NUMERICAL-SIMULATION AND OPTIMAL SHAPE FOR VISCOUS-FLOW BY A FICTITIOUS DOMAIN METHOD

In this article we discuss the fictitious domain solution of the Navie r-Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary co nditions to be satisfied and is particularly well suited to the treatm ent of no-slip boundary conditions. This approach allows the use of st ructured meshes and fast specialized solvers for problems on complicat ed geometries. Another interesting feature of the fictitious domain ap proach is that it allows the solution of optimal shape problems withou t regriding. The resulting methodology is applied to the solution of f low problems including external incompressible viscous flow modelled b y the Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier-Stokes flow.