  We present a cut-cell method for the simulation of 2D incompressible flows
past obstacles. It consists in using the MAC scheme on cartesian grids and
imposing Dirchlet boundary conditions for the velocity field on the boundary of
solid structures following the Shortley-Weller formulation. In order to ensure
local conservation properties, viscous and convecting terms are discretized in
a finite volume way. The scheme is second order implicit in time for the linear
part, the linear systems are solved by the use of the capacitance matrix method
for non-moving obstacles. Numerical results of flows around an impulsively
started circular cylinder are presented which confirm the efficiency of the
method, for Reynolds numbers 1000 and 3000. An example of flows around a moving
rigid body at Reynolds number 800 is also shown, a solver using the
PETSc-Library has been prefered in this context to solve the linear systems.
