John M. Stockie

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A linear stability analysis is performed on a two-dimensional version of the \immersed ber problem", formulated by C. Peskin to model the ow of uid in the presence of a mesh of moving, elastic bers. The purpose of the analysis is to isolate the modes in the solution which are associated with the ber, and thereby determine the eeect of the presence of a ber(More)
In this paper, we investigate the stability of a fluid-structure interaction problem in which a flexible elastic membrane immersed in a fluid is excited via periodic variations in the elastic stiffness parameter. This model can be viewed as a prototype for active biological tissues such as the basilar membrane in the inner ear, or heart muscle fibers(More)
In this paper, we investigate a traffic model similar to the Lighthill–Whitham– Richards model, consisting of a hyperbolic conservation law with a discontinuous, non-convex, piecewise-linear flux. Using Dias and Figueira's mollification framework, analytical solutions to the corresponding Riemann problem are derived. For certain initial data, these Riemann(More)
We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev that uses a directional splitting strategy to discretize the(More)
We present an approach for numerically simulating the dynamics of flexible fibers in a three-dimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev's pseudo-compressible fluid solver. The fibers are treated as one-dimensional Kirchhoff rods that resist stretching, bending, and twisting, within the generalized IB(More)