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On the coupling between an ideal fluid and immersed particles
In this paper we use Lagrange-Poincare reduction to understand the coupling
between a fluid and a set of Lagrangian particles that are supposed to simulate
it. In particular, we reinterpret the work of Cendra et al. by substituting
velocity interpolation from particle velocities for their principal connection.
The consequence of writing evolution equations in terms of interpolation is
two-fold. First, it gives estimates on the error incurred when interpolation is
used to derive the evolution of the system. Second, this form of the equations
of motion can inspire a family of particle and hybrid particle-spectral methods
where the error analysis is "built-in". We also discuss the influence of other
parameters attached to the particles, such as shape, orientation, or
higher-order deformations, and how they can help with conservation of momenta
in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom
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