A new fast numerical method for solving the three dimensional Stokes' equations in the presence of discrete suspended particles is presented. The fluid dynamics equations are solved on a grid. The particles are represented by configurations of localized forces which are not constrained to move on the grid. These forces contribute to the force density term in the Stokes' equations. As a result, a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries. Computational work increases only linearly with the number of particles, so large numbers (500-1000) of particles may be studied efficiently. Particle size, shape, and deformability may be prescribed. The method was implemented to run on all CRAY computers: the implementation exploits the CRAY's vectorized arithmetic, and on machines with insufficient memory, it performs efficient disk I/O while storing most of the data on the disk. Applications of the method to sedimentation of one, two, and many particle systems are described. Trajectories and settling speeds for two particle sedimentation, and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories.
|Original language||English (US)|
|Title of host publication||Unknown Host Publication Title|
|Publisher||Soc. Ind. & Appl. Math|
|ISBN (Print)||0898712122, 9780898712124|
|State||Published - 1986|
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