A distributed lagrange multiplier/fictitious domain method for flows around moving rigid bodies: Application to particulate flow

This article discusses 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 motions are due to hydrodynamical forces and gravity. 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 study concludes with the presentation of numerical results concerning four test problems, namely the simulation of an incompressible viscous flow around a NACA0012 airfoil with a fixed center but free to rotate, then the sedimentation of 200 and 1008 cylinders in a two-dimensional channel, and finally the sedimentation of two spherical balls in a rectangular cylinder.