SEMINAR

Direct Numerical Simulation of the Sedimentation of Rigid Bodies in an Incompressible Viscous Fluid

Department of Mathematics
University of Houston

ABSTRACT

In this work the direct numerical simulation of the motion of rigid bodies falling in an incompressible viscous fluid is considered. The motion of the bodies is due to the hydrodynamical forces and external forces such as gravity, particle-particle and particle-wall collisions (when present). The flow is modeled by the Navier-Stokes equations, while the motion of the bodies is modeled by the Newton-Euler equations. The interaction between the fluid and the rigid bodies is implicitly modeled by the global variational formulation, so that we do not compute the hydrodynamical forces explicitly during the simulation. The methodology applied to solve the resulting problem relies on the combination of:

(1) a fistitious domain method, that allows the flow computation to be done on a fixed region with a simple structured grid
(2) Lagrange multipliers defined on the regions ocupied by the rigid bodies, to enforce the fluid flow as a rigid body motion over these regions
(3) the Taylor-Hood finite element approximation, to take advantage of the global variational formulation of the coupled flow-rigid body motion
(4) Operator splitting for time integration, to treat separately the various operators associated to the physics and numerics of the computational model
(5) a simple model to take in account the particle-particle and particle-wall collisions.

This methodology is applied to the direct numerical simulation of the sedimentation of two circular particles in a Newtonian incompressible viscous flow. For this problem we are able to reproduce the fundamental and well known phenomenon of drafting, kissing, and tumbling. Related problems are the numerical simulation of the sedimentation of a elliptic body, and the sedimentation of a dipole, for which we show how the bodyes rotate so that their broad side tend to be perpendicular to the falling direction. We also present some results of the sedimentation of 100 and 504 circular particles.

WHERE: TEC 205

WHEN(day): Friday, March 9th, 2001

WHEN(time): 2:00pm

EVERYBODY IS INVITED