PRECONDITIONED FINITE-ELEMENT ALGORITHMS FOR 3D STOKES FLOWS

Preconditioned conjugate gradient algorithms for solving 3D Stokes pro blems by stable piecewise discontinuous pressure finite elements are p resented. The emphasis is on the preconditioning schemes and their num erical implementation for use with Hermitian based discontinuous press ure elements. For the piecewise constant discontinuous pressure elemen ts, 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 preconditione r is presented. Numerical examples are presented for the cubic lid-dri ven cavity problem with two representative elements, i.e. the Q2-P0 an d the Q2-P1 brick elements. Numerical results show that the preconditi oning schemes are very effective in reducing the number of pressure it erations at very reasonable costs. It is also shown that they are inse nsitive to the mesh Reynolds number except for nearly steady flows (Re (m) --> 0) and are almost independent of mesh sizes. It is demonstrate d that the schemes perform reasonably well on non-uniform meshes.