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Dynamic simulation of the hydrodynamic interaction among immersed particles in Stokes flow
Author(s) -
Ingber Marc S.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650100706
Subject(s) - stokes flow , discretization , mechanics , classical mechanics , flow (mathematics) , boundary element method , physics , coefficient matrix , matrix (chemical analysis) , surface (topology) , navier–stokes equations , kinematics , mathematics , finite element method , geometry , mathematical analysis , materials science , compressibility , thermodynamics , eigenvalues and eigenvectors , quantum mechanics , composite material
A numerical method for the dynamic simulation of the hydrodynamic interaction among particles in Stokes flow is developed. The method couples the quasi‐static Stokes equations for the fluid with the equilibrium equations for the particles. The boundary element method is used to represent the velocity at a general field point in terms of surface velocities and stresses. However, neither the stresses nor the velocities are assumed to be known on the surface of the particles. Kinematic equations relating the linear and angular velocities at the centroids of the particles to the surface velocities are combined with the discretized boundary element equations and the equilibrium equations to generate a system of linear equations. The associated coefficient matrix is correspondent to the grand resistance matrix which relates the velocities of the particles to a given geometry.