturing procedures are required to suppress
oscillations ne
ar strong discontinuities while preserving the high order of the scheme in
smooth regions.
Currently, the above limitations and weaknesses hinder the acceptance of higher

order
methods in an industrial environment. The high potential of this approach, how
ever, is very
well recognized by industry. Promising prototype applications relevant for industry have been
condu
cted with adaptive
Discontinuous Galerkin methods.
Figure 2
shows three examples:
results of the
2
nd
order
inviscid simulation of blade/vortex
interaction of a two

bladed rotor in
forward flight
[13]
,
[22]
(left

hand side figure), the
2
nd
order
simulation of the laminar flow
around a delta wing at Re=40.000, M=0.3 and
=12.5
0
[25]
(middle figure) and the unsteady
simulation of
turbulent vortex shedding behind a turbine vane
using 3
rd
order spatial
discretization
(right

hand side figure)
[26]
.
Figure
2:
Pr
ototype computations with DG methods for industrial relevant test cases
(all computations performed by partners within the consortium)
The ADIGMA project aims at overcoming the existing limitations and shortcomings of
higher

order
variatio
nal methods
and will support the exploitation of these technologies for
robust and efficient applications in the aeronautical industry.
N. Kroll
7
2.2
L
ocal g
rid adaptation
A well known strategy for minimizing the cost of a computational simulation while
achieving a
given level of accuracy is adaptive mesh refinement. The basic idea is to locally
refine the mesh in regions which most adversely affect the accuracy of the solution and to
coarsen the mesh in more benign areas. Local mesh refinement is available in many
of the
finite volume codes used by the aeronautical industry (e.g.
[31]
). A number of adaptation
techniques have been developed to refine and de

refine isotropic volume meshes driven by
feature

based sensors. They have clearly
demonstrated their capability for relevant industrial
applications. Recent efforts have been focused on developing effective methods for
anisotropic volume meshes, although further work is required to enhance these methods to
handle collapsed elements and
hanging nodes. However, continuous local refinement of the
dominant features of the flow does not necessarily guarantee that certain measures of the
global error will be simultaneously reduced. Research is still ongoing to find computationally
efficient an
d reliable adaptation sensors and error estimators.
Recent work on adjoint methods has shown a lot of promise regarding reliable mesh
adaptation
[18]
,
[32]
,
[33]
. Indee
d, adjoint methods have enabled the development of error
estimators for general functionals of the solution such as lift or drag. Error estimation and
goal

oriented, adjoint

based refinement has been developed for 2D laminar flow. The
capability of the goa
l

oriented adaptation technique is demonstrated in Figure
3.
For a laminar
flow at Mach number M=1.2 a residual

based refined mesh is shown
[33]
. The refinement
criterion aims at resolving
all major features such as the
extensi
ve bow shock, the weak
shocks emanating from the trailing edge and the wake behind the airfoil. In contrast to that,
the right figure shows the refinement of the mesh produced by employing the goal

oriented
(adjoint

based) indicator with pressure drag bein
g the goal functional. Despite the difference
in resolving the flow features, the drag coefficient is significantly more accurate on the mesh
on the right

hand side (error: 1.6*10

4
) than computed on the mesh on the left

hand side
(error: 1.9*10

3
) even th
ough significantly less grid points are used in the former case.
Figure
3:
Mesh adaptation for laminar airfoil flow, M=1.2,
residual

feature based (left) and goal

oriented (right)
[33]
N. Kroll
8
F
urther
research
is
necessary in order to utilize this novel adaptation approach for
industrial applications
.
This
in particular
includes the extension
to
3D high Reynolds number
flows and
to multiple target quantities.
Moreover, i
n order to fully explore t
he capabilities of
adaptation, significant development activities with respect to the
hp

refinement as well as
anisotropic refi
nement for compressible flows are
required.
3
SCIENTIFIC OBJECTIVE
AND EXPECTED RESULTS
OF THE PROJECT
The goal of the ADIGMA pr
oject is to add a major step towards the development of next
generation CFD tools with significant improvements in accuracy and efficiency.
The
project
will focus on the development of novel and innovative
adaptive higher

order discretization
methods for t
he solution of the Navier

Stokes equations at high Reynolds numbers.
The final
aim is the ability to perform large scale computations typical in aircraft industry with higher
accuracy per given computing time than performed by today’s state

of

the

art solv
ers.
Moreover, advanced and reliable error estimation and adaptation techniques will be made
available which are indispensable for reliable and efficient automatic shape optimization.
The ADIGMA project will concentrate on technologies showing the highest
potential for
efficient higher

order discretizations. These are the Discontinuous Galerkin (DG) methods
and Continuous Residual Distribution (CRD) schemes. The main scientific objectives of the
ambitious ADIGMA project are summarized as follows:
Further d
evelopment and improvement of key ingredients for higher

order space
discretization methods for compressible Euler, Navier

Stokes and RANS equations
Development of higher order space

time discretizations for unsteady flows including
moving geometries
Devel
opment of novel solution strategies to improve efficiency and robustness of
higher

order methods enabling large

scale aerodynamic applications
Development of reliable adaptation strategies including error estimation, goal

oriented
isotropic and anisotropic
mesh refinement and the combination of mesh refinement
with local variation of the order of accuracy (
hp

refinement)
Utilization of innovative concepts in higher

order approximations and adaptation
strategies for industrial applications
Critical assessmen
t of newly developed adaptive higher

order methods for industrial
aerodynamic applications; measurement of benefits compared to state

of

the

art flow
solvers currently used in industry
Identification of the best strategies for the integration as major buil
ding blocks for the
next generation industrial flow solvers
3
PARTNERS
The consortium is comprised of 22 organizations. It gathers the main European aircraft
manufacturers, the major European research establishments and several universities, all being
we
ll recognized for playing an active role in the development and utilization of advanced high
N. Kroll
9
fidelity CFD methods for aerodynamic applications.
The role of the different organizations is
quite complementary. Universities are dealing with upstream research
and their mai
n
objective is to provide
new technologies with improved capabilities. However, their focus is
very often limited to academic problems. On the other hand, the national research
centers are
addressing applied research and thus closing the gap b
etween upstream research and industry.
In terms of computational methods, new algorithms and technologies developed at
universities are adapted and enhanced for large scale applications. They are implemented in
the production codes used by industry. The ro
le of industry covers the specification of
requirements for future CFD tools and the final assessment of newly developed technologies
based on
industry relevant
application.
Industrial partners
in ADIGMA
are Alenia Aeronautica (Italy), Airbus (France and
G
ermany), Dassault Aviation (France), EADS

MAS (Germany) and CENAERO (Belgium).
Research organizations involved are ARA (United Kingdom), DLR (Germany), INRIA
(France), NLR (The Netherlands), ONERA (France), and VKI (Belgium).
Participating
Universities are
Università degli Studi di Bergamo (Italy), Ecole Nationale Supérieure d’Arts
et Métiers Paris
(France)
, University of Nottingham
(United Kingdom)
, Charles University
Prague
(Czech Republic)
, University of Wales Swansea
(U
nited Kingdom)
, University of
Stut
tgart
(Germany)
,
Uppsala University (Sweden),
University of Twente
(The Netherlands)
,
Warsaw University of Technology
(Poland)
, Nanjing University (China)
. The project is co

ordinated by DLR.
4
DESCRIPTION OF WORK
In order to concentrate effort, the ADIGMA
project focuses on two major innovative
technologies: higher

order methods and reliable adaptation techniques. They have shown high
potential to provide major achievements in CFD for aircraft design. Since the computational
efficiency of higher

order meth
ods is
currently
not compatible with the performance of
classical lower order methods, dedicated developments to improve this situation need to be
addressed.
Since ADIGMA is aiming at novel computational strategies for future industrial
applications, it i
s indispensable that industrial partners specify the requirements on next
generation solvers at the beginning of the project and carry out a critical assessment of the
newly developed technologies at midterm and towards the end of the project.
The
technic
al work in
ADIGMA is
split into 5
work packages.
Work package
Industrial Specification
Industrial partners will specify the requirements and outline the evaluation procedure for
the methods newly developed in ADIGMA
. A test case suite of increasing compl
exity will be
specifie
d including the necessary data.
Moreover, the status of adaptive higher

order methods
at the start of the project will be
evaluated and reported by prototype computations in order to
provid
e a firm basis for comparison at
midterm and
the end of the report.
Work package
Higher

order Discretization
This work package
is the core of the ADIGMA project. It
aims at the improvement and
enhancement of higher

order
discretizations for the solution of the Navier

Stokes equations at
N. Kroll
10
high Reyno
lds numbers, covering the flow regimes of aeronautical applications. From the
state of the art it has become clear that two variational technologies have the highest chance
for success, namely Discontinuous Galerkin (DG) methods and Continuous Residual

bas
ed
discretizations. Although these methods have shown their potential for improved accuracy,
many aspects are incomplete and need further development, especially with respect to
efficiency and robustness for complex applications. The objective of this work
package is
therefore to imp
rove key ingredients of higher

order
spatial discretization
related to
stabilization and monotone shock capturing for hyperbolic conservation laws, discretization of
turbulent high Reynolds number Navier

Stokes equatio
ns, ensuri
ng
higher

order accuracy in
presence of complex bodies with curved boundaries,
robustness
in the vicinity of sharp ridges
and in cases of highly stretched meshes needed in high Reynolds number boundary layers.
Moreover, development activities with respect
to higher

order space

time discretizations for
time

accurate flows including moving geometries will be carried out.
Work package
Solution Strategies
Computational efficiency is a crucial aspect for higher

order methods.
The aim of this
work package is t
he development of solution strategies which meet the industrial
requirements in terms of memory storage, computing time and efficient utilization of parallel
low cost computers.
The proposed developments are based on tools and techniques well

known and eff
icient in the context of second

order finite volume schemes but they require
further
theoretical studies
and developments
in the context of
adaptive
higher

order methods.
Research activities will include improvements and further developments with respect t
o
multigrid
strategies (h

p multigrid) and
fully implicit schemes based on Newton iterations
.
Since in case of higher

order schemes parallel computing becomes a key element to make
them applicable to 3D turbulent flow simulations,
specific activities are d
edicated to efficient
parallelization of the various numerical strategies considered in the project.
Work package
Adaptation
This work package addresses the effectiveness and reliability of adaptation techniques in
combination with higher

order methods
developed in
the previous work packages.
The aim of
adaptation algorithms is to achieve accurate flow features and flow quantities like
ae
rodynamic
force coefficients, for example, on meshes with the minimal amount of degrees
of freedom with the numerical
solution being computed with the minimal amount of
computational effort. Adaptation algorithms generally consist of three parts: the type of
adaptation (
h

refinement: local mesh refinement,
p

refinement: local increase of the
polynomial degree of the flow
representation), the refinement indicators (which decide where
to adapt), and the control of the adaptation (error estimation as stopping criteria to limit the
mesh size). Main emphasis of the work package is on the refinement indicator type, the error
est
imation and the combination of
h

and
p

refinement.
The various
nove
l adaptation
algorithms will be extended to real

life applications. .
Work package
Verification and Assessment
The objective of this work package is to provide a critical assessment of t
he methods and
technologies developed in
the previous work packages
under the specific aspect of a later
N. Kroll
11
industrial use for complex aerodynamic problems. The assessment is based on the evaluation
plan and the test case suite defined in
the first work packa
ge
.
Identification of the best
strategies and best practice guidelines will ensure technology transfer to industry.
5
EXPECTED RESULTS
The ADIGMA project focuses the up to now fragmented research in higher

order methods
in Europe. It will foster the scient
ific co

operation between the universities, research
establishments and the aeronautical industry. The transfer from innovative upstream
technologies in CFD into the industrial design cycle will be significantly improved.
The novel
higher

order adaptive me
thods
developed within ADIGMA
are expected to yield essential
progress on several items:
Improved simulation accuracy in reduced time and at lower cost
Enabling automatic and reliable shape optimization and multi

disciplinary simulation
and optimization th
rough improved flow solvers
Enabling accurate flow control simulations based on advanced physical modeling of
flow control phenomena e.g. controlled flow, rece
p
tivity issues
Mesh independent predictions of aerodynamic forces through error estimation and
go
al

oriented adaptation
Automatic and reliable resolution of physical effects that have become relevant to
aerodynamic design (confluent boundary layers, vortex sheets, trailing vortices, etc.)
Support and exploitation of advanced physical models (DES, LES)
Provision of highly accurate aer
odynamic input for aeroacoustic
simulation
s
To summarize, firstly, the ADIGMA project will be an essential and indispe
n
sable brick to
fully exploit the potential of Comput
a
tional Fluid Dynamics
as
the major source for
dete
rmin
a
tion of data required to drive the aerodynamic design process
.
Secondly, to support
the design of advanced flow control technologies (mainly driven by ec
o
logical topics like
noise, emissions and by economic (DOC) effects), very precise CFD solutions

fulfil
l
ing the
needs of e.g. aeroacoustics, complex flow control physics
–
are the key enablers to reach the
ACARE
Vision 2020
oriented design goals.
ADIGMA is an important corner stone to support
the competitiveness of both the European research communit
y and European aircraft
manufacturers.
6
CONCLUSIONS
Within the 6
th
European Research Framew
ork Programme the project ADIGMA
has been
set up to significantly improve the capabilities of the aerodynami
c simulation tools for aircraft
design
. The project focu
ses on the development
and utilization
of innovative
higher

order
variational methods in combination with reliable adaptive solution strategies.
Since t
he
project gathers
well known partners
from
academia and research organizations
in Europe
with
proven
ex
pertise in
this particular field of
CFD, a major breakthrough in numerical simulation
of high Reynolds number flows is expected. The involvement of the European aircraft
N. Kroll
12
industry will ensure t
hat
the research work has a clear path to industrial exploitatio
n. The
project will start in the second half of 2006 and will last for 3 years.
ADIGMA is
seen as
an
important corner stone to support the competitiveness of both the European research
community and European aircraft manufacturers.
6
ACKNOWLEDGMENTS
The au
thor would like to thank
R. Abgrall, F. Bassi, M. Berggren,
H. Bieler,
F. Chalot,
V. Couaillier, H. Deconinck, V. Dolejsi,
R. Hartmann
,
K. Hillewaert, P. Houston, P. Larrieu,
A.
Lerat
,
K. Morgan, C. Munz,
A. Peace, H. Rieger,
J. Rokicki, V. Selmin, Jianxi
an Qiu,
J. van der Vegt
and H. von der Ven
for their contribution
s
to this paper.
7
R
EFERENCES
[1]
Vos,
J.B
.; R
izzi
, A.
;
Darracq
, D.
,
Navier

Stokes solvers in European aircraft design
,
Progress in Aerospace Sciences
,
38
,
601

697
2002.
[2]
Levy, D.W.; Zickuhr, Th
.; Vassberg, J.; Agrawal, S.K Wahls, R., A.; Pirzadeh, A.,
Hemsch, M. J.: Data summary from the First AIAA Computational Fluid Dynamics Drag
Prediction Workshop,
Journal of Aircraft
, Vol 40, pp 875

882, 2003.
[3]
Laflin, K., R.; Vassberg, J.; Wahls, R. A.; Mor
rison, J. H.; Brodersen, O.; Rakowitz, M.;
Tinoco, E. N.; Godard, J.: Summary of data from the Second AIAA CFD Drag
Prediction Workshop,
AIAA Paper
, 2004

0555, 2004.
[4]
Ekaterinaris, J. A.: “High

order accurate. Low diffusion methods for aerodynamics”,
Progre
ss in Aerospace Sciences 41, pp192

300, 2005.
[5]
Lerat, A.; Corre, C.: A residual

based compact scheme for the compressible Navier

Stokes equations,
J. Comput.
Phys.
, Vol 170, pp 642

675, 2001.
[6]
Michel, B.: Corre, C.; Lerat, A.: Numerical study of a supersonic
air intake with flow
control device,
16th Congrès Francais de Méchanique
, Nice, September 2003.
[7]
Hartmann, R.; Housten, P.; Symmetric Interior Penalty DG Methods for the
Compressible Navier

Stokes Equations I: Method Formulation,
Int. J. Numer.
Anal.
Model
.
Vol.3
(1)
,
pp
1

20
, 2006.
[8]
Shakib, F.; Hughes, T.J.R.; Johan, Z.: A new finite element formulation for
computational fluid dynamics: The compressible Euler and Navier

Stokes equations,
Computer Methods in Applied Mechanics and Engineering,
Vol.89, pp 141

219, 1991.
[9]
Bassi,
F.;
Rebay
, S.:
A High

Order Accurate Discontinuous Finite Element Method for
the Numerical Solution of the Compressible Navier

Stokes Equations
. J. Comput. Phys.,
Vol 131, pp
267

279
, 1997.
[10]
Bassi,
F.;
Rebay,
S;
Mariotti,
G.;
Pedinotti,
S
.;
Savini
, M.:
A high

order accurate
discontinuous finite element method for inviscid and viscous turbomachinery flows.
In:
R. Decuypere, G. Dibelius (Eds.), Proceedings of
the 2nd European Conference on
Turbomachinery

Fluid Dynamics and
Thermodynamics
,
Technologisch Instituut,
Antwerpen, Belgium, pp. 99

108
, 1997.
N. Kroll
13
[11]
Bassi, F.; Rebay, S.: GMRES discontinuous Galerkin solution of the compressible
Navier

Stokes equations. In B. Cockburn, G. Karniadakis, and C.

W. Shu, editors,
Discontinuous Galerkin Methods
, volume 11, pages 197

208.
Springer, 1999.
[12]
Bassi, F.; Rebay, S.: A high

order discontinuous Galerkin method for compressible
turbulent flows. In B. Cockburn, G. Karniadakis, and C.

W. Shu, editors,
Discontinuous
Galerkin Methods
, volume 11, Springer, 1999
.
[13]
Boelens, O. J.; van der Ven, H.; Oskam, B.; Hassan, A. A.: The boundary conforming
discontinuous Galerkin finite element approach to rotorcraft simulations.
J. of Aircraft
,
39(5):776

785, 2002.
[14]
Cockburn, B.; Karniadakis, G.; Shu, C.

W.: The development o
f discontinuous Galerkin
methods. In B. Cockburn, G. Karniadakis, and C.

W. Shu, editors,
Discontinuous
Galerkin Methods
, volume 11, pages 3

50.
Springer, 1999.
[15]
Dolejsi, V.: On the discontinuous Galerkin method for the numerical solution of the
Navier

Stok
es equations.
Int. J. Numer. Meth. Fluids
, 45:1083

1106, 2004.
[16]
Dumbser, M.; Munz, C.

D.: Building blocks for arbitrary high

order discontinuous
Galerkin methods.
Journal of Scientific Computing
, 2005. To appear.
[17]
K. Fidkowski, D. L. Darmofal, Development of
a higher

order solver for aerodynamic
applications,
AIAA Paper
, Reno, 2004.
[18]
Hartmann, R.; Houston, P.: Adaptive discontinuous Galerkin finite element methods for
the compressible
Euler equations
.
J. Comput. Phys. 183 pp
508

532
, 2002.
[19]
Sudirham,J.J; van d
er Vegt, J.J.W; van Damme, R.M.J.;.
Space

time discontinuous
Galerkin method for advection

diffusion problems. Submitted to
Appl. Numer. Math.
,
2005, see also http://www.math.utwente.nl/publication.
[20]
van der Vegt, J.J.W.; van der Ven, H.;.
Slip boundary c
onditions in discontinuous
Galerkin discretizations of the Euler equations of gas dynamics. In
Proceedings Fifth
World Congress on Computational Mechanics, July 7

12, 2002
, available from
http:://wccm.tuwien.ac.at/.
[21]
van der Vegt, J.J.W.; van der Ven, H.:
Space

time discontinuous Galerkin finite element
method with dynamic grid motion for inviscid compressible flows, I. General
formulation.
J. Comp. Phys.
, 182:546

585, 2002.
[22]
van der Ven, H.; Boelens, O.J.: A framework for aeroelastic simulations of trimmed
rotor
systems in forward flight. In
Proceedings of the 30
th
European Rotorcraft Forum
,
Marseille, France, September 14

16, 2004.
[23]
van der Ven, H.; van der Vegt, J.J.W.: Space

time discontinuous Galerkin finite element
method with dynamic grid motion for inv
iscid compressible flows, II.
Efficient flux
quadrature.
Comput. Meth. Appl. Mech. Engrg.
, 191:4747

4780, 2002.
[24]
Houston, P.; Senior, B.; and Süli, E.;
hp

Discontinuous Galerkin finite element methods
for hyperbolic problem: error analysis and adaptivity.
I
nt. J. Numer. Meth. Fluids
,
40:153

169, 2002.
N. Kroll
14
[25]
Klaij, C.M.; van der Vegt, J.J.W; van der Ven, H.: A space

time discontinuous Galerkin
fort he compressible Navier

Stokes equations.
In preparation for
J. Comput. Phys
. 2005.
[26]
Bassi, F.; Crivellini, A.; Rebay,
S.; Savini, M.: Discontinuous Galerkin solution of the
Reynolds averaged Navier

Stokes and k

turbulence model equations.
Computers
&
Fluids,
34:507

540, 2005.
[27]
Deconinck, H.; Sermeus, K.; Abgrall; R.: Status of Multidimensional Upwind Residual
Distribution schemes and application in aeronautics.
AIAA paper 2000

2328, 2000
.
[28]
33
rd
von Karman Institu
te Lecture Series on CFD: Novel Methods for Advection
Dominated Flow. H. Deconinck Ed.
VKI LS03

05, von Karman Institute, Belgium,
2003
.
[29]
Ricchiuto, M.; Construction and analysis of compact residual discretizations for
conservation laws on unstructured mes
hes, PhD thesis University of Brussels, 2005.
[30]
Ricchiuto, M.; Abgrall, R.; Deconinck, H.: Construction of very high

order residual
distribution schemes for unsteady advection: preliminary results. In 33
rd
von Karman
Institute Lecture Series on CFD: Novel Me
thods for Advection Dominated Flow, VKI
2003.
[31]
Alrutz, Th.: Hybrid Grid Adaptation in TAU,
Notes on Numerical Fluid Mechanics and
Multidisciplinary Design
, Volume 89, Springer, 2005.
[32]
Venditti, D.A; Darmofal, D.L.: Anisotropic grid adaptation for functional
outputs:
application to two

dimensional viscous flows.
J. Comp. Phys.
, 187:22

46, 2003.
[33]
Hartmann, R.: Adaptive discontinuous Galerkin methods with shock

capturing for the
compressible Navier

Stokes equations,
to appear in
Int. J. Numer.
Meth. Fluids
, 2006
.
Enter the password to open this PDF file:
File name:

File size:

Title:

Author:

Subject:

Keywords:

Creation Date:

Modification Date:

Creator:

PDF Producer:

PDF Version:

Page Count:

Preparing document for printing…
0%
Comments 0
Log in to post a comment