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An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at high Reynolds number. (arXiv:1810.03315v1 [math.NA])
来源于:arXiv
In Benzi & Olshanskii (SIAM J.~Sci.~Comput., 28(6) (2006)) a preconditioner
of augmented Lagrangian type was presented for the two-dimensional stationary
incompressible Navier--Stokes equations that exhibits convergence almost
independent of Reynolds number. The algorithm relies on a highly specialized
multigrid method involving a custom prolongation operator and is tightly
coupled to the use of piecewise constant finite elements for the pressure.
However, the prolongation operator and velocity element used do not directly
extend to three dimensions: the local solves necessary in the prolongation
operator do not satisfy the inf-sup condition. In this work we generalize the
preconditioner to three dimensions, proposing alternative finite elements for
the velocity and prolongation operators for which the preconditioner works
robustly. The solver is effective at high Reynolds number: on a
three-dimensional lid-driven cavity problem with approximately one billion
degrees of freedom, th 查看全文>>