Workshop on Iterative Errors in Unsteady Flow Simulations L. Eça, G. Vaz and M. Hoekstra. 3-5 May 2017
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1 Workshop on Iterative Errors in Unsteady Flow Simulations L. Eça, G. Vaz and M. Hoekstra 3-5 May 2017
2 Contents Objective Test Case - Definition of flow problem - Quantities of interest Participants Overview of Codes and Solution Strategies Submitted Results Observations and Future Work
3 Objective ASME V&V Symposium, 3-5 May 2017 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.
4 Test Case ASME V&V Symposium, 3-5 May 2017 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).
5 Test Case ASME V&V Symposium, 3-5 May 2017 = 0 = y x V V V = 0 p 0 0 0; = = = n y x y p V V 0 0; 0 = = = y p y V V x y
6 Test Case ASME V&V Symposium, 3-5 May 2017 Number of cells and grid refinement ratio of the set Grid Numberof cells Number of Faces on cylindersurface
7 Test Case ASME V&V Symposium, 3-5 May 2017 Quantities of interest: Time-averaged (C D ) avg and standard deviation (C D ) std of the drag coefficient C D Standard deviation (C L ) std of the lift coefficient C L Strouhal number St Time-averaged base pressure coefficient, (Cp b ) avg Time-averaged flow separation point, (θ sep ) avg
8 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)
9 Overview of Codes ANSYS Fluent CFX 14.5 OpenFoam (pimplefoam) ReFRESCO 2.1 SATURNE
10 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
11 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
12 Submitted Results Re=100 ASME V&V Symposium, 3-5 May PISO; Second order upwind for convection; Second-order backwards for time. Normalized absolute residual (average value) with a maximum of 100 iterations ( a). Grids 3 and 4 with t= SIMPLE; Second order upwind for convection; Second-order backwards for time. Normalized residual (maximum value, ) Grids 1, 2, 3 and 4 with several t
13 Submitted Results Re=100 ASME V&V Symposium, 3-5 May SIMPLE; Second order upwind for convection; First-order backwards for time. Normalized residual (maximum value, ) Grid 4 with t = SIMPLEC; Central differences for convection First-order backwards for time. Global sum of squares of cells residuals ( b) Grids 1, 2, 3 and 4 with t =0.01 to t =0.02
14 (C D ) avg Submitted Results Re=100, Grid ASME V&V Symposium, 3-5 May Time-averaged drag coefficient a,1 st,0.01 b,1 st,0.02,2 nd,0.02,2 nd,0.005,2 nd,0.05,1 st,0.05
15 (C D ) avg Submitted Results Re=100, Grid ASME V&V Symposium, 3-5 May Time-averaged drag coefficient a,1 st,0.01 b,1 st,0.016,2 nd,0.016,2 nd,0.004,2 nd,0.04
16 (C D ) avg Submitted Results Re=100, Grid ASME V&V Symposium, 3-5 May Time-averaged drag coefficient b,1 st,0.013,2 nd,0.013,2 nd,0.0033,2 nd,0.033
17 (C D ) avg Submitted Results Re=100, Grid ASME V&V Symposium, 3-5 May Time-averaged drag coefficient b,1 st,0.01,2 nd,0.01,2 nd,0.0025,2 nd,0.025
18 (C D ) std Submitted Results Re=100, Grid a,1 st,0.01 b,1 st,0.02,2 nd,0.02,2 nd,0.005,2 nd,0.05,1 st, Standard deviation drag coefficient
19 (C D ) std Submitted Results Re=100, Grid a,1 st,0.01 b,1 st,0.016,2 nd,0.016,2 nd,0.004,2 nd, Standard deviation drag coefficient
20 (C D ) std Submitted Results Re=100, Grid b,1 st,0.013,2 nd,0.013,2 nd,0.0033,2 nd, Standard deviation drag coefficient
21 (C D ) std Submitted Results Re=100, Grid b,1 st,0.01,2 nd,0.01,2 nd,0.0025,2 nd, Standard deviation drag coefficient
22 (C L ) std Submitted Results Re=100, Grid a,1 st,0.01 b,1 st,0.02,2 nd,0.02,2 nd,0.005,2 nd,0.05,1 st, Standard deviation lift coefficient
23 (C L ) std Submitted Results Re=100, Grid a,1 st,0.01 b,1 st,0.016,2 nd,0.016,2 nd,0.004,2 nd, Standard deviation lift coefficient
24 Submitted Results Re=100, Grid b,1 st,0.013,2 nd,0.013,2 nd,0.0033,2 nd,0.033 (C L ) std Standard deviation lift coefficient
25 Submitted Results Re=100, Grid b,1 st,0.01,2 nd,0.01,2 nd,0.0025,2 nd,0.025 (C L ) std Standard deviation lift coefficient
26 Submitted Results Re=100, Grid a,1 st,0.01 b,1 st,0.02,2 nd,0.02,2 nd,0.005,2 nd,0.05,1 st,0.05 St Strouhal number
27 Submitted Results Re=100, Grid a,1 st,0.01 b,1 st,0.016,2 nd,0.016,2 nd,0.004,2 nd,0.04 St Strouhal number
28 Submitted Results Re=100, Grid b,1 st,0.013,2 nd,0.013,2 nd,0.0033,2 nd,0.033 St Strouhal number
29 Submitted Results Re=100, Grid b,1 st,0.01,2 nd,0.01,2 nd,0.0025,2 nd,0.025 St Strouhal number
30 (Cp b ) avg Submitted Results Re=100, Grid a,1 st,0.01,2 nd,0.02,2 nd,0.005,2 nd,0.05,1 st, Time-averaged base pressure coefficient
31 Submitted Results Re=100, Grid a,1 st,0.01,2 nd,0.016,2 nd,0.004,2 nd,0.04 (Cp b ) avg Time-averaged base pressure coefficient
32 Submitted Results Re=100, Grid ,2 nd,0.013,2 nd,0.0033,2 nd,0.033 (Cp b ) avg Time-averaged base pressure coefficient
33 Submitted Results Re=100, Grid ,2 nd,0.01,2 nd,0.0025,2 nd,0.025 (Cp b ) avg Time-averaged base pressure coefficient
34 (θ sep ) avg Submitted Results Re=100, Grid ,2 nd,0.02,2 nd,0.005,2 nd,0.05,1 st, Time-averaged separation point
35 Submitted Results Re=100, Grid ,2 nd,0.016,2 nd,0.004,2 nd,0.04 (θ sep ) avg Time-averaged separation point
36 Submitted Results Re=100, Grid ,2 nd,0.013,2 nd,0.0033,2 nd,0.033 (θ sep ) avg Time-averaged separation point
37 Submitted Results Re=100, Grid ,2 nd,0.01,2 nd,0.0025,2 nd,0.025 (θ sep ) avg Time-averaged separation point
38 Submitted Results Re=100, Grid Grid 4, Courant max = / (φ) N iter V x V y C p 50 Number of iterations Tol it Influence of iterative convergence criteria at each time step (Tol it ) on the number of iterations performed (N iter ) and ratio between and norms of the residuals
39 Submitted Results Re=100, Grid Grid 4, Courant max = / (φ) N iter V x V y C p 50 Number of iterations Tol it Influence of iterative convergence criteria at each time step (Tol it ) on the number of iterations performed (N iter ) and ratio between and norms of the residuals
40 Submitted Results Re=100, Grid Grid 4, Courant max = / (φ) N iter V x V y C p 50 Number of iterations Tol it Influence of iterative convergence criteria at each time step (Tol it ) on the number of iterations performed (N iter ) and ratio between and norms of the residuals
41 Submitted Results Re=100 (C D ) avg Tol it =10-3 p=2 Tol it =10-4 p=2 Tol it =10-6 p= r i Estimation of the discretization error of the Time-averaged drag coefficient using data from three different levels of Tol it.
42 Submitted Results Re=150 ASME V&V Symposium, 3-5 May 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 ( a, c). 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 (N it ). Grid 4 with maximum Courant numbers of 1, 5 and 10
43 Submitted Results Re=150 ASME V&V Symposium, 3-5 May PISO; Second order upwind for convection; First-order backwards for time. Normalized absolute residual (average value) with a maximum of 100 iterations ( b). Grids 3 and 4 with t= SIMPLE; Second order upwind for convection; Second-order backwards for time. Normalized residual (maximum value, ) Grids 1, 2, 3 and 4 with t=0.01 to t=0.02
44 (C D ) avg Submitted Results Re=150, Grid ASME V&V Symposium, 3-5 May 2017 Number of iterations Time-averaged drag coefficient a,2 nd,0.1 c,2 nd,0.1 N it,2 nd,0.003 N it,2 nd,0.016 N it,2 nd,0.03 L b,1 st,0.01,2 nd,0.02
45 Submitted Results Re=150, Grid 3 ASME V&V Symposium, 3-5 May 2017 (C D ) avg Time-averaged drag coefficient L b,1 st,0.01,2 nd,0.02
46 Submitted Results Re=150, Grid 2 ASME V&V Symposium, 3-5 May 2017 (C D ) avg Time-averaged drag coefficient,2 nd,0.02
47 Submitted Results Re=150, Grid 1 ASME V&V Symposium, 3-5 May 2017 (C D ) avg Time-averaged drag coefficient c,2 nd,0.1,2 nd,0.02
48 Submitted Results Re=150, Grid Number of iterations (C D ) std Standard deviation drag coefficient a,2 nd,0.1 c,2 nd,0.1 N it,2 nd,0.003 N it,2 nd,0.016 N it,2 nd,0.03 L b,1 st,0.01,2 nd,0.02
49 Submitted Results Re=150, Grid 3 ASME V&V Symposium, 3-5 May (C D ) std L b,1 st,0.01,2 nd, Standard deviation drag coefficient
50 Submitted Results Re=150, Grid 2 ASME V&V Symposium, 3-5 May (C D ) std ,2 nd, Standard deviation drag coefficient
51 Submitted Results Re=150, Grid 1 ASME V&V Symposium, 3-5 May (C D ) std c,2 nd,0.1,2 nd, Standard deviation drag coefficient
52 Submitted Results Re=150, Grid Number of iterations (C L ) std Standard deviation lift coefficient a,2 nd,0.1 c,2 nd,0.1 N it,2 nd,0.003 N it,2 nd,0.016 N it,2 nd,0.03 L b,1 st,0.01,2 nd,0.02
53 Submitted Results Re=150, Grid 3 ASME V&V Symposium, 3-5 May (C L ) std 0.4 L b,1 st,0.01,2 nd, Standard deviation lift coefficient
54 Submitted Results Re=150, Grid 2 ASME V&V Symposium, 3-5 May (C L ) std 0.4,2 nd, Standard deviation lift coefficient
55 Submitted Results Re=150, Grid 1 ASME V&V Symposium, 3-5 May (C L ) std 0.4 c,2 nd,0.1,2 nd, Standard deviation lift coefficient
56 Submitted Results Re=150, Grid Number of iterations St Strouhal number a,2 nd,0.1 c,2 nd,0.1 N it,2 nd,0.003 N it,2 nd,0.016 N it,2 nd,0.03 L b,1 st,0.01,2 nd,0.02
57 Submitted Results Re=150, Grid 3 ASME V&V Symposium, 3-5 May St 0.17 L b,1 st,0.01,2 nd, Strouhal number
58 Submitted Results Re=150, Grid 2 ASME V&V Symposium, 3-5 May St 0.17,2 nd, Strouhal number
59 Submitted Results Re=150, Grid 1 ASME V&V Symposium, 3-5 May St 0.17 c,2 nd,0.1,2 nd, Strouhal number
60 Submitted Results Re=150, Grid Number of iterations (Cp b ) avg Time-averaged base pressure coefficient a,2 nd,0.1 c,2 nd,0.1 N it,2 nd,0.003 N it,2 nd,0.016 N it,2 nd,0.03 L b,1 st,0.01,2 nd,0.02
61 Submitted Results Re=150, Grid 3 ASME V&V Symposium, 3-5 May (Cp b ) avg L b,1 st,0.01,2 nd, Time-averaged base pressure coefficient
62 Submitted Results Re=150, Grid 2 ASME V&V Symposium, 3-5 May (Cp b ) avg ,2 nd, Time-averaged base pressure coefficient
63 Submitted Results Re=150, Grid 1 ASME V&V Symposium, 3-5 May (Cp b ) avg c,2 nd,0.1,2 nd, Time-averaged base pressure coefficient
64 Submitted Results Re=150, Grid Number of iterations (θ sep ) avg a,2 nd,0.1 c,2 nd,0.1 N it,2 nd,0.003 N it,2 nd,0.016 N it,2 nd,0.03,2 nd, Time-averaged separation point
65 Submitted Results Re=150, Grid 3 ASME V&V Symposium, 3-5 May (θ sep ) avg ,2 nd, Time-averaged separation point
66 Submitted Results Re=150, Grid 2 ASME V&V Symposium, 3-5 May (θ sep ) avg ,2 nd, Time-averaged separation point
67 Submitted Results Re=150, Grid 1 ASME V&V Symposium, 3-5 May (θ sep ) avg c,2 nd,0.1,2 nd, Time-averaged separation point
68 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.
69 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.
70 Future Work A second edition of the Workshop will be proposed for the V&V Symposium of 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.
71 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.
72 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 ( in the preparation of this Workshop is gratefully acknowledge.
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