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Numerical simulation and optimal shape for viscous flow by a fictitious domain method. (English) Zbl 0837.76068
Summary: We discuss the fictitious domain solution of the Navier-Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no-slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier- Stokes flow.

MSC:
76M30 Variational methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
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