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RECENT years the understanding of the basic mechanism of separation by filtration and sedimentation operations has been considerably advanced and unified. The essential similarity of the two processes is well illustrated by comparing the Kozeny equation ( 7), " = _Si__Pi_

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We present novel coupling schemes for partitioned multiphysics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multirate time stepping, and higher-order convergence in time. To achieve this, we combine waveform relaxation-a known method to achieve higher-order in applications with split time stepping based on continuous representations of coupling variables in time-with interface quasi-Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black-box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic testcases-a heat transfer scenario and a fluid-structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first-order-in-time coupling.

Particulate fluidization and sedimentation data were taken over the Reynolds number range of 0.005 to 1,800 by means of glass spheres in both water and ethylene glycol. Porosities for each series of measurements varied from about 0.50 to 0.91 and larger. The closely sized samples of spheres used were obtained by grinding between glass plates.The data for Reynolds numbers up to about 0.5 are in excellent agreement with the laminar theory of Ruth and the porosity function from Ruth's theory gave a satisfactory correlation of all the data, both laminar and turbulent.