We would like to discuss the application of a Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modelled by the Navier-Stokes equations around moving bodies. The solution method combines finite element approximations, time discretization by operator splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method. The advantage of fictitious domain techniques is that we can use uniform structured mesh and hence fast solvers (future plans to use parallel solvers will be discussed). The results of numerical experiments for 100 sedimenting cylinders in a two-dimensional channel will be presented.
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