Domain Embedding Methods for Incompressible Viscous Flow around Moving Rigid Bodies(Domain Decomposition Methods and Related Topics)

In this article we discuss the application of a Lagrange multiplier based domain embedding method (also called 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 results of several numerical experiments for two-dimensional flow around a moving disk are presented.