Data assimilation for OpenFOAM Combining measurements and modelling

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1 Data assimilation for OpenFOAM Combining measurements and modelling Henk Seubers, Aerospace Engineering 8 januari 2013 () Data assimilation for OpenFOAM 1 / 27

2 Main goal The purpose of this project is to provide a coupling between OpenDA and OpenFOAM and to demonstrate the results on a test case. () Data assimilation for OpenFOAM 3 / 27

3 What is data assimilation Data assimilation Incorporation of measurement results into simulation estimates Assimilation: Finding the most likely state of the model Calibration: Finding the most likely model fitting the data vs () Data assimilation for OpenFOAM 4 / 27

4 Examples () Data assimilation for OpenFOAM 5 / 27

5 Why data-assimilation? Possible uses of data-assimilation in aerodynamics: Predicting flow fields. Interpolating measured quantities. Extracting meaningful data from noisy measurements. Estimating uncertain terms in governing equations. Assisting in the selection of measurement locations. () Data assimilation for OpenFOAM 6 / 27

6 Why use OpenDA Various data assimilation and model calibration algorithms. Separate the data assimilation from the model. Deal with measurement data, uncertainties. Acquire results for postprocessing: Matlab, NetCDF Efficient parallel execution of model instances. Assimilation Calibration EnKF CG EnSR GLUE 3D-var Simplex particle filter Dud () Data assimilation for OpenFOAM 7 / 27

7 Black box concept () Data assimilation for OpenFOAM 8 / 27

8 Objective Compute P(current state observations) given P(previous state) and P(observations) and P(external forcing) and P(modelling error) and P(discretization error) and... () Data assimilation for OpenFOAM 9 / 27

9 Kalman filter concept () Data assimilation for OpenFOAM 10 / 27

10 Kalman filter concept () Data assimilation for OpenFOAM 11 / 27

11 Model Navier-Stokes simulation of a lid-driven cavity. Forcing f : u(x, 1)+η(x) Re = 1000 Observations H(x) : v(x, 0.5) Model state x : u(x, y) v(x, y) η(x) () Data assimilation for OpenFOAM 12 / 27

12 Statistics State size = 5017 Uncertainty dimension 17, σ = 0.05 Ensemble size 15 Observation count 51 () Data assimilation for OpenFOAM 13 / 27

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22 Important observations Kalman filtering for Navier-Stokes problems is feasible The results converge for an inconsistent initial condition Conservation of mass and momentum not affected by filtering Analysis/Compute/IO time (5%/85%/10%) () Data assimilation for OpenFOAM 23 / 27

23 Observability Change of observation location Vorticity (mean) centerline top () Data assimilation for OpenFOAM 24 / 27

24 Observability Change of observation location Vorticity (standard deviation) centerline top () Data assimilation for OpenFOAM 25 / 27

25 Conclusions and recommendations Data assimilation concepts available to OpenFOAM Usable with any OpenFOAM solver, field, parameter, observation Uncertainty models based on arbitrary OpenFOAM meshes Support for large model sizes, reduced order uncertainty () Data assimilation for OpenFOAM 26 / 27

26 Possible uses of data-assimilation in aerodynamics: Predicting flow fields. Interpolating measured quantities. Extracting meaningful data from noisy measurements. Estimating uncertain terms in governing equations. Assisting in the selection of measurement locations. Navier-Stokes simulation of a lid-driven cavity. Re = 1000 Forcing f : u(x, 1)+η(x) Observations H(x) : v(x, 0.5) u(x, y) Model state x : v(x, y) η(x) Various data assimilation and model calibration algorithms. Separate the data assimilation from the model. Deal with measurement data, uncertainties. Acquire results for postprocessing: Matlab, NetCDF Efficient parallel execution of model instances. Assimilation Calibration EnKF CG EnSR GLUE 3D-var Simplex particle filter Dud () Data assimilation for OpenFOAM 5 / 27 Questions?? Kalman filter concept Model () Data assimilation for OpenFOAM 11 / 27 () Data assimilation for OpenFOAM 12 / 27?? Black box concept Examples () Data assimilation for OpenFOAM 8 / 27?? Why data-assimilation? Why use OpenDA () Data assimilation for OpenFOAM 6 / 27 () Data assimilation for OpenFOAM 7 / 27 For more information: henkseubers@gmail.com nils.vanvelzen@vortech.nl () Data assimilation for OpenFOAM 27 / 27