Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration: results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Braunschweig [u.a.]
Vieweg
1997
|
| Series: | Notes on numerical fluid mechanics
57 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 569 S. graph. Darst. 23 cm |
| ISBN: | 3528069570 |
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MARC
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| 245 | 1 | 0 | |a Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration |b results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 |c ed. by Herman Deconinck and Barry Koren |
| 264 | 1 | |a Braunschweig [u.a.] |b Vieweg |c 1997 | |
| 300 | |a XVI, 569 S. |b graph. Darst. |c 23 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Notes on numerical fluid mechanics |v 57 | |
| 650 | 4 | |a Lagrange equations |x Numerical solutions | |
| 650 | 4 | |a Multigrid methods (Numerical analysis) | |
| 650 | 4 | |a Navier-Stokes equations |x Numerical solutions | |
| 650 | 0 | 7 | |a Upwind-Verfahren |0 (DE-588)4482840-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Bewegungsgleichung |0 (DE-588)4006321-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrgitterverfahren |0 (DE-588)4038376-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Aerodynamik |0 (DE-588)4000589-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Adaptives Gitter |0 (DE-588)4333769-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eulersche Bewegungsgleichungen |0 (DE-588)4219070-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4155043-2 |a Forschungsbericht |2 gnd-content | |
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| 689 | 1 | 2 | |a Adaptives Gitter |0 (DE-588)4333769-7 |D s |
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| 689 | 2 | 1 | |a Upwind-Verfahren |0 (DE-588)4482840-8 |D s |
| 689 | 2 | |5 DE-604 | |
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| 700 | 1 | |a Deconinck, Herman |e Sonstige |4 oth | |
| 830 | 0 | |a Notes on numerical fluid mechanics |v 57 |w (DE-604)BV000898664 |9 57 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007613092 | |
Record in the Search Index
| _version_ | 1807594168161140736 |
|---|---|
| adam_text |
CONTENTS
PAGE
COMPACT
CELL
VERTEX
CONVECTION
SCHEMES
ON
UNSTRUCTURED
MESHES.
(H.
PAILLERE
AND
H.
DECONINCK)
.
1
1.
INTRODUCTION
.
1
2.
LINEAR
CONVECTION
.
4
2.1.
NOTATION
AND
DEFINITIONS
.
4
2.1.1.
GEOMETRY
.
4
2.1.2.
LINEAR
AND
NON-LINEAR
SCHEMES
.
5
2.1.3.
CONVECTION
MATRIX
.
6
2.2.
LOCAL
PROPERTIES
OF
THE
DISTRIBUTION
.
.
6
2.2.1.
MULTI-DIMENSIONAL
UPWINDING
(Z/)
.
6
2.2.2.
POSITIVITY
(P)
.
7
2.2.3.
LINEARITY
PRESERVATION
(P)
.
8
2.2.4.
CONTINUITY
(C)
.
9
2.2.5.
GODUNOV
'
S
THEOREM
(Q)
.
9
3.
LINEAR
FLUCTUATION-SPLITTING
SCHEMES
.
10
3.1.
LINEAR
SCHEMES
SATISFYING
LINEARITY
PRESERVATION
.
10
3.1.1.
THE
LOW
DIFFUSION
SCHEMES
(W,
CP,C)
.
10
3.1.2.
THE
LAX-WENDROFF
SCHEME
(P,C)
.
11
3.1.3.
THE
SUPG
SCHEME
(P,C)
.
12
3.1.4.
THE
UPWIND
CONTROL
VOLUME
SCHEME
OF
GILES
ET
AL.
(P,
C)
.
13
3.1.5.
THE
FLUX
BALANCE
SPLITTING
SCHEME
OF
ROSSOW
(P,C)
.
13
3.2.
LINEAR
SCHEMES
SATISFYING
POSITIVITY
.
14
3.2.1.
THE
N
SCHEME
(U,
P,
C)
.
14
3.2.2.
THE
UPWIND
FINITE
VOLUME
SCHEME
(P,
C)
.
15
3.2.3.
POSITIVITY
DIAGRAM
FOR
LINEAR
TWO-TARGET
SCHEMES
.
17
3.3.
NUMERICAL
RESULTS
.
18
4.
NON-LINEAR
FLUCTUATION-SPLITTING
SCHEMES
.
19
4.1.
LINEAR
AND
NON-LINEAR
SPEEDS
.
19
4.1.1.
THE
PETROV-GALERKIN
SCHEME
OF
MIZUKAMI-HUGHES
(M,
P,
CP)
.
21
4.1.2.
THE
LEVEL
SCHEME
(W,
P,
CP)
.
23
4.1.3.
THE
PSI
SCHEME
(M,
P,
CP,
C)
.
24
4.1.4.
EXAMPLE
OF
ALGORITHM
FOR
UPWIND
POSITIVE
NON-LINEAR
SCHEME
.
25
4.1.5.
THE
SUPG
SCHEME
WITH
ARTIFICIAL
VISCOSITY
(CP,C)
.
26
4.2.
NON-LINEAR
SCHEMES
REVISITED
.
26
4.2.1.
LIMITERS
AND
LINEARITY
PRESERVATION:
SIDILKOVER
'
S
ANALYSIS
.
27
4.2.2.
LIMITERS
AND
POSITIVITY:
SIDILKOVER
'
S
ANALYSIS
.
27
4.2.3.
EQUIVALENCE
BETWEEN
PSI
SCHEME
AND
MINMOD
.
28
4.2.4.
DISTRIBUTION
COEFFICIENTS
AND
LIMITING
.
29
4.2.5.
THE
'
LIMITED
'
FINITE
VOLUME
SCHEME
.
30
4.3.
CONTINUITY
OF
THE
NON-LINEAR
SCHEMES
.
30
4.4.
NUMERICAL
RESULTS:
CONVECTION
SKEWED
TO
THE
MESH
.
30
5.
ACCURACY
OF
THE
FLUCTUATION-SPLITTING
SCHEMES
.
33
5.1.
NUMERICAL
GRID
CONVERGENCE
STUDY
.
33
CONTENTS
(CONTINUED)
PAGE
5.1.1.
ORDER
OF
ACCURACY
ON
REGULAR
MESHES
.
33
5.1.2.
EFFECT
OF
GRID
DISTORTION
.
34
6.
NON-LINEAR
CONSERVATION
LAW
AND
CONSERVATIVE
LINEARIZATIONS
.
38
6.1.
CONSERVATIVE
LINEARIZATIONS
.
38
6.1.1.
DIMENSION
BY
DIMENSION
EXTENSION
1D
(A)
.
40
6.1.2.
DIMENSION
BY
DIMENSION
LINEARIZATION
1D
(V'U)
.
40
6.1.3.
LINEARIZATION
(U)
.
41
6.1.4.
ABGRALL
'
S
LINEARIZATION
A
(U)
.
41
6.2.
NUMERICAL
RESULTS
.
42
7.
CONCLUSIONS
.
45
REFERENCES
.
46
MULTIDIMENSIONAL
UPWIND
RESIDUAL
DISTRIBUTION
SCHEMES
FOR
THE
2D
EULER
EQUATIONS.
(H.
PAILLERE
AND
H.
DECONINCK)
.
51
1.
INTRODUCTION
.
51
2.
RESIDUAL
DISTRIBUTION
METHOD
FOR
THE
ID
EULER
EQUATIONS
.
55
2.1.
CHARACTERISTIC
DECOMPOSITION
.
56
2.2.
CONSERVATIVE
LINEARIZATION
.
56
2.3.
DISTRIBUTION
SCHEME
.
57
3.
RESIDUAL
DECOMPOSITION
FOR
THE
2D
EULER
EQUATIONS
.
58
3.1.
MULTIDIMENSIONAL
WAVE
MODELS
.
58
3.2.
CHARACTERISTIC
SPLITTINGS
IN
2D
.
61
3.2.1.
SIMILARITY
TRANSFORMATIONS
.
62
3.2.2.
THE
HYPERBOLIC/ELLIPTIC
SPLITTING
.
64
3.3.
CONSERVATIVE
LINEARIZATION
.
66
4.
RESIDUAL
DISTRIBUTION
SCHEMES
.
67
4.1.
SCALAR
CONVECTION
SCHEMES
.
67
4.1.1.
PROPERTIES
OF
THE
DISTRIBUTION
.
68
4.1.2.
EXAMPLES
OF
FLUCTUATION-SPLITTING
SCHEMES
.
70
4.2.
SYSTEM
DISTRIBUTION
SCHEMES
.
70
4.2.1.
DIAGONALIZABLE
SYSTEMS
.
71
4.2.2.
NON-DIAGONALIZABLE
SYSTEMS
.
72
5.
NUMERICAL
RESULTS
.
74
5.1.
SUBSONIC
FLOW
OVER
SINE
BUMP
.
74
5.1.1.
NUMERICAL
GRID
CONVERGENCE
STUDY
.
75
5.2.
SUBCRITICAL
CYLINDER
.
78
5.3.
OBLIQUE
SHOCK
REFLECTION
.
83
5.4.
JET
INTERACTION
.
83
5.5.
MULTI-ELEMENT
AIRFOIL
.
86
5.5.1.
SUBCRITICAL
FLOW
(AFOO
=
0.2)
.
86
5.5.2.
LOW
MACH
NUMBER
FLOW
(AFOO
=
0.01)
.
86
5.6.
NACA0012
AIRFOIL
.
90
5.6.1.
SUBCRITICAL
FLOW
(AFOO
=
0.63,2
ANGLE
OF
ATTACK)
.
90
5.6.2.
LOW
MACH
NUMBER
FLOW
(AFOO
=
0.01)
.
91
5.6.3.
SUPERCRITICAL
FLOW
(AFOO
=
0.85,1
ANGLE
OF
ATTACK)
.
91
5.7.
SUPERCRITICAL
RAE-2822
AIRFOIL
.
99
CONTENTS
(CONTINUED)
PAGE
5.8.
SCRAMJET
INLET
.
102
5.9.
VKI
TURBINE
.
102
6.
CONCLUSIONS
.
106
REFERENCES
.
106
MATRIX
DISTRIBUTION
SCHEMES
FOR
THE
SYSTEM
OF
EULER
EQUATIONS.
(E.
VAN
DER
WEIDE
AND
H.
DECONINCK)
.
113
1.
INTRODUCTION
.
113
2.
REVIEW
OF
SCALAR
DISTRIBUTION
SCHEMES
.
114
3.
SYSTEM
RESIDUAL
DISTRIBUTION
SCHEMES
.
118
4.
LINEAR
SECOND
ORDER
MATRIX
DISTRIBUTION
SCHEMES
.
120
4.1.
SYSTEM
LAX-WENDROFF
SCHEME
.
120
4.2.
SYSTEM
SUPG-SCHEME
.
121
4.3.
SYSTEM
LDA-SCHEME
.
121
5.
FIRST
ORDER
MATRIX
DISTRIBUTION
SCHEMES
.
121
5.1.
THE
SYSTEM
FIRST
ORDER
FV-SCHEME
.
121
5.2.
THE
SYSTEM
FIRST
ORDER
N-SCHEME
.
122
6.
NONLINEAR
SECOND
ORDER
MATRIX
DISTRIBUTION
SCHEMES
.
123
6.1.
LIMITED
FV-SCHEME
(LFV)
.
123
6.2.
THE
LIMITED
SYSTEM
N-SCHEME
(LN
OR
PSI)
.
124
7.
PRECONDITIONING
.
125
8.
NUMERICAL
RESULTS
.
125
8.1.
SUBSONIC
NACA0012,
M
X
=
0.63,
A
=
2
.
125
8.1.1.
COMPARISON
OF
FIRST
ORDER
SCHEMES
.
126
8.1.2.
COMPARISON
OF
SECOND
ORDER
SYSTEM
SCHEMES
.
126
8.2.
TRANSONIC
FLOW
OVER
NACA0012
AIRFOIL
.
130
8.2.1.
TRANSONIC
NACA0012,
M
X
=
0.85,
A
=
1
.
130
8.2.2.
TRANSONIC
NACA0012,
M
X
=
0.80,
A
=
1.25
.
130
8.3.
FLOW
OVER
HYPERSONIC
DOUBLE
ELLIPSE,
=
8.15,
A
=
30
.
132
8.4.
LAMINAR
AXISYMMETRIC
VISCOUS
FLOW
OVER
HYPERSONIC
HYPERBOLOID
FLARE,
MOO
=
6.73
.
133
9.
CONCLUSION
.
134
REFERENCES
.
135
MULTIDIMENSIONAL
UPWIND
SCHEMES
FOR
THE
3D
EULER
EQUATIONS
ON
UNSTRUCTURED
TETRAHEDRAL
MESHES.
(A.
BONFIGLIOLI
AND
H.
DECONINCK)
.
141
1.
INTRODUCTION
.
141
2.
FLUCTUATION
SPLITTING
SCHEMES
IN
3D
.
144
2.1.
PROBLEM
STATEMENT
.
145
2.2.
GEOMETRY
AND
NOTATION
.
146
2.2.1.
INFLOW
AND
OUTFLOW
FACES
.
148
2.2.2.
UPSTREAM
AND
DOWNSTREAM
VERTICES
.
148
2.2.3.
THE
UPSTREAM
AND
DOWNSTREAM
MANIFOLDS
.
148
2.2.4.
INFLOW
AND
OUTFLOW
POINTS
.
148
2.3.
LINEAR
AND
NON-LINEAR
SCHEMES
.
151
2.4.
PROPERTIES
OF
THE
DISTRIBUTION
.
151
CONTENTS
(CONTINUED)
PAGE
2.4.1.
UPWINDING
.
152
2.4.2.
POSITIVITY
.
152
2.4.3.
LINEARITY
PRESERVATION
.
153
2.5.
LINEAR
SCHEMES
.
153
2.5.1.
LOW
DIFFUSION
A
SCHEME
.
153
2.5.2.
N
SCHEME
.
154
2.5.3.
FINITE
VOLUME
FIRST
ORDER
UPWIND
SCHEME
.
157
2.6.
NON
LINEAR
SCHEMES
.
159
2.6.1.
PSI
SCHEME
.
159
3.
THE
COMPRESSIBLE
EULER
EQUATIONS
.
160
3.1.
EQUATIONS
IN
CONSERVED
VARIABLES
.
160
3.2.
SYMMETRIZING
VARIABLES
.
162
3.3.
CANONICAL
VARIABLES
.
162
4.
CONSERVATIVE
LINEARIZATION
.
163
5.
PRECONDITIONING
.
164
5.1.
HYPERBOLIC-HYBRID
SPLITTING
.
164
5.2.
HYPERBOLIC-ELLIPTIC
SPLITTING
.
169
6.
NUMERICAL
RESULTS
.
172
6.1.
THREE
DIMENSIONAL
CHANNEL
FLOW
.
173
6.1.1.
SUPERSONIC
(M
X
=
1.4)
FLOW
.
173
6.1.2.
SUBSONIC
(AF
M
=
0.5)
FLOW
.
173
6.2.
ONERA
M6
WING
.
177
6.3.
HYPERSONIC
FLOW
OVER
A
BLUNT
BODY
.
180
7.
CONCLUSIONS
.
183
REFERENCES
.
183
A
VERY
EFFICIENT
LOCAL-ADAPTIVE
MULTIGRID
METHOD
BASED
ON
A
SIMPLE-WAVE
DECOMPOSITION
OF
THE
EULER
EQUATIONS.
(L.A.
CATALANO,
P.
DE
PALMA,
M.
NAPOLITANO
AND
G.
PASCAZIO)
.
187
1.
INTRODUCTION
.
190
2.
SIMPLE-WAVE
EULER
SOLVER
.
191
2.1.
SIMPLE-WAVE
DECOMPOSITION
.
191
2.2.
SCALAR
FLUCTUATION
SPLITTING
SPACE
DISCRETIZATION
.
194
2.3.
BOUNDARY
CONDITIONS
.
196
2.4.
TIME
INTEGRATION
.
197
3.
LIMITS
OF
THE
FLUCTUATION
SPLITTING
SIMPLE-WAVE
APPROACH
.
198
3.1.
SCALAR
ADVECTION
EQUATION
.
198
3.2.
EULER
EQUATIONS
.
201
4.
A
CONSERVATIVE
TECHNIQUE
FOR
LOCALLY-REFINED
AND
PATCHED
GRIDS
.
202
4.1.
MULTIGRID
LOCAL-REFINEMENT
STRATEGY
.
202
4.2.
PATCHED
GRIDS
.
204
5.
RESULTS
.
205
5.1.
SOLID
WALL
BOUNDARY
TREATMENT
.
205
5.2.
ANALYSIS
OF
THE
VARIOUS
MODELS
AND
SCHEMES
.
207
5.3.
ADAPTIVE
LOCAL
REFINEMENT
AND
PATCHED
GRIDS
.
210
6.
CONCLUSIONS
.
214
REFERENCES
.
217
CONTENTS
(CONTINUED)
PAGE
GENUINELY
MULTIDIMENSIONAL
UPWIND
METHODS
FOR
ACCURATE
AND
EFFICIENT
SOLUTIONS
OF
COMPRESSIBLE
FLOWS.
(L.A.
CATALANO,
P.
DE
PALMA,
M.
NAPOLITANO
AND
G.
PASCAZIO)
.
221
1.
INTRODUCTION
.
224
2.
NAVIER-STOKES
EQUATIONS
.
225
3.
CHARACTERISTIC
DECOMPOSITION
OF
THE
EULER
EQUATIONS
.
225
4.
DISCRETIZATION
OF
THE
INVISCID
TERMS
.
227
4.1.
SCALAR
FLUCTUATION
SPLITTING
SCHEMES
.
227
4.2.
MATRIX
FLUCTUATION
SPLITTING
SCHEMES
.
230
5.
DISCRETIZATION
OF
THE
VISCOUS
TERMS
.
232
6.
BOUNDARY
CONDITIONS
.
233
7.
MULTIGRID
ADAPTIVE
STRATEGY
.
233
8.
EULER
RESULTS
.
234
9.
NAVIER-STOKES
RESULTS
.
243
10.
CONCLUSIONS
.
248
REFERENCES
.
248
A
GENERAL
ANALYSIS
OF
2D/3D
MULTIDIMENSIONAL
UPWIND
CONVECTION
SCHEMES.
(P.
VAN
RANSBEECK
AND
CH.
HIRSCH)
.
251
1.
INTRODUCTION
.
251
2.
2D
LINEAR
CONVECTION
EQUATION
.
252
2.1.
GENERAL
NINE-POINT
MOLECULES
.
253
2.2.
STREAMLINE
COORDINATES
.
254
2.3.
CONDITIONS
FOR
SECOND
ORDER
ACCURACY
.
255
2.3.1.
STATIONARY
CONVECTION
EQUATION
.
255
2.3.2.
SCHEMES
WITH
NO
CROSS-DIFFUSION
.
255
2.3.3.
UNSTEADY
CONVECTION
EQUATION
.
255
2.3.4.
SECOND
ORDER
ACCURACY
FOR
HOMOGENEOUS
CONVECTION
EQUATION.
.
256
2.4.
CELL-CENTERED
FINITE
VOLUME
FORMULATION
.
256
3.
2D
UPWIND
SCHEMES
FOR
6-POINT
MOLECULES
.
257
3.1.
TRIANGLE
CONFIGURATION
I
.
257
3.2.
TRIANGLE
CONFIGURATION
II
.
258
3.3.
GENERAL
COMPACT
SCHEMES
WITH
SECOND
ORDER
ACCURACY
.
259
3.4.
SECOND
ORDER
COMPACT
SCHEMES
IN
SPACE
AND
TIME
.
259
3.5.
UPWIND
SCHEMES
WITH
ZERO
CROSS-DIFFUSION
.
260
3.6.
MONOTONICITY
CONDITIONS
FOR
6-POINT
SCHEMES
.
262
4.
2D
UPWIND
SCHEMES
FOR
5-POINT
MOLECULES
.
262
4.1.
CONTINUOUS
ZERO
CROSS-DIFFUSION
SCHEME
-
CONFIG.
1
.
262
4.2.
ZERO
CROSS-DIFFUSION
SCHEME
WITH
DM
=
DU
=
0
-
CONFIG.
1
.
263
4.3.
LOW
DIFFUSION
SCHEME
A
-
CONFIG.
II
.
264
4.4.
LOW
DIFFUSION
SCHEME
B.
CONFIG.
II
.
265
5.
2D
UPWIND
SCHEMES
FOR
4-POINT
MOLECULES
.
265
5.1.
THE
UNIQUE
4-POINT
SCHEME
WITH
ZERO
CROSS-DIFFUSION
.
266
5.2.
RAITHBY
'
S
SUDS
SCHEME
.
266
5.3.
MONOTONE
FIRST
ORDER
SCHEME
WITH
MINIMUM
CROSS-DIFFUSION
.
267
5.4.
MONOTONE
FIRST
ORDER
SCHEME
WITH
DU
=
0
.
269
CONTENTS
(CONTINUED)
PAGE
6.
2D
LINEAR
UPWIND
DISSIPATION
MODELS
.
269
6.1.
INTRODUCTION
.
269
6.2.
DIMENSIONAL-SPLIT
UPWIND
DISSIPATION
.
270
6.3.
MULTIDIMENSIONAL
2D
UPWIND
DISSIPATION
.
271
6.4.
LINEAR
MULTI-D
UPWIND
DISSIPATION
.
272
6.4.1.
SIX-POINT
AND
FIVE-POINT
SCHEMES
.
272
6.4.2.
FOUR-POINT
SCHEMES
.
273
6.4.3.
FIRST
ORDER
MULTI-D
UPWIND
DISSIPATION
.
273
6.4.4.
SECOND
ORDER
NON-MONOTONE
MULTI-D
UPWIND
DISSIPATION
.
273
6.4.5.
MULTI-D
UPWIND
DISSIPATION
-
STENCIL
.
274
7.
2D
SECOND
ORDER
LED
UPWIND
DISSIPATION
.
275
7.1.
MULTIDIMENSIONAL
LIMITER
FUNCTIONS
AND
RATIOS
.
275
7.2.
LOCAL
EXTREMUM
DIMINISHING
CONDITIONS
.
277
7.3.
EXAMPLES
OF
MULTI-D
RATIOS
.
278
7.4.
CONTINUOUS
SECOND
ORDER
LED
DISSIPATION
.
279
7.4.1.
FIVE-POINT
LINEAR
CONTINUOUS
DISSIPATION
.
279
7.4.2.
CONTINUOUS
2ND
ORDER
LED
DISSIPATION
.
279
8.
3D
LINEAR
CONVECTION
EQUATION
.
280
8.1.
GENERAL
27-POINT
MOLECULE
.
281
8.2.
CONSISTENCY
CONDITIONS
.
283
8.3.
FORMULATION
IN
STREAMLINE
COORDINATES
.
284
8.4.
CROSS-DIFFUSION
TERMS
.
285
8.5.
CELL-CENTERED
FINITE
VOLUME
APPROACH
.
286
9.
3D
UPWIND
SCHEMES
FOR
8-POINT
MOLECULES
.
287
9.1.
3D
FIRST
ORDER
MONOTONE
MINIMUM
CROSS-DIFLFUSION
SCHEME
.
288
9.1.1.
MONOTONICITY
CONDITION
.
288
9.1.2.
MINIMUM
CROSS-DIFLFUSION
.
289
9.1.3.
INTERPOLATION
STRATEGY
.
291
9.2.
SUBCLASS
OF
ZERO
CROSS-DIFLFUSION
SCHEMES
.
293
9.2.1.
ZERO
CROSS-DIFLFUSION
CONDITION
.
293
9.2.2.
INTERPOLATION
STRATEGY
.
293
10.
3D
LINEAR
UPWIND
DISSIPATION
MODELS
.
297
10.1.
LINEAR
MULTI-D
UPWIND
DISSIPATION
.
297
10.1.1.
LINEAR
8-POINT
UPWIND
SCHEMES
.
297
10.1.2.
MULTI-D
UPWIND
DISSIPATION
-
STENCIL
.
298
10.1.3.
FIRST
ORDER
UPWIND
DISSIPATION
.
298
10.1.4.
SECOND
ORDER
UPWIND
DISSIPATION
.
298
11.
3D
SECOND
ORDER
LED
UPWIND
DISSIPATION
.
299
11.1.
MULTIDIMENSIONAL
LIMITER
FUNCTIONS
AND
RATIOS
.
299
11.2.
MONOTONICITY
CONDITIONS
.
301
12.
CONCLUSIONS
.
301
REFERENCES
.
302
MULTIDIMENSIONAL
UPWIND
SCHEMES
FOR
THE
EULER/NAVIER-STOKES
EQUATIONS
ON
STRUCTURED
GRIDS.
(P.
VAN
RANSBEECK
AND
CH.
HIRSCH)
.
305
1.
INTRODUCTION
.
305
CONTENTS
(CONTINUED)
PAGE
2.
DIMENSIONAL-SPLIT
UPWIND
DISSIPATION
.
306
3.
MULTIDIMENSIONAL
UPWIND
DISSIPATION
.
308
3.1.
2D
SCALAR
UPWIND
DISSIPATION
.
308
3.1.1.
LINEAR
2D
UPWIND
SCHEMES
.
309
3.1.2.
NON-LINEAR
2D
UPWIND
SCHEMES
.
311
3.2.
3D
SCALAR
UPWIND
DISSIPATION
.
312
3.2.1.
LINEAR
3D
UPWIND
SCHEMES
.
312
3.2.2.
NON-LINEAR
3D
UPWIND
SCHEMES
.
314
4.
EXTENSION
FOR
THE
EULER/NS
EQUATIONS
.
316
4.1.
2D
CHARACTERISTIC
DECOMPOSITION
.
316
4.1.1.
CHARACTERISTIC
VARIABLES/COMPATIBILITY
EQUATIONS
.
316
4.1.2.
PROPAGATION
DIRECTIONS
.
318
4.1.3.
NUMERICAL
FLUX
FORMULATION
.
320
4.2.
3D
CHARACTERISTIC
DECOMPOSITION
.
321
5.
RESULTS
.
322
5.1.
2D
SUPERSONIC
LAVAL
NOZZLE
.
322
5.2.
RAE2822
AIRFOIL
(M
=
0.75,
A
=
3)
.
322
5.3.
2D
FLAT
PLATE
(AF
=
0.3,
RE
=
5.0
X
10
8
)
.
328
5.4.
RAE2822
(M
=
0.734,
RE
=
6.5
X
10
6
,
A
=
2.54)
.
331
5.5.
3D
SUPERSONIC
COMER
FLOW
.
331
6.
CONCLUSIONS
.
333
REFERENCES
.
335
MULTIDIMENSIONAL
UPWIND
SCHEME
FOR
THE
PSEUDO-COMPRESSIBLE
EULER
EQUATIONS.
(J.A.
MICHELSEN)
.
339
1.
INTRODUCTION
.
339
2.
GOVERNING
EQUATIONS
.
340
3.
EIGENVALUE
ANALYSIS
.
342
4.
CHARACTERISTIC
DECOMPOSITION
.
344
4.1.
STREAMWISE
SPLITTING
.
344
4.2.
PSEUDO
MACH
ANGLE
SPLITTING
(PMA)
.
345
4.3.
STREAMWISE-CROSSWISE
SPLITTING
.
./
.
346
5.
FLUCTUATION
SPLITTING
.
./
.
349
5.1.
THE
LDA
SCHEME
.
351
6.
BOUNDARY
CONDITIONS
.
352
6.1.
INLET
CONDITION
.
352
6.2.
OUTLET
CONDITION
.
352
6.3.
FARFIELD
CONDITION
.
353
6.4.
WALL
CONDITION
.
.
.
353
7.
TIMESTEPPING
PROCEDURE
.
354
8.
RESULTS
.
355
8.1.
FLOW
OVER
SINE-BUMP
.
355
8.2.
FLOW
OVER
CIRCULAR
CYLINDER
.
356
9.
CONCLUSION
.
357
REFERENCES
.
360
CONTENTS
(CONTINUED)
PAGE
LOCAL
GRID
REFINEMENTS
FOR
THE
NAVIER-STOKES
EQUATIONS
BASED
ON
TRUNCATION
ERROR
ESTIMATES.
(P.
EKSTRAND)
.
363
1.
INTRODUCTION
.
363
2.
GOVERNING
EQUATIONS
.
365
3.
NUMERICAL
METHODS
.
368
3.1.
SPATIAL
DISCRETIZATION
.
368
3.2.
ADAPTIVE
DISSIPATION
.
369
3.3.
RUNGE
KUTTA
TIME
MARCHING
.
371
3.4.
MULTI
GRID
.
372
4.
LOCAL
REFINEMENT
.
374
4.1.
ADAPTIVE
CRITERIA
.
374
4.2.
LOCAL
REFINED
MESH
TYPES
.
376
5.
COMPUTATIONAL
RESULTS
.
378
5.1.
ACCURACY
.
378
5.2.
EFFICIENCY
.
387
5.3.
CHOICE
OF
REFINEMENT
PARAMETER
.
389
6.
CONCLUSION
.
391
REFERENCES
.
391
MULTIGRID
FOR
STEADY
GAS
DYNAMICS
PROBLEMS.
(P.W.
HEMKER,
B.
KOREN,
W.M.
LIOEN,
M.
NOOL
AND
H.T.M.
VAN
DER
MAAREL)
.
393
1.
A
SOLUTION-ADAPTIVE
MULTIGRID
METHOD
FOR
THE
STEADY
EULER
EQUATIONS
.
393
1.1.
MULTIGRID
AND
ITERATIVE
DEFECT
CORRECTION
.
394
1.1.1.
THE
FIRST-ORDER
FINITE
VOLUME
DISCRETISATION
.
394
1.1.2.
A
LOCALLY
NESTED
SEQUENCE
OF
DISCRETISATIONS
.
396
1.1.3.
FAS
AND
FMG
.
397
1.1.4.
ITERATIVE
DEFECT
CORRECTION
.
398
1.2.
REFINEMENT
CYCLES
.
399
1.3.
A
SCALAR
IMPLEMENTATION
.
400
1.4.
NUMERICAL
RESULTS
.
401
1.4.1.
SHOCK
REFLECTION
.
401
1.4.2.
TRANSONIC
AIRFOIL
FLOW
.
406
2.
EUVEL:
AN
EULER
VECTOR
EXTENSION
LIBRARY
.
408
2.1.
EXTENSIONS
TO
BASIS
.
408
2.2.
VECTORISATION
OF
SOME
OF
THE
EULER
SUBROUTINES
.
410
2.2.1.
COMPUTATION
OF
THE
FLUX,
TRANSPORT
AND
THEIR
DERIVATIVES
.
410
2.2.2.
RIGHT-HAND
SIDE
COMPUTATION
.
411
2.2.3.
THE
RESIDUAL
.
412
2.2.4.
THE
RELAXATION
.
412
2.2.5.
SOME
OTHER
VECTORISED
SUBROUTINES
.
413
2.3.
VECTOR
PERFORMANCE
.
413
2.3.1.
SHOCK
REFLECTION
.
413
2.3.2.
TRANSONIC
AIRFOIL
FLOW
.
413
2.4.
CONCLUSIONS
.
414
REFERENCES
.
415
CONTENTS
(CONTINUED)
PAGE
IMPROVING
EULER
COMPUTATIONS
AT
LOW
MACH
NUMBERS.
(B.
KOREN
AND
B.
VAN
LEER)
.
419
1.
PRECONDITIONING
OF
JACOBIANS
.
420
1.1.
INTRODUCTION
.
420
1.2.
EQUATIONS
.
421
1.2.1.
CONTINUOUS
EQUATIONS
.
421
1.2.2.
DISCRETE
EQUATIONS
.
422
1.3.
CONVERGENCE
.
422
1.3.1.
CONVERGENCE
THROUGH
ERROR
SMOOTHING
.
422
1.3.2.
CONVERGENCE
THROUGH
ERROR
CONVECTION
.
423
1.4.
ACCURACY
.
424
1.5.
PRECONDITIONING
.
424
1.5.1.
REMOVING
STIFFNESS
.
424
1.5.2.
CONCERNING
INACCURACY
.
426
1.6.
IMPLEMENTING
PRECONDITIONING
.
427
1.7.
OPTIMIZING
LOCALLY
IMPLICIT
ITERATION
STEP
.
428
1.7.1.
QUALITATIVE
OPTIMIZATION
.
428
1.7.2.
QUANTITATIVE
OPTIMIZATION
.
429
1.8.
CONVERGENCE
FOR
PRECONDITIONED
EQUATIONS
.
430
1.8.1.
ERROR
SMOOTHING
.
430
1.8.2.
ERROR
CONVECTION
.
430
2.
CONDITIONING
OF
ABSOLUTE
EIGENVALUE
MATRICES
.
431
2.1.
INTRODUCTION
.
431
2.2.
FIXES
TO
ILL
CONDITIONS
SUBSONIC,
ABSOLUTE-EIGENVALUE
MATRICES
.
433
2.2.1.
TRIMMING
2-D
SINGULAR
MATRIX
.
433
2.2.2.
ADDING
1-D
AND
2-D
REGULARIZING
MATRICES
.
434
2.3.
SMOOTHING
FOR
ADDITIVE
CONDITIONING
.
436
2.4.
APPLYING
ADDITIVE
CONDITIONING
.
437
2.4.1.
2-D
CONSERVATIVE
IMPLEMENTATION
.
437
2.4.2.
NUMERICAL
RESULTS
.
438
3.
CONCLUSIONS
.
439
REFERENCES
.
441
BASIS3,
A
DATA
STRUCTURE
FOR
3-DIMENSIONAL
SPARSE
GRIDS.
(P.W.
HEMKER
AND
P.M.
DE
ZEEUW)
.
443
1.
THE
GEOMETRIC
STRUCTURE
.
443
1.1.
COORDINATES,
GRIDS
AND
CELL
ELEMENTS
.
443
1.2.
PATCHES
.
446
1.3.
NEIGHBOURS
AND
KIDS
.
449
1.4.
GHOST
PATCHES,
THE
ROOT
PATCH
.
449
1.5.
LOCAL
REFINEMENTS,
BOUNDARIES
.
450
2.
THE
DATA
STRUCTURE
.
452
2.1.
PATCH
NUMBERS
AND
POINTERS
.
452
2.2.
POINTERS
AND
COORDINATES:
THE
ARRAY
PNTR
.
453
2.3.
PROPERTIES:
THE
ARRAY
PPTY
.
454
2.4.
DATA
CONTENTS:
THE
ARRAY
DATA
.
454
3.
THE
ACTIONS
ON
THE
DATA
STRUCTURE
.
455
CONTENTS
(CONTINUED)
PAGE
3.1.
CONSTRUCTION
OF
THE
DATA
STRUCTURE
.
455
3.2.
SCANNING
THE
PATCHES
.
456
A
APPENDIX:
THE
IMPLEMENTATION
.
458
A.L.
THE
PASCAL
PROTOTYPE
.
458
A.
2.
ABOUT
THE
FORTRAN
IMPLEMENTATION
.
473
A.
3.
THE
FORTRAN
INCLUDE
FILE
.
474
A.
4.
THE
FORTRAN
IMPLEMENTATION
MANUAL
.
475
FINITE
VOLUME
MULTIGRID
FOR
3D-PROBLEMS.
(P.W.
HEMKER)
.
485
1.
INTRODUCTION
.
485
2.
FINITE
VOLUME
SPARSE
GRIDS
.
486
2.1.
A
MULTI-D
MULTIRESOLUTION
ANALYSIS
.
486
2.2.
PIECEWISE
CONSTANT
FUNCTION
SPACES
.
486
2.3.
MORE-DIMENSIONAL
WAVELETS
.
487
2.4.
APPROXIMATION
RESULTS
.
490
3.
A
MULTIGRID
ALGORITHM
IN
THREE
DIMENSIONS
.
493
4.
CONVERGENCE
ANALYSIS
.
496
4.1.
FOURIER
ANALYSIS
FOR
BOX
GRIDS
.
497
4.2.
CONVERGENCE
ANALYSIS
RESULTS
.
504
5.
CONCLUSION
.
.
.
508
REFERENCES
.
508
MULTIPLE
SEMI-COARSENING
TECHNIQUES.
(P.M.
DE
ZEEUW)
.
511
1.
INTRODUCTION
.
511
2.
THE
MULTI-LEVEL
METHOD
ON
A
GRID
OF
GRIDS
.
513
2.1.
GRIDS
OF
GRIDS
.
513
2.2.
RESTRICTION
OPERATORS
.
516
2.3.
PROLONGATION
OPERATORS
.
517
2.4.
COHERENCE
.
521
2.5.
GALERKIN
APPROXIMATIONS
.
525
2.6.
SAWTOOTH
MULTI-LEVEL
METHOD
.
529
2.7.
THE
ACCURACY
CONDITION
FOR
GRID
TRANSFER
OPERATORS
.
532
2.8.
THE
SMOOTHING
METHOD
.
533
2.9.
NUMERICAL
RESULTS
.
533
3.
INCOMPLETE
GRID
OF
GRIDS
.
539
3.1.
SPARSE
GRIDS
.
539
3.2.
NUMERICAL
RESULTS
.
541
3.3.
EXPLANATION
OF
RESULTS
.
541
3.4.
REMEDIES
AND
ALTERNATIVES
.
541
3.5.
HIERARCHICAL
BASIS
FOR
FINITE
VOLUMES
.
542
4.
CONCLUSIONS
.
543
REFERENCES
.
543
CONTENTS
(CONTINUED)
PAGE
SEMI-COARSENING
IN
THREE
DIRECTIONS
FOR
EULER-FLOW
COMPUTATIONS
IN
THREE
DIMENSIONS.
(B.
KOREN,
P.W.
HEMKER
AND
P.M.
DE
ZEEUW)
.
547
1.
INTRODUCTION
.
547
2.
EQUATIONS
.
549
2.1.
CONTINUOUS
EQUATIONS
.
549
2.2.
DISCRETIZED
EQUATIONS
.
550
3.
MULTIGRID
METHODS
.
551
3.1.
STANDARD
MULTIGRID
.
551
3.2.
MULTIPLE
SEMI-COARSENED
MULTIGRID
METHOD
.
552
4.
NUMERICAL
RESULTS
.
553
4.1.
TEST
CASE
.
553
4.2.
CONVERGENCE
RESULTS
.
553
5.
OUTLOOK
.
553
REFERENCES
.
554
A.
APPENDIX:
PROLONGATION
OF
SOLUTION
.
556
B.
APPENDIX:
RESTRICTION
OF
DEFECTS
.
558
C.
APPENDIX:
PROLONGATION
OF
SOLUTION
CORRECTIONS
.
559
CONTACT
PERSONS
.
569 |
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV011330104 |
| callnumber-first | Q - Science |
| callnumber-label | QA911 |
| callnumber-raw | QA911 |
| callnumber-search | QA911 |
| callnumber-sort | QA 3911 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 4000 |
| ctrlnum | (OCoLC)37877270 (DE-599)BVBBV011330104 |
| dewey-full | 532/.0533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0533 |
| dewey-search | 532/.0533 |
| dewey-sort | 3532 3533 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| genre | 1\p (DE-588)4155043-2 Forschungsbericht gnd-content |
| genre_facet | Forschungsbericht |
| id | DE-604.BV011330104 |
| illustrated | Illustrated |
| indexdate | 2024-08-17T00:55:30Z |
| institution | BVB |
| isbn | 3528069570 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007613092 |
| oclc_num | 37877270 |
| open_access_boolean | |
| owner | DE-703 DE-210 DE-83 |
| owner_facet | DE-703 DE-210 DE-83 |
| physical | XVI, 569 S. graph. Darst. 23 cm |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Vieweg |
| record_format | marc |
| series | Notes on numerical fluid mechanics |
| series2 | Notes on numerical fluid mechanics |
| spelling | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 ed. by Herman Deconinck and Barry Koren Braunschweig [u.a.] Vieweg 1997 XVI, 569 S. graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier Notes on numerical fluid mechanics 57 Lagrange equations Numerical solutions Multigrid methods (Numerical analysis) Navier-Stokes equations Numerical solutions Upwind-Verfahren (DE-588)4482840-8 gnd rswk-swf Bewegungsgleichung (DE-588)4006321-5 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Aerodynamik (DE-588)4000589-6 gnd rswk-swf Adaptives Gitter (DE-588)4333769-7 gnd rswk-swf Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd rswk-swf 1\p (DE-588)4155043-2 Forschungsbericht gnd-content Navier-Stokes-Gleichung (DE-588)4041456-5 s Mehrgitterverfahren (DE-588)4038376-3 s Adaptives Gitter (DE-588)4333769-7 s DE-604 Eulersche Bewegungsgleichungen (DE-588)4219070-8 s Upwind-Verfahren (DE-588)4482840-8 s Bewegungsgleichung (DE-588)4006321-5 s 2\p DE-604 Aerodynamik (DE-588)4000589-6 s 3\p DE-604 Deconinck, Herman Sonstige oth Notes on numerical fluid mechanics 57 (DE-604)BV000898664 57 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007613092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 Notes on numerical fluid mechanics Lagrange equations Numerical solutions Multigrid methods (Numerical analysis) Navier-Stokes equations Numerical solutions Upwind-Verfahren (DE-588)4482840-8 gnd Bewegungsgleichung (DE-588)4006321-5 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Aerodynamik (DE-588)4000589-6 gnd Adaptives Gitter (DE-588)4333769-7 gnd Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd |
| subject_GND | (DE-588)4482840-8 (DE-588)4006321-5 (DE-588)4038376-3 (DE-588)4041456-5 (DE-588)4000589-6 (DE-588)4333769-7 (DE-588)4219070-8 (DE-588)4155043-2 |
| title | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 |
| title_auth | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 |
| title_exact_search | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 |
| title_full | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 ed. by Herman Deconinck and Barry Koren |
| title_fullStr | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 ed. by Herman Deconinck and Barry Koren |
| title_full_unstemmed | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 ed. by Herman Deconinck and Barry Koren |
| title_short | Euler and Navier stokes solvers using multi-dimensional upwind schemes and multigrid acceleration |
| title_sort | euler and navier stokes solvers using multi dimensional upwind schemes and multigrid acceleration results of the brite euram projects aero ct89 0003 and aer2 ct92 00040 1989 1995 |
| title_sub | results of the BRITE/EURAM projects AERO-CT89-0003 and AER2-CT92-00040, 1989 - 1995 |
| topic | Lagrange equations Numerical solutions Multigrid methods (Numerical analysis) Navier-Stokes equations Numerical solutions Upwind-Verfahren (DE-588)4482840-8 gnd Bewegungsgleichung (DE-588)4006321-5 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Aerodynamik (DE-588)4000589-6 gnd Adaptives Gitter (DE-588)4333769-7 gnd Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd |
| topic_facet | Lagrange equations Numerical solutions Multigrid methods (Numerical analysis) Navier-Stokes equations Numerical solutions Upwind-Verfahren Bewegungsgleichung Mehrgitterverfahren Navier-Stokes-Gleichung Aerodynamik Adaptives Gitter Eulersche Bewegungsgleichungen Forschungsbericht |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007613092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000898664 |
| work_keys_str_mv | AT deconinckherman eulerandnavierstokessolversusingmultidimensionalupwindschemesandmultigridaccelerationresultsofthebriteeuramprojectsaeroct890003andaer2ct920004019891995 |