Published paperAbstract A range of problems is investigated, involving the gravity-driven inertial flow of a thin viscous liquid film over a planar surface containing topographical features, modelled via a depth-averaged form of the governing unsteady Navier-Stokes equations. The discrete analogue of the resulting coupled equation set, employing a staggered mesh arrangement for the dependent variables, is solved accurately using an efficient Full Approximation Storage (FAS) algorithm and Full Multigrid (FMG) technique together with adaptive timestepping and proper treatment of the nonlinear convective terms. A unique, comprehensive set of results is presented for both one-and two-dimensional topographical features, and errors quantified via detailed comparisons drawn with complementary experimental data and predictions from finite element analyses where they exist. It is found in the case of one-dimensional (spanwise) topography that for small Reynolds number and shallow/short features the depth-averaged form produces results that are in close agreement with corresponding finite element solutions of the full free-surface problem. For the case of flow over two-dimensional (localised) topography the free-surface disturbance observed is influenced significantly by the presence of inertia. It leads, as in the case of spanwise topography, to an increase in the magnitude and severity of the capillary ridge/trough patterns which form.

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights CFD validation of the two existing models for the estimation of power density in oscillatory baffled devices is for the first time investigated.  Based on our CFD validation, the best fit would require the revision of the "quasi-steady" model with a power law dependency on the number-of-baffles term and an appropriate orifice discharge coefficient.  Likewise, the "eddy enhancement" model has been revised and updated with the same power law dependency and an empirical model to appropriately estimate "mixing length", as we have demonstrated that the "mixing length" is not a constant for a given device.  Both models are validated for a much wider application range than originally stated and for both batch and continuous operations.  Both revised models can be used interchangeably with high confidence.

The occurrence and proliferation of reef-forming corals is of vast importance in terms of the biodiversity they support and the ecosystem services they provide. The complex three-dimensional structures engineered by corals are comprised of both live and dead coral, and the function, growth and stability of these systems will depend on the ratio of both. To model how the ratio of live : dead coral may change, the ‘Goldilocks Principle’ can be used, where organisms will only flourish if conditions are ‘just right’. With data from particle imaging velocimetry and numerical smooth particle hydrodynamic modelling with two simple rules, we demonstrate how this principle can be applied to a model reef system, and how corals are effectively optimizing their own local flow requirements through habitat engineering. Building on advances here, these approaches can be used in conjunction with numerical modelling to investigate the growth and mortality of biodiversity supporting framework in present-day and future coral reef structures.

Abstract. An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H * , of a thin energetically stable wetting layer, or precursor film, over the entire substrate. The necessity that H * be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H * near wetting lines, increases the computational demands significantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly efficient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the effect of H * and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet flows down an inclined plane.