Parallel finite element calculation of flow in a three-dimensional lid-driven cavity using the CM-5 and T3D

Steady flows in a three-dimensional lid-driven cavity at moderate Reynolds number are studied using various methods of parallel programming on the Cray T3D and Thinking Machines CM-5. These three-dimensional flows are compared with flows computed in a two-dimensional cavity. Solutions at Reynolds number up to 500 agree well with the experimental data of Aidun et al. (Phys. Fluids A, 3, 2081-2091 (1991)) for the location of separation of the secondary eddy at the downstream wall. Convergence of the three-dimensional problem using GMRES with diagonal preconditioning could not be obtained at Reynolds number greater than about 500. We speculate that the source of the difficulty is the loss of stability via pitchfork and Hopf bifurcations identified by Aidun et al. The relative performance of various methods of message passing on the Cray T3D is compared with the data-parallel mode of programming on the CM-5. No clear advantage between machines or message-passing methods is distinguished.