This paper discusses the design and implementation of solution algorithms suitable for performing transient, incompressible viscous ow simulations on massively parallel computers. The nite element formulation for incompressible ow along with the ad-hoc modi cations for explicit time integration are discussed with an emphasis on implementation aspects for achieving scalable, parallel computations. The issues associated with a domain-decomposition message-passing paradigm are presented in the context of explicit time integration and the solution of a pressure Poisson equation using a staggered grid. An element-by-element conjugate gradient algorithm for the pressure equation is outlined with a parallel sub-domain preconditioner. Sample calculations are presented with scaled speedup and e ciency results to demonstrate the scalability of the domain-decomposition message-passing approach.