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A numerical method for simulations of rigid fiber suspensions
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-8998-985X
2006 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 215, no 1, 172-196 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

Place, publisher, year, edition, pages
2006. Vol. 215, no 1, 172-196 p.
Keyword [en]
slender-body theory, stokes-flow, semidilute suspensions, cross-section, viscous-flow, particles, sedimentation, equations, dilute, computation
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-15632DOI: 10.1016/ 000237002000010ScopusID: 2-s2.0-33645877069OAI: diva2:333674
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-01-11Bibliographically approved

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Tornberg, Anna-KarinGustavsson, Katarina
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