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Here we analyze Navier-Stokes equations,
which govern the behavior of viscous incompressible flows:
These equations can be rewritten in a dimensionless form:
where 
is known as the flow Reynolds number.
Solving these equations shows mainly two difficulties:
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Nonlinear convective terms |
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Stabilized formulations have to be used to ensure
a stable solution when dealing with high Reynolds number flows.
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Incompressibility constraint |
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The unknowns (velocity and pressure) cannot be discretized anyhow.
Solution is guaranteed if interpolation spaces verify a stability condition
known as inf-sup or LBB condition.
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Besides, when the unsteady case is considered, we have to find
proper techniques to trace the transient solution.
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Stokes problem with analytical solution
Cavity flow problem
Plane jet simulation
Unsteady Convection-Diffusion