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Numerical simulation and optimal shape for viscous flow by a fictitious domain method
Author(s) -
Glowinski Roland,
Pan TsorngWhay,
Kearsley Anthony J.,
Periaux Jacques
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650200803
Subject(s) - lagrange multiplier , navier–stokes equations , fictitious domain method , stokes flow , mathematics , polygon mesh , domain (mathematical analysis) , compressibility , flow (mathematics) , incompressible flow , boundary value problem , immersed boundary method , slip (aerodynamics) , computational fluid dynamics , boundary (topology) , mathematical analysis , mechanics , mathematical optimization , geometry , physics , thermodynamics
In this article 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.