Preconditioned Finite Element Algorithms For 3D Stokes Flows
International Journal for Numerical Methods in Fluids, Vol. 17, pp. 667-685, 1993
Posted: 13 Mar 2012
Date Written: 1993
Preconditioned conjugate gradient algorithms for solving 3D Stokes problems by stable piecewise discontinuous pressure finite elements are presented. The emphasis is on the preconditioning schemes and their numerical implementation for use with Hermitian based discontinuous pressure elements. For the piecewise constant discontinuous pressure elements, a variant implementation of the preconditioner proposed by Cahouet and Chabard for the continuous pressure elements is employed. For the piecewise linear discontinuous pressure elements, a new preconditioner is presented. Numerical examples are presented for the cubic lid-driven cavity problem with two representative elements, i.e. the Q2-PO and the Q2-Pl brick elements. Numerical results show that the preconditioning schemes are very effective in reducing the number of pressure iterations at very reasonable costs. It is also shown that they are insensitive to the mesh Reynolds number except for nearly steady flows (Re, O) and are almost independent of mesh sizes. It is demonstrated that the schemes perform reasonably well on non-uniform meshes.
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