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    On the effect of the intrinsic viscosity in a two-layer shallow water lattice Boltzmann model of axisymmetric density currents

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    "In this work, a numerical assessment of the suitability of a Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM) model to simulate axisymmetric gravity currents is carried out. The model results are compared with both experimental data and other numerical models. The particular SRT formulation employed is known to converge, in the limit of low Knudsen number, to the two-layer 2D Shallow Water Equations (SWEs) set with a viscosity term featuring a closed theoretical formulation. Even with the lowest viscosity achievable by the method, its effect is shown to become important in most of the cases analysed, thus posing some serious constraints on possible application of the single relaxation time LBM method to simulate the lock-release generated-type gravity currents analysed here. The comparison with classical numerical models shows that the the viscous effects in the LBM model can be well reproduced employing coefficients derived from the above-mentioned theoretical formulation.

    On the validity of plane state assumptions in the bending of bimorph piezoelectric cantilevers

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    We assess the accuracy of plane state assumptions in modeling the bending of bimorph piezoelectric cantilevers. Reference solutions are obtained by means of fully three-dimensional simulations. We solve a model, compliant with the standard theoretical background, able to deal with large deflections, and aimed at estimating the electrical energy har- vesting potential. We show that the two assumptions of plane stress and plane strain yield very different results in terms of strain and therefore lead to substantially different estimates of electrical power. The plane stress state is the best approximation of narrow cantilevers, while the plane strain is suited for wide ones. The validity ranges are defined for each of the two, in terms of the generated electrical power. More specifically, the plane stress assumption better approx- imates the reference solution in the range W=H. By contrast, the plane strain condition yields results closer to three-dimensional solution for ratios W=H*10^3 with W the width and H the total thickness of the solid. Other aspects are affected by the modeling approach, such as the estimation of maximum deformation and, to a minor extent, of reso- nance frequencies
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