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OCR for page 721

Summary of the Group Discussion on Navier-Stokes Solvers
Chairman: J. Piquet
ENSM
Nantes, France
Co-cha~rman: Y. Kodama
Ship Research Institute
Tokyo, Japan
First, questions, fields and issues on which this
Group Dicussion should be focused are given(Kodama).
Then a general table, given hereafter, of the meth-
ods presented during the meeting is briefly dis-
cussed(Piquet). It appears that, among the fourteen
papers presenting numerical solutions of Navier-Stokes
equations, only three methodologies are used; an unseg-
regated approach (Hoekstra) in which the solenoidal-
ity of the flow is enforced at each iteration; other
contributions satisfy the incompressibility condition
at convergence either by means of the so-called ar-
tificial compressibility method(Yang, Kodama) or by
means of a pressure correction technique-projection
type method(Zhu, Hino, Doi) or simple-like meth-
ods(Tzabiras, Larsson, Oh, Masuko, Piquet, Stern).
It should be therefore necessary to compare in a
more detailed way the methods, in order to isolate their
differences and the resulting effects (Stern). As a first
important difference, the choice of independent vari-
ables is felt significant(Tzabiras) although no clear evi-
dence of optimal choice has been provided.
Several specific aspects are then addressed in the
discussion: geometric singularities created by the curvi-
linear structured grid, averaging procedures(Kodama);
orthogonality constraints on the grid, needed regular-
ity of the control functions in the elliptic grid gen-
eration procedure(Ju), convergence problems on fine
grids(Piquet). The question of accuracy measures is
posed, from a 2D example, for an inner problem where
momentum conservation implies strongly different re-
sults on the drag forces coefficients CDP and CDM when
computed from the integration of forces and from the
global momentum balance(Kubota). The problem of
conservation of mass, close to the boundaries - e.g. the
free surface(Hino) -as well as that of momentum is dis-
cussed.
Problems connected to the turbulence model are
then addressed. Corrrections for the free-surface prom
le~ns(Hino) and existence of a model adequate for lift-
ing problems(Tzabiras) are questionned. The need to
avoid the "highly convenient" wall function approach is
721
emphasized(Hoekstra). In any case, it appears difficult
to check the influence of the turbulence model on the
numerical results in an unbiased way.
The discussion is then displaced towards what
should be done now (Tzabiras), given the existence of
several Navier-Stokes codes able in principle to deal
with complex problems. A few possibilities are putfor-
ward and, among the noticed fields of applications, the
impact of Navier-Stokes codes on the propeller research
is not considered "too optimistically" (Hoekstra).
Endly, the boundary conditions are discussed
mainly in relation with the numerical scheme consid-
ered(Tzabiras, Kodama) although the natural mathe-
matical character of the Neumann pressure condition is
pointed out (Hoekstra).
To try a tentative evaluation, the chairmen of the
discussion feel that the brief survey of technical prob-
lems that has been attempted gives a good picture of
collective weaknesses, given the rather small size of the
community working on Navier-Stokes solvers for hydro-
dynamic problems.
The discussion was felt either too specific - and so
could be considered as a disappointing specialist discus-
sion(Himeno) - or not detailed enough to allow an ap-
preciation of the pros. and cons. of the presented works
and methodologies. May be, this can be attributed to
the fact that not only our mutual work is not known in
enough details, but also that the concerned aspects are
so numerous that a complete assessment of each detail
of the used methods is difficult.
The weaknesses of the discussions appeared also
on a conceptual level, for instance in the treatment of
boundary conditions and on the views over accuracy.
Recognized inadequacies in the treatment of the geom-
etry- e.g. the HSVA tanker- did not raised the ques-
tion of the use of partially unstructured girds. Recog-
nized difficulties in enforcing conservativity (geometri-
cal, mass, momentum) did not raised the question of the
use of Galerkin - type methods. May be, these problems
should call for a better consideration of the literature

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issued from applied mathematics.
Because a lot of time has been spent on the tech-
nical aspects of the work, and probably also because of
the way the discussion has been conducted, the practi-
cal importance of the whole set of aforementioned prom
lems was not evaluated. A fortiori, the ability to use
Navier-Stokes solvers to understand flow situations was
not considered, although these solvers offer a unique
opportunity to get information on the flow at a level of
details not possible with experiments.
Table of the 14 papers related to Nav~er-Stokes solvers presented during INC-5 (Part 1~.
AUTHORS VARIABLES GRID INCOMPRESS. PRESSURE MOMENTUM
& LAYO UT GENERATION CONSTRAINT SOLVER SO EVER
HOEKSTRA covariant VW Schwarz multiple relax.
contravariant U Christoffel Unsegregated sweep CSIP
collocated transv. ortho.
YANG UVWP Algebraic artif. comp. relaxation relaxation
et A1. collocated + IAF ~ IAF
KODAMA UVWP Geometrical artif. comp. IAF(Implicit IAF
collocated [interp. btw.] Approximate
surface grids Factorization)
ZH U contravariant Elliptic MAC relaxation explicit
HINO UVWP collocated Algebraic MAC relaxation explicit
node-centered
KINOSHITA UV\VP Algebraic MAC relaxation explicit
et A1. collocated
Ix U BO TA U V VV P Geometrical compressible rel axation explicit
et A1. collocated (cavitation)
DOI No Projection
(channel flow)
TZABIRAS UVWP Elliptic SIMPLE relaxation relaxation
LOUKAKIS staggered
LARSSON contravariant Elliptic SIMPLER relaxation relaxation
et A1. staggered
OH phys. polar Elliptic SINIPLE relaxation relaxation
et A1. staggered
MASU KO UVWP Elliptic SIMPLE relaxation relaxation
OGI\VARA staggered
PIQU ET UV\NJP Transfinite PISO ILU-PBCG relaxation
VISONNEAU collocated ~ Elliptic
STERN UV\VP Elliptic SILIPLER plane ADI plane ADI
IxIM staggered
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Table of the 14 papers related to Navier-Stokes solvers presented during INC-5 (Part 2,).
AUTHORS TURBU LENCE WALL SPACE TIME FREE
SURFACE
HOEhSTRA Mixing length damping pressure implicit no
(CS) factor downstream
2nd-order
V upstream
YANG Baldwin-Lomax damping TVD(Roe) implicit no
et A1. factor if\ form)
KODAMA Baldwin-Lomax damping centered 2nd-order implicit no
factor artif.dissipation (~ form)
ZHU SGS damping centered 4th-order explicit no
et A1. factor artif.dissipation
HINO Baldwin-Lomax wall 2nd-order P explicit yes
function 3rd-order cony. Fn=0.25
KINOSHITA none no slip 2nd-order P explicit no
et A1. 3rd-order cony.
KU BOTA none no slip 2nd-order P explicit cavitation
et A1. . 3rd-order cony.
DOI SGS damping 3rd-order cony. Adams-Bashforth no
factor artif.dissipation (explicit)
TZABIRAS k-e wall ftn. Hybrid implicit no
LOUKAKIS
LARSSON k-e wall fin. Finite-Analytic implicit no
et A1.
OH k-e wall fin. Finite-Analytic implicit no
et A1.
MASUKO k-e wall ftn. Hybrid implicit no
OGIWARA
PIQUET k-e wall ftn. Finite-Analytic implicit no
VISONNEAU
STERN laminar wall ftn. Finite-Analytic implicit no
KIM k-e
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Table of the 14 papers related to Navier-Stokes solvers presented during INC-5 (Part 3~.
AUTHORS START INLET FAR GRID NO. of CPU TIME TEST CASES
FIELD (, 0, ~ ITER.
HOEKSTRA potential thin B.L. potential 45x49x29 24 .5-lie Cray2 HSVA tanker
P77 = 0 midship 10-3 resid
YANG 91x25x29 220 17' Afterbodies 1,2,5
et A1. Cray YMP Bodies at incidence
40"/iter. Flat plate,Wigley,
IxODAMA far uniform 5000 Stellar Series 60
l | upstream l l l | 4~S1000 | (cb=o.6~17'o8)
ZH U rest far uniform 170x30x50 20h Wigley hull
et A1. upstream (255000 to Hitac
340000 pts) S820/80
HINO rest far uniform 100x20x38 11000 2h/ 1000stps Wigley hull
upstream ACOS 910 Series 60 (Cb=0.6)
KIN OSHITA rest rest rest 140x60 40000 70' Oscillating
et A1. VP- 100 circular cylinder
I&U BOTA uniform far uniform 101x31x3 Hitac NACA0015
et A1. upstream M-680H wing section
DOI rest periodic no Channel flow
LES
TZABIRAS rest thin B.L. potential 44x32x30 35 (20% 60hrs. SSPA ship liner
LOUKAKIS midship resi.red. ,u Vax
/ iter)
SSPA ship liner
LARSSON rest thin B.L. 60x21x15
et A1. midship
OH rest 1/7 + eq uniform 54~32x25 190 1600" SSPA ship liner
et A1. midship VP-100
MASUKO rest far uniform 94x25x21 Series 60 (Cb=0.6)
OGIWARA | | ups ream | l l l | IHI-BO anker
PIQUET rest thin B.L. uniform 80x40x31 ;2hrs HSVA tanker
VISONNEAU midship Cray 2
STERN rest thin B.L. uniform 80000 Cray XMP Propeller shaft
KIM +rot. (relative
case frame ~
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