The following is a data-assimilation optimization case where we try to find the inlet velocity field based on pressure data on the bottom wall.
Case: Data assimilation optimization Geometry: Ramp Objective function: Regularized pressure prediction errors on the bottom wall Design variables: Velocity profile at the inlet Constraints: None Reynolds number: ~1 million Mesh cells: 5000 Solver: DASimpleFoam
To run this case, first download tutorials and untar it. Then go to tutorials-main/Ramp_DA/steady and run the “preProcessing.sh” script to generate the training data.
./preProcessing.sh
Then, use the following command to run the optimization with 4 CPU cores:
mpirun -np 4 python runScript.py 2>&1 | tee logOpt.txt
The case ran for 18 steps and took about 15 mins using Intel 3.0 GHz CPU with 4 cores. According to “logOpt.txt” and “opt_SNOPT_summary.txt”, the initial and optimized objective functions are 5.2079934E+01 and 1.3298352E+00 with one order of reduction.
The animations of the optimization are as follows. We can see that the overall velocity and pressure fields agree with the reference, but there are some velocity oscillations at the inlet. We may need to tweak the regularization term “UVar” to improve the results.
Fig. 1. Velocity contour evolution during the optimization.
Fig. 2. Inlet velocity and bottom wall pressure distributions during the optimization.