Direct simulation of the motion of settling ellipsoids in Newtonian fluid

T.-W. Pan, R. Glowinski, , D. D. Joseph, ¹, R. Bai¹

University of Houston, Department of mathematics, Houston, Texas 77204

¹Department of Aerospace Engineering and Mechanics
University of Minnesota Minneapolis, MN 55455

Abstract

In this article we first discuss the generalization of a LaGrange multiplier based fictitious domain method [Glowinski, Pan, Hesla, Joseph 1999, Glowinski, Pan, Hesla, Joseph, Periaux 2001.] to the simulation of the motion of particles of general shape in a Newtonian fluid. Unlike the cases where the particles are spheres, we attach two points, besides the center of mass, to each particle of general shape and move them according to the rigid-body motion of the particle in order to track this motion. The equations describing the motion of those two points are solved by a distance preserving scheme so that rigidity can be maintained. We then apply it to simulate ellipsoids settling in a narrow channel filled with a Newtonian fluid. In the simulations, when there is only one ellipsoid it turns its broadside orthogonal to the stream as expected; for the two ellipsoid case they interact with each other as observed in experiments.

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