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Workshop on Iterative Errors inUnsteady Flow Simulations
L. Eça, G. Vaz and M. Hoekstra
3-5 May2017
Contents• Objective
• Test Case- Definition of flow problem
- Quantities of interest
• Participants
• Overview of Codes andSolution Strategies
• Submitted Results
• Observations and Future Work
Workshop on Iterative Errors in Unsteady Flow Simulations
ASME V&V Symposium, 3-5 May 2017
Objective
• Investigate the influence of iterative errors on
unsteady flow simulations performed with flow
solvers using implicit time integration
─ Check if different flow solvers exhibit the
the same trends.
─ Create awareness to the problem.
─ Use the available data to develop iterative
error estimators that can be used in the
so-called “practical applications” where
tight iterative convergence criteria may
become too expensive.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Test Case
• Flow around a circular cylinder with Reynolds
number equal to 100 or 150. Two-dimensional
flow of an incompressible fluid.
(Nearly DNS ☺!)
�� =���
�
• Fixed computational domain and boundary
conditions.
• Four multiblock structured grids available in
different formats (CGNS, MSH, CFX,
OpenFoam).
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Test Case
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
0=
= ∞
y
x
V
VV
0=p
0
0;0
=∂
∂
==
n
yx
y
p
VV
0;0
0
=∂
∂=
∂
∂
=
y
p
y
V
V
x
y
Test Case
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Number of cells and grid refinement ratio of the set
Grid Number of cells Number of Faces on cylinder surface �
�
1 503640 1920 1
2 282174 1440 1.33
3 196266 1200 1.6
4 125910 960 2
Test Case
• Quantities of interest:
─ Time-averaged (CD )avg and standard
deviation (CD )std of the drag coefficient CD
─ Standard deviation (CL )std of the lift
coefficient CL
─ Strouhal number St
─ Time-averaged base pressure coefficient,
(Cpb)avg
─ Time-averaged flow separation point,
(θsep)avg
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Participants
• A. Jones (Rolls-Royce PLC)
• S. Guda, I. Çelik (West Virgina University)
• Y. Chen, K.J. Maki, H. Ye (University of Michigan)
• Sanjeeb Pal (ASME member)
• L. Eça, G.Vaz, M.Hoekstra (MARIN/IST)
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Overview of Codes
• ANSYS Fluent
• CFX 14.5
• OpenFoam (pimpleFoam)
• ReFRESCO 2.1
• SATURNE
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Solution Strategies
• Pressure-velocity coupling
- Fully-coupled
- SIMPLE, SIMPLEC
- PISO/SIMPLE
- PISO
• Time discretization
- First-order backward differencing
- Second-order backward differencing
• Space discretization
- Second-order diffusion
- Convection: Linear upwind (β=1);
Second-order upwind
Central differences
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Solution Strategies
• Iterative convergence criteria at each
time step:
- Normalized residuals corresponding to a
solution change in a simple Jacobi iteration
(Maximum or RMS values)
- Average normalized residuals (absolute value)
- Global sum of squares of cells residuals
- Maximum number of iterations
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Submitted Results
• Re=100
- PISO; Second order upwind for convection;
Second-order backwards for time.
Normalized absolute residual (average value) with
a maximum of 100 iterations (L2a).
Grids 3 and 4 with ∆t=0.01
- SIMPLE; Second order upwind for convection;
Second-order backwards for time.
Normalized residual (maximum value, L∞)
Grids 1, 2, 3 and 4 with several ∆t
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Submitted Results
• Re=100
- SIMPLE; Second order upwind for convection;
First-order backwards for time.
Normalized residual (maximum value, L∞)
Grid 4 with ∆t =0.05
- SIMPLEC; Central differences for convection
First-order backwards for time.
Global sum of squares of cells residuals (L2b)
Grids 1, 2, 3 and 4 with ∆t =0.01 to ∆t =0.02
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Submitted Results• Re=100, Grid 4
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.26
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34L
2a,1
st,0.01
L2b,1
st,0.02
L∞,2
nd,0.02
L∞,2
nd,0.005
L∞,2
nd,0.05
L∞,1
st,0.05
Norm, Time, ∆t
Submitted Results• Re=100, Grid 3
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.26
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34L
2a,1
st,0.01
L2b,1
st,0.016
L∞,2
nd,0.016
L∞,2
nd,0.004
L∞,2
nd,0.04
Norm, Time, ∆t
Submitted Results• Re=100, Grid 2
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.26
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34L
2b,1
st,0.013
L∞,2
nd,0.013
L∞,2
nd,0.0033
L∞,2
nd,0.033
Norm, Time, ∆t
Submitted Results• Re=100, Grid 1
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.26
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34L
2b,1
st,0.01
L∞,2
nd,0.01
L∞,2
nd,0.0025
L∞,2
nd,0.025
Norm, Time, ∆t
Submitted Results• Re=100, Grid 4
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.002
0.004
0.006
0.008
L2a,1
st,0.01
L2b,1
st,0.02
L∞,2
nd,0.02
L∞,2
nd,0.005
L∞,2
nd,0.05
L∞,1
st,0.05
Norm, Time, ∆t
Submitted Results• Re=100, Grid 3
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.002
0.004
0.006
0.008
L2a,1
st,0.01
L2b,1
st,0.016
L∞,2
nd,0.016
L∞,2
nd,0.004
L∞,2
nd,0.04
Norm, Time, ∆t
Submitted Results• Re=100, Grid 2
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.002
0.004
0.006
0.008
L2b,1
st,0.013
L∞,2
nd,0.013
L∞,2
nd,0.0033
L∞,2
nd,0.033
Norm, Time, ∆t
Submitted Results• Re=100, Grid 1
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.002
0.004
0.006
0.008
L2b,1
st,0.01
L∞,2
nd,0.01
L∞,2
nd,0.0025
L∞,2
nd,0.025
Norm, Time, ∆t
Submitted Results• Re=100, Grid 4
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.15
0.2
0.25
0.3
L2a,1
st,0.01
L2b,1
st,0.02
L∞,2
nd,0.02
L∞,2
nd,0.005
L∞,2
nd,0.05
L∞,1
st,0.05
Norm, Time, ∆t
Submitted Results• Re=100, Grid 3
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.15
0.2
0.25
0.3
L2a,1
st,0.01
L2b,1
st,0.016
L∞,2
nd,0.016
L∞,2
nd,0.004
L∞,2
nd,0.04
Norm, Time, ∆t
Submitted Results• Re=100, Grid 2
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.15
0.2
0.25
0.3
L2b,1
st,0.013
L∞,2
nd,0.013
L∞,2
nd,0.0033
L∞,2
nd,0.033
Norm, Time, ∆t
Submitted Results• Re=100, Grid 1
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.15
0.2
0.25
0.3
L2b,1
st,0.01
L∞,2
nd,0.01
L∞,2
nd,0.0025
L∞,2
nd,0.025
Norm, Time, ∆t
Submitted Results• Re=100, Grid 4
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.125
0.15
0.175
L2a,1
st,0.01
L2b,1
st,0.02
L∞,2
nd,0.02
L∞,2
nd,0.005
L∞,2
nd,0.05
L∞,1
st,0.05
Norm, Time, ∆t
Submitted Results• Re=100, Grid 3
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.125
0.15
0.175
L2a,1
st,0.01
L2b,1
st,0.016
L∞,2
nd,0.016
L∞,2
nd,0.004
L∞,2
nd,0.04
Norm, Time, ∆t
Submitted Results• Re=100, Grid 2
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.125
0.15
0.175
L2b,1
st,0.013
L∞,2
nd,0.013
L∞,2
nd,0.0033
L∞,2
nd,0.033
Norm, Time, ∆t
Submitted Results• Re=100, Grid 1
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.1
0.125
0.15
0.175
L2b,1
st,0.01
L∞,2
nd,0.01
L∞,2
nd,0.0025
L∞,2
nd,0.025
Norm, Time, ∆t
Submitted Results• Re=100, Grid 4
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-0.75
-0.7
-0.65
-0.6
-0.55
L2a,1
st,0.01
L∞,2
nd,0.02
L∞,2
nd,0.005
L∞,2
nd,0.05
L∞,1
st,0.05
Norm, Time, ∆t
Submitted Results• Re=100, Grid 3
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-0.75
-0.7
-0.65
-0.6
-0.55
L2a,1
st,0.01
L∞,2
nd,0.016
L∞,2
nd,0.004
L∞,2
nd,0.04
Norm, Time, ∆t
Submitted Results• Re=100, Grid 2
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-0.75
-0.7
-0.65
-0.6
-0.55
L∞,2
nd,0.013
L∞,2
nd,0.0033
L∞,2
nd,0.033
Norm, Time, ∆t
Submitted Results• Re=100, Grid 1
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-0.75
-0.7
-0.65
-0.6
-0.55
L∞,2
nd,0.01
L∞,2
nd,0.0025
L∞,2
nd,0.025
Norm, Time, ∆t
Submitted Results• Re=100, Grid 4
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θsep)avg
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100116
116.25
116.5
116.75
117
L∞,2
nd,0.02
L∞,2
nd,0.005
L∞,2
nd,0.05
L∞,1
st,0.05
Norm, Time, ∆t
Submitted Results• Re=100, Grid 3
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θsep)avg
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100116
116.25
116.5
116.75
117
L∞,2
nd,0.016
L∞,2
nd,0.004
L∞,2
nd,0.04
Norm, Time, ∆t
Submitted Results• Re=100, Grid 2
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θsep)avg
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100116
116.25
116.5
116.75
117
L∞,2
nd,0.013
L∞,2
nd,0.0033
L∞,2
nd,0.033
Norm, Time, ∆t
Submitted Results• Re=100, Grid 1
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θsep)avg
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100116
116.25
116.5
116.75
117
L∞,2
nd,0.01
L∞,2
nd,0.0025
L∞,2
nd,0.025
Norm, Time, ∆t
Submitted Results• Re=100, Grid 4
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Tolit
L2/L
∞(φ
)
Nu
mb
erof
iter
ati
on
s
10-6
10-5
10-4
10-3
10-2
0.05
0.1
0.15
0.2
0
50
100
150
Niter
Vx
Vy
Cp
Grid 4, Courantmax
=1.6
Influence of iterative convergence criteria at each time
step (Tolit) on the number of iterations performed (Niter)and ratio between L2 and L
∞norms of the residuals
Submitted Results• Re=100, Grid 4
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Tolit
L2/L
∞(φ
)
Nu
mb
erof
iter
ati
on
s
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0.05
0.1
0.15
0.2
0
50
100
150
Niter
Vx
Vy
Cp
Grid 4, Courantmax
=6.2
Influence of iterative convergence criteria at each time
step (Tolit) on the number of iterations performed (Niter)and ratio between L2 and L
∞norms of the residuals
Submitted Results• Re=100, Grid 4
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Tolit
L2/L
∞(φ
)
Nu
mb
erof
iter
ati
on
s
10-6
10-5
10-4
10-3
10-2
0.05
0.1
0.15
0.2
0
50
100
150
Niter
Vx
Vy
Cp
Grid 4, Courantmax
=15.4
Influence of iterative convergence criteria at each time
step (Tolit) on the number of iterations performed (Niter)and ratio between L2 and L
∞norms of the residuals
Submitted Results• Re=100
• Estimation of the discretization error of the
Time-averaged drag coefficient using data
from three different levels of Tolit.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
ri
(CD) a
vg
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21.29
1.3
1.31
1.32
1.33
1.34
1.35Tol
it=10
-3
p=2
Tolit=10
-4
p=2
Tolit=10
-6
p= 1.7
Submitted Results
• Re=150
- Fully-coupled solution; Linear upwind for convection;
Second-order backwards for time.
RMS of normalized residuals and “Conservation
Imbalance” (CI) with a maximum of 10 iterations per
time step (L2a, L2c).
Grids 1 (finest) and 4 (coarsest) with ∆t=0.1
- PISO/SIMPLE; Linear upwind for convection;
Second-order backwards for time.
Maximum number of iterations (Nit).
Grid 4 with maximum Courant numbers of 1, 5
and 10
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Submitted Results
• Re=150
- PISO; Second order upwind for convection;
First-order backwards for time.
Normalized absolute residual (average value) with
a maximum of 100 iterations (L2b).
Grids 3 and 4 with ∆t=0.01
- SIMPLE; Second order upwind for convection;
Second-order backwards for time.
Normalized residual (maximum value, L∞)
Grids 1, 2, 3 and 4 with ∆t=0.01 to ∆t=0.02
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Submitted Results• Re=150, Grid 4
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
Number of iterations
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
01234567
1.2
1.225
1.25
1.275
1.3
1.325
1.35
1.375
1.4
L2a,2
nd,0.1
L2c,2
nd,0.1
Nit,2
nd,0.003
Nit,2
nd,0.016
Nit,2
nd,0.03
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 3
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.2
1.225
1.25
1.275
1.3
1.325
1.35
1.375
1.4
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 2
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.2
1.225
1.25
1.275
1.3
1.325
1.35
1.375
1.4
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 1
Time-averaged drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1001.2
1.225
1.25
1.275
1.3
1.325
1.35
1.375
1.4
L2c,2
nd,0.1
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 4
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
Number of iterations
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
01234567
0.01
0.02
0.03
0.04
0.05
L2a,2
nd,0.1
L2c,2
nd,0.1
Nit,2
nd,0.003
Nit,2
nd,0.016
Nit,2
nd,0.03
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 3
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0.01
0.02
0.03
0.04
0.05
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 2
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0.01
0.02
0.03
0.04
0.05
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 1
Standard deviation drag coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CD) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0.01
0.02
0.03
0.04
0.05
L2c,2
nd,0.1
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 4
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
Number of iterations
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
01234567
0.2
0.3
0.4
0.5
0.6
L2a,2
nd,0.1
L2c,2
nd,0.1
Nit,2
nd,0.003
Nit,2
nd,0.016
Nit,2
nd,0.03
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 3
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.2
0.3
0.4
0.5
0.6
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 2
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.2
0.3
0.4
0.5
0.6
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 1
Standard deviation lift coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(CL) st
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.2
0.3
0.4
0.5
0.6
L2c,2
nd,0.1
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 4
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
Number of iterations
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
01234567
0.15
0.16
0.17
0.18
0.19
L2a,2
nd,0.1
L2c,2
nd,0.1
Nit,2
nd,0.003
Nit,2
nd,0.016
Nit,2
nd,0.03
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 3
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.15
0.16
0.17
0.18
0.19
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 2
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.15
0.16
0.17
0.18
0.19
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 1
Strouhal number
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
St
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1000.15
0.16
0.17
0.18
0.19
L2c,2
nd,0.1
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 4
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
Number of iterations
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
01234567
-1
-0.9
-0.8
-0.7
L2a,2
nd,0.1
L2c,2
nd,0.1
Nit,2
nd,0.003
Nit,2
nd,0.016
Nit,2
nd,0.03
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 3
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-1
-0.9
-0.8
-0.7
L″b,1
st,0.01
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 2
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-1
-0.9
-0.8
-0.7
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 1
Time-averaged base pressure coefficient
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(Cp
b) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100-1
-0.9
-0.8
-0.7
L2c,2
nd,0.1
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 4
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
Number of iterations
(θse
p) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
01234567
105
110
115
120
L2a,2
nd,0.1
L2c,2
nd,0.1
Nit,2
nd,0.003
Nit,2
nd,0.016
Nit,2
nd,0.03
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 3
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θse
p) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100105
110
115
120
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 2
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θse
p) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100105
110
115
120
L∞,2
nd,0.02
Norm, Time, ∆t
Submitted Results• Re=150, Grid 1
Time-averaged separation point
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Residual
(θse
p) av
g
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100105
110
115
120
L2c,2
nd,0.1
L∞,2
nd,0.02
Norm, Time, ∆t
Observations
• Convergence criteria applied at each time
step of flow solvers that use implicit time
integration may have a significant influence
on the numerical accuracy of the solution.
• Obtaining statistical convergence (periodic
solution) and observed orders of grid/time
convergence matching the formal order of the
discretization does not guarantee that the
iterative error is negligible.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Observations
• Results submitted to the Workshop use several
different convergence criteria at each time step,
distinct accuracies of time discretization and/or
various strategies to define the time step.
Therefore, comparison between different data
of different codes is troublesome.
• However, submitted data suggest that convergence
criteria that guarantee a negligible influence of
the iterative error depend on the grid refinement,
time step (Courant number) and accuracy of the
time integration technique.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Future Work
• A second edition of the Workshop will be
proposed for the V&V Symposium of 2018.
Test case (and grids) remain identical, but
simulations will be performed only at Re=100.
• Quantities of interest remain the same and
the number of levels of the iterative convergence
criteria at each time step should be preferably
larger or equal than 3, discarding conditions that
lead to solutions without vortex shedding or with an
unreasonable value of the Strouhal number.
• Three different time steps (or maximum Courant
numbers) will be prescribed.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Future Work
• Participants will be requested to report the
following information:
- Average and maximum values of the residuals
at each time step;
- Average and maximum number of iterations
performed at each time step;
- Procedure adopted to normalize the residuals;
- Number of cycles used to obtain the quantities
of interest and maximum changes obtained in
these cycles.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
Acknowledgement
• We would like to thank all the groups that
submitted data and to all the participants
that attended this Workshop.
• The use of the computing resources of the
Laboratory for Advanced Computing at
University of Coimbra (http://www.lca.uc.pt)
in the preparation of this Workshop is gratefully
acknowledge.
ASME V&V Symposium, 3-5 May 2017
Workshop on Iterative Errors in Unsteady Flow Simulations
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