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Michael Shearer : Continuum Models of Granular Flow

Continuum models of the flow of granular materials in a hopper admit so-called radial solutions. These describe steady flows that appear realistic, and have been used extensively to design commercial hoppers. However, numerical results demonstrate that these solutions may not be robust to perturbation. Moreover, the time dependent equations are (notoriously) ill-posed. In this talk, I describe preliminary research designed to investigate the extent to which steady solutions may be used to represent granular flow. Using a combination of analysis and numerical experiments, we have explored simple models that are linearly ill posed. While there may be a stable steady state, it is a solution of a discretized continuum model, rather than the original equations. Moreover, the survival time of transients is inversely related to the mesh width, suggesting that the continuum limit is meaningless. While these results are not intended to invalidate the radial solutions, they do raise serious concerns about continuum modeling, and the possibility of designing a robust code that can be used to simulate a variety of granular flows.

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