Abstract
In this work we discuss an application of a distributed Lagrange multiplier based fictitious domain method, to the numerical simulation of the motion of rigid bodies settling in an incompressible viscous fluid. The solution method combines a third order finite element approximation, and time integration by operator splitting. Convergence results are shown for a simple Stokes flow with a circular rigid body that rotates with constant angular velocity. Results of numerical experiments for two sedimenting cylinders in a two-dimensional channel are presented. We present also results for the sedimentation of 100 and 504 cylinders.
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Juárez, L.H., Glowinski, R. & Pan, T.W. Numerical Simulation of the Sedimentation of Rigid Bodies in an Incompressible Viscous Fluid by Lagrange Multiplier/Fictitious Domain Methods Combined with the Taylor–Hood Finite Element Approximation. Journal of Scientific Computing 17, 683–694 (2002). https://doi.org/10.1023/A:1015191101744
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DOI: https://doi.org/10.1023/A:1015191101744