A V&V Overview of the 31st Symposium on Naval Hydrodynamics V&V 20 Supplement about Solution Verification for Unsteady Flow Calculations Workshop Sessions at the 2017 V&V ASME Symposium - Iterative errors in unsteady flow simulations - Discretization error estimation

L. Eça (IST-Lisbon, MARIN Academy) A V&V Overview of the 31st Symposium on Naval Hydrodynamics 11th to 16th September 2016 L. Eça (IST-Lisbon, MARIN Academy)

31st Symposium on Naval Hydrodynamics Symposium organized by the Office of Naval Research every 2 years 106 papers presented at the Symposium and 7 invited lectures 4 of the invited lectures addressed CFD, but Verification was not addressed and Validation was most of the times presented as graphical comparisons of movies or plots with no experimental or numerical uncertainties

31st Symposium on Naval Hydrodynamics A keyword search of the contents of the 106 papers produced the following results: Keyword Papers Simulation 93 Error bar 8 Experiment 103 Uncertainty 42 Keyword Papers Numerical uncertainty 8 Numerical error 10 Experimental uncertainty Experimental error 2

31st Symposium on Naval Hydrodynamics A keyword search of the contents of the 106 papers produced the following results: Keyword Papers Verification 24 Iterative error or convergence 3 Validation 60 Validated 33 Validation Uncertainty 5 Verified 19 Code Verification Grid refinement 12 Accuracy 58 Convergence 40

31st Symposium on Naval Hydrodynamics 31 of the 33 papers that mention Validated do not refer to Validation Uncertainty The 2 papers that “claim” Validated is a consequence of E<Uval (independently of the value of Uval) Error bars or experimental uncertainties are always estimated with power series expansions (grid refinement studies) Iterative errors are rarely mentioned. From the 3 papers that address iterative errors only 2 are checking the effect of these errors (RANS models)

31st Symposium on Naval Hydrodynamics Unexpected conclusions... - “It may be noted that the conclusions regarding turbulence models are dependent on the grid characteristics” - “The computation is carried out by an in-house code, which have been discussed, applied, verified and validated for ship flows and have been proved to be competent in simulating the unsteady viscous flow around ships”

31st Symposium on Naval Hydrodynamics Unexpected conclusions... - “It has been seen that the predicted steady-state solution is grid-independent, both in terms of forces and local pressure coefficient, although discrepancies have been observed in the lift being too low compared to the experimental data and the minimum pressure coefficient being higher than in other numerical studies. This could potentially explain the under-prediction of cavitation extent”

Solution Verification of Unsteady Flow Calculations L. Eça (IST-Lisbon, MARIN Academy)

Solution Verification in Unsteady Flows Estimating numerical errors in unsteady flow simulations can be significantly different from steady flow Contributions to the numerical error depend on time integration technique and initial conditions A possible future supplement of V&V 20 should address this topic to provide information about the different contributions to the numerical error and techniques to estimate them

Solution Verification in Unsteady Flows Specific problems of CFD formulations should not be discussed (most of these problems should be addressed by Code Verification) Nonetheless, implicit/explicit time integration or exact/approximate initial conditions must be addressed (time accurate simulations or periodic flows) Defining contributions to numerical errors is (almost) as important as describing techniques there able to estimate these errors Next few slides illustrate a proposal for the layout

Solution Verification in Unsteady Flows Standard Contents - Introduction (what is different from steady flow) - Numerical errors Explicit vs implict time-integration Time-accurate vs periodic flow simulations - Estimation of Numerical Uncertainty Round-off error Statistical error (dependent on type of simulation) Iterative error (dependent on type of simulation) Discretization error (how general?)

Solution Verification in Unsteady Flows Standard Contents - Examples - Manufactured Solutions Transient flow Periodic flow - Flow around a circular cylinder Re=100

L. Eça (IST-Lisbon, MARIN Academy) Workshop Sessions at the 2017 V&V ASME Symposium L. Eça (IST-Lisbon, MARIN Academy)

Iterative Errors in Unsteady Flows The goal of this Workshop is to discuss the influence of iterative errors on unsteady flow simulations and test methods to estimate them Proposed test case is a laminar, two-dimensional flow of an incompressible fluid around a circular cylinder Reynolds number based on incoming flow velocity V∞ and cylinder diameter D is 100 or 150 Four geometrical similar grids available to all participants, which means domain is fixed but boundary conditions are only suggested

Iterative Errors in Unsteady Flows Inflow Outflow Wall External Symmetry

Iterative Errors in Unsteady Flows Participants are requested to perform calculations with at least 3 different levels of the iterative convergence criteria Quantities of interest are: - Mean drag and lift coefficients - Standard deviation of drag and lift coefficients - Strouhal number - Base pressure coefficient of time-averaged flow - Separation point location of time-averaged flow

Discretization Errors in Steady Flows The goal of this Workshop is to evaluate methods for the estimation of numerical uncertainty based on grid refinement studies Data from grid refinement studies performed with geometrically similar grids with a grid refinement ratio of at least 4 Participants are requested to estimate the contribution of the discretization error to the numerical uncertainty for two or three grid levels The goal is to check the consistency (overlap) of the estimated error bars

Discretization Errors in Steady Flows Test cases available: Flow over a flat plate at different Reynolds numbers (107, 108 and 109) calculated in several grid sets with different near-wall grid line spacing Flow around a NACA 0012 airfoil at Reynolds number of 6×106 and angles of attack of 0º and 4º calculated in several grid sets with different near-wall grid line spacing Both cases have results for 3 eddy-viscosity models