Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

A species conserving genetic algorithm for multimodal function optimization

This paper introduces a new technique called species conservation for evolving parallel subpopulations. The technique is based on the concept of dividing the population into several species according to their similarity. Each of these species is built around a dominating individual called the species seed. Species seeds found in the current generation are saved (conserved) by moving them into the next generation. Our technique has proved to be very effective in finding multiple solutions of multimodal optimization problems. We demonstrate this by applying it to a set of test problems, including some problems known to be deceptive to genetic algorithms.

Influence of ion energy and substrate temperature on the optical and electronic properties of tetrahedral amorphous carbon (ta-C) films

The properties of amorphous carbon (a-C) deposited using a filtered cathodic vacuum arc as a function of the ion energy and substrate temperature are reported. The sp3 fraction was found to strongly depend on the ion energy, giving a highly sp3 bonded a-C denoted as tetrahedral amorphous carbon (ta-C) at ion energies around 100 eV. The optical band gap was found to follow similar trends to other diamondlike carbon films, varying almost linearly with sp2 fraction. The dependence of the electronic properties are discussed in terms of models of the electronic structure of a-C. The structure of ta-C was also strongly dependent on the deposition temperature, changing sharply to sp2 above a transition temperature, T1, of ≈200°C. Furthermore, T1 was found to decrease with increasing ion energy. Most film properties, such as compressive stress and plasmon energy, were correlated to the sp3 fraction. However, the optical and electrical properties were found to undergo a more gradual transition with the deposition temperature which we attribute to the medium range order of sp2 sites. We attribute the variation in film properties with the deposition temperature to diffusion of interstitials to the surface above T1 due to thermal activation, leading to the relaxation of density in context of a growth model. © 1997 American Institute of Physics.

The plastic collapse and energy absorption capacity of egg-box panels

The plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression has been measured and modelled. It is observed that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism. Drop weight tests have been performed at speeds of up to 6 m s-1, and an elevation in strength with impact velocity is noted. A 3D finite element shell model is needed in order to reproduce the observed behaviours. Additional calculations using an axisymmetric finite element model give the correct collapse modes but are less accurate than the more sophisticated 3D model. The finite element simulations suggest that the observed velocity dependence of strength is primarily due to strain-rate sensitivity of the aluminium sheet, with material inertia playing a negligible role. Finally, it is shown that the energy absorption capacity of the egg-box material is comparable to that of metallic foams. © 2003 Elsevier Ltd. All rights reserved.