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A distributed Lagrange multiplier/fictious domain method for the simulation of flow around moving rigid bodies: Application to particulate flow. (English) Zbl 0970.76057

Summary: We discuss the application of a Lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by Navier-Stokes equations around moving rigid bodies; the rigid body motion is 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 linearly constrained quadratic minimization problems coming from the splitting method. We conclude this article by the presentation of numerical results concerning an incompressible viscous flow around NACA0012 airfoil with a fixed center, but free to rotate, then we examine the sedimentation of circular cylinders in two-dimensional channels, and finally the sedimentation of spherical balls in cylinders with square cross-sections.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T20 Suspensions
76D05 Navier-Stokes equations for incompressible viscous fluids
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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