High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

In this article, we detail the methodology developed to construct arbitrarily high order schemes - linear and WENO - on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set. © 2012 Global-Science Press.

Plastic limit solution for the response of plate anchors under combined translational and torsional undrained loading

Plate anchors are increasingly being used to moor large floating offshore structures in deep and ultradeep water. These facilities impart substantial vertical uplift loading to plate anchors. However, extreme operating conditions such as hurricane loading often result in partial system failures, with significant change in the orientation of the remaining intact mooring lines. The purpose of this study is to investigate the undrained pure translational (parallel to plate) and torsional bearing capacity of anchor plates idealized as square and rectangular shaped plates. Moreover, the interaction response of plate anchors under combined translational and torsional loading is studied using a modified plastic limit analysis (PLA) approach. The previous PLA formulation which did not account for shear-normal force interaction on the vertical end faces of the plate provides an exact solution to the idealized problem of an infinitely thin plate but only an approximate solution to the problem of a plate of finite thickness. This is also confirmed by the three-dimensional finite element (FE) results, since the PLA values exceed FE results as the thickness of the plate increases. By incorporating the shear-normal interaction relationship in the modified solution, the torsional bearing capacity factors, as well as the plate interaction responses are enhanced as they show satisfactory agreement with the FE results. The interaction relationship is then obtained for square and rectangular plates of different aspect ratios and thicknesses. The new interaction relationships could also be used as an associated plastic failure locus for combined shear and torsional loading to predict plastic displacements and rotations in translational and torsional loading modes as well. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Wave propagation in nonlinear one-dimensional soil model

The objective of the research conducted by the authors is to explore the feasibility of determining reliable in situ values of shear modulus as a function of strain. In this paper the meaning of the material stiffness obtained from impact and harmonic excitation tests on a surface slab is discussed. A one-dimensional discrete model with the nonlinear material stiffness is used for this purpose. When a static load is applied followed by an impact excitation, if the amplitude of the impact is very small, the measured wave velocity using the cross-correlation indicates the wave velocity calculated from the tangent modulus corresponding to the state of stress caused by the applied static load. The duration of the impact affects the magnitude of the displacement and the particle velocity but has very little effect on the estimation of the wave velocity for the magnitudes considered herein. When a harmonic excitation is applied, the cross-correlation of the time histories at different depths estimates a wave velocity close to the one calculated from the secant modulus in the stress-strain loop under steady-state condition. Copyright © 2008 John Wiley & Sons, Ltd.

Cabaret finite-difference schemes for the one-dimensional Euler equations

In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one-dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two-time-layer form, which makes it most simple and robust. Supersonic and subsonic shock-tube tests are used to compare the new schemes with several well-known second-order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second-order Roe scheme with MUSCL flux splitting.

Binder free three-dimensional sulphur/few-layer graphene foam cathode with enhanced high-rate capability for rechargeable lithium sulphur batteries.

A novel ultra-lightweight three-dimensional (3-D) cathode system for lithium sulphur (Li-S) batteries has been synthesised by loading sulphur on to an interconnected 3-D network of few-layered graphene (FLG) via a sulphur solution infiltration method. A free-standing FLG monolithic network foam was formed as a negative of a Ni metallic foam template by CVD followed by etching away of Ni. The FLG foam offers excellent electrical conductivity, an appropriate hierarchical pore structure for containing the electro-active sulphur and facilitates rapid electron/ion transport. This cathode system does not require any additional binding agents, conductive additives or a separate metallic current collector thus decreasing the weight of the cathode by typically ∼20-30 wt%. A Li-S battery with the sulphur-FLG foam cathode shows good electrochemical stability and high rate discharge capacity retention for up to 400 discharge/charge cycles at a high current density of 3200 mA g(-1). Even after 400 cycles the capacity decay is only ∼0.064% per cycle relative to the early (e.g. the 5th cycle) discharge capacity, while yielding an average columbic efficiency of ∼96.2%. Our results indicate the potential suitability of graphene foam for efficient, ultra-light and high-performance batteries.