4,306 research outputs found

    An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

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    We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialised treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretisation, in which viscous terms are treated semi-implicitly and projection methods are utilised to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects

    THE LOGIC OF STATISTICAL INFERENCE SIGNIFICANCE TESTING AND DECISION THEORY

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    Modification of the simple mass balance equation for calculation of critical loads of acidity.

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    Over the last few years, the simple mass balance equation for the calculation of critical loads of acidity has been gradually modified as the underlying critical load concepts have developed and as problems with particular forms of the equation have been identified, through application in particular countries. The first major update of the equation took place following a workshop held in Vienna, Austria (Hojesky et al. 1993). The workshop was held to discuss problems which had been identified when the then current form of the equation was applied in countries with high rainfall. The problems had largely arisen because of simplifications and assumptions incorporated into the early formulation of the equation. The equation was reformulated to overcome the problems identified at the workshop. However, further problems were identified when the reformulated equation was applied in the UK in situations with a combination of high rainfall, large marine inputs and widespread occurrence of organic soils. A small workshop was, therefore held in Grange-over-Sands, UK in late 1993 to dicuss the problems and to further re-evaluate the equation. The problems had arisen in the UK because of simplifications and assumptions made in the formulation concerning, in particular, cation leaching and uptake. As a result, a more rigorous treatment of these variables was incorporated into the equation. The reformulation of the equation, as derived at the September 1993 workshop is described below

    Hydrologic Transport of Dissolved Inorganic Carbon and Its Control on Chemical Weathering

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    Chemical weathering is one of the major processes interacting with climate and tectonics to form clays, supply nutrients to soil microorganisms and plants, and sequester atmospheric CO2. Hydrology and dissolution kinetics have been emphasized as factors controlling chemical weathering rates. However, the interaction between hydrology and transport of dissolved inorganic carbon (DIC) in controlling weathering has received less attention. In this paper, we present an analytical model that couples subsurface water and chemical molar balance equations to analyze the roles of hydrology and DIC transport on chemical weathering. The balance equations form a dynamical system that fully determines the dynamics of the weathering zone chemistry as forced by the transport of DIC. The model is formulated specifically for the silicate mineral albite, but it can be extended to other minerals, and is studied as a function of percolation rate and water transit time. Three weathering regimes are elucidated. For very small or large values of transit time, the weathering is limited by reaction kinetics or transport, respectively. For intermediate values, the system is transport controlled and is sensitive to transit time. We apply the model to a series of watersheds for which we estimate transit times and identify the type of weathering regime. The results suggest that hydrologic transport of DIC may be as important as reaction kinetics and dilution in determining chemical weathering rates
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