The IGR method enables us to study the singular structures of the
blow up solutions of Prandtl equations. The numerical solutions to
the incompressible Navier-Stokes equations with Navier boundary
conditions are discussed. An unconditionally stable time
discretization which is implicit in viscosity and explicit in both
pressure and convection terms and finite difference discretization
with local pressure boundary condition are employed. A two level
preconditioned conjugate gradient method is introdeced to solve the
elliptic type system.
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