Abstract
In this article we discuss the application of a Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the Navier–Stokes equations around moving rigid bodies; the rigid body motion is due to hydrodynamical forces and gravity. The solution method combines finite element approximations, time discretization by operators splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method. We conclude this article by the presentation of numerical results concerning the simulation of an incompressible viscous flow around a NACA0012 airfoil with a fixed center, but free to rotate, then the sedimentation of circular cylinders in 2-D channels, and finally the sedimentation of spherical balls in cylinders with square cross-sections.
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