Shujing Xu, Ali Nadim
Abstract:
We consider three model problems that describe rectilinear particle motion
in a viscous fluid under the influence of the Basset history force.
These problems consist of sedimentation starting from rest, impulsive
motion in a quiescent fluid, and oscillatory sliding motion.
The equations of motion are integro-differential equations with a weakly
singular kernel. We derive analytical solutions to all three problems
using Laplace transforms and discuss the mathematical relation between the
sedimentation and impulsive start problems. We also compare several numerical
schemes for solving the integro-differential equations and benchmark them
against the analytical results.
Submitted November 7, 2014. Published April 21, 2015.
Math Subject Classifications: 76T20, 45J05, 65L05.
Key Words: Particle motion; history force; integro-differential equations;
Laplace transforms; numerical methods; multiphase flow.
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Shujing Xu Institute of Mathematical Sciences Claremont Graduate University Claremont, CA 91711, USA email: flora.xushujing@gmail.com | |
Ali Nadim Institute of Mathematical Sciences Claremont Graduate University Claremont, CA 91711, USA email: ali.nadim@cgu.edu |
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