Solution of generalized Stokes problems using hierarchical methods and incremental unknowns. (English) Zbl 0853.76044

Summary: We present a nonstandard hierarchization of the MAC meshing associated with a second order finite difference discretization for the solution of generalized Stokes problems. Two families of hierarchization are considered: one for the components of the velocity (\(u\) and \(v\)) and one for the pressure \((p)\). The introduction of the incremental unknowns on the pressure is proposed as an efficient hierarchical preconditioner of the Uzawa operator. We give numerical results concerning the solution of generalized Stokes problem in a driven square cavity. These results point out a much better speed of convergence for the new method than the classical one.


76M20 Finite difference methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
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