On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems

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Implicit second-order immersed boundary methods with boundary mass (2008, methodology): “Following [27] we demonstrate second-order accuracy of the present methods with a smooth problem where the elastic membrane is replaced by an elastic shell with tapered elastic stiffness and tapered mass density.”
A New Drag Correlation from Fully Resolved Simulations of Flow Past Monodisperse Static Arrays of Spheres (2015, background): “resolution (particle diameter/grid size ratio) is usually required especially for problems involving high solids volume fraction and/or high Reynolds number flows.(33,34,51) In fact, even for low Reynolds numbers, Kriebitzsch(40) observed a departure of the finite-resolution simulation results from ”
Penalty immersed boundary method for an elastic boundary with mass (2007, methodology): “Note that Griffith and Peskin [10] have also observed that, when the Reynolds number is too high, the convergence rate drops but recovers again to almost 2 when the grid resolution becomes fine enough.”
An adaptive, formally second order accurate version of the immersed boundary method (2007, methodology): “Our algorithm, first introduced in [3], extends to the viscous case the hybrid approximate projection method (‘‘version 5’’) introduced by Almgren et al.”