  We provide spatial discretizations of nonlinear incompressible Navier-Stokes
equations with inputs and outputs in the form of matrices ready to use in any
numerical linear algebra package. We discuss the assembling of the system
operators and the realization of boundary conditions and inputs and outputs. We
describe the two benchmark problems - the driven cavity and the cylinder wake -
and provide the corresponding data. The use of the data is illustrated by
numerous example setups. The test cases are provided as plain PYTHON or
OCTAVE/MATLAB script files for immediate replication.
