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We provide spatial discretizations of nonlinear incompressible Navier-Stokesequations with inputs and outputs in the form of matrices ready to use in anynumerical linear algebra package. We discuss the assembling of the systemoperators and the realization of boundary conditions and inputs and outputs. Wedescribe the two benchmark problems - the driven cavity and the cylinder wake -and provide the corresponding data. The use of the data is illustrated bynumerous example setups. The test cases are provided as plain PYTHON orOCTAVE/MATLAB script files for immediate replication.

Example Setups of Navier-Stokes Equations with Control and Observation:  Spatial Discretization and Representation via Linear-quadratic Matrix  Coefficients