Numerical study of Stokes flows with suspended particles
The author solves the Stokes equations in three space dimensions in the region outside a collection of spheres, with and without an outer boundary. The method of solution is the reflection method, in which one iteratively solves the problem outside each single sphere. The idea is to reduce the problem of finding a Stokes flow past a number of particles to a series of problems of finding a Stokes flow past one single particle. The method can also be used to find the motion of sedimenting spheres. The author demonstrates numerically the convergence of the method for all sphere configurations in the case of unbounded domains. The author uses the method to find periodic solutions of the problem of three sedimenting spheres in a Stokes fluid. Long time periodic solutions are obtained when the initial positions of the spheres are symmetric and modulated long time scale periodic solutions are obtained when the initial positions are asymmetric. The author further develops a fast numerical algorithm for the solution of steady Stokes equations in a bounded domain in both two and three dimensions. The method is second order accurate and has an operation count of order O(N log N) where N is the number of grid points in the domain. This algorithm is then used to extend the method of reflections to bounded domains. The convergence of the method is this case is studied for various spheres configurations. The method is used to evaluate the effective viscosity of fluid with suspended spheres in a shear flow.
- Research Organization:
- California Univ., Berkeley, CA (United States)
- OSTI ID:
- 7113796
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
36 MATERIALS SCIENCE
FLUIDS
VISCOSITY
VISCOUS FLOW
STOKES LAW
THREE-DIMENSIONAL CALCULATIONS
FLUID MECHANICS
ITERATIVE METHODS
NUMERICAL ANALYSIS
SEDIMENTATION
SPHERES
CALCULATION METHODS
FLUID FLOW
MATHEMATICS
MECHANICS
420400* - Engineering- Heat Transfer & Fluid Flow
360603 - Materials- Properties