R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

Simplifying mooring analysis for deepwater systems using truncation

Over recent years academia and industry have engaged with the challenge of model testing deepwater structures at conventional scales. One approach to the limited depth problem has been to truncate the lines. This concept will be introduced, highlighting the need to better understand line dynamic processes. The type of line truncation developed here models the upper sections of each line in detail, capturing wave action and all coupling effects with the vessel, terminating to an approximate analytical model that aims to simulate the remainder of the line. A rationale for this is that in deep water transverse elastic waves of a line are likely to decay before they are reflected at the seabed because of nonlinear hydrodynamic drag forces. The first part of this paper is centered on verification of this rationale. A simplified model of a mooring line that describes the transverse dynamics in wave frequency is used, adopting the equation of motion of an inextensible taut string. The line is submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it can be useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. This is followed by developing a truncation mechanism, formulating an end approximation that can reproduce the correct impedance, had the line been continuous to full depth. It has been found that below a certain length criterion, which is also universal, the transverse vibrational characteristics for each line are inertia driven. As such the truncated model can assume a linear damper whose coefficient depends on the line properties and frequency of vibration. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Efficient truncation scheme for modeling deepwater mooring lines

This paper is aimed at enabling the confident use of existing model test facilities for ultra deepwater application without having to compromise on the widely accepted range of scales currently used by the floating production industry. Passive line truncation has traditionally been the preferred method of creating an equivalent numerical model at reduced depth; however, these techniques tend to suffer in capturing accurately line dynamic response and so reproducing peak tensions. In an attempt to improve credibility of model test data the proposed truncation procedure sets up the truncated model, based on line dynamic response rather than quasi-static system stiffness. The upper sections of each line are modeled in detail, capturing the wave action zone and all coupling effects with the vessel. These terminate to an approximate analytical model that aims to simulate the remainder of the line. Stages 1 & 2 are used to derive a water depth truncation ratio. Here vibration decay of transverse elastic waves is assessed and it is found that below a certain length criterion, the transverse vibrational characteristics for each line are inertia driven, hence with respect to these motions the truncated model can assume a linear damper whose coefficient depends on the local line properties and vibration frequency. Stage 3 endeavors to match the individual line stiffness between the full depth and truncated models. In deepwater it is likely that taut polyester moorings will be used which are predominantly straight and have high axial stiffness that provides the principal restoring force to static and low frequency vessel motions. Consequently, it means that the natural frequencies of axial vibrations are above the typical wave frequency range allowing for a quasi-static solution. In cases of exceptionally large wave frequency vessel motions, localized curvature at the chain seabed segment and tangential skin drag on the polyester rope can increase dynamic peak tensions considerably. The focus of this paper is to develop an efficient scheme based on analytic formulation, for replicating these forces at the truncation. The paper will close with an example case study of a single mooring under extreme conditions that replicates exactly the static and dynamic characteristics of the full depth line. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE).

Vibration decay along deepwater moorings with complex geometry and configuration, as a tool for truncation

This paper is concerned with the difficulties in model testing deepwater structures at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation. Passive truncation has traditionally been the preferred method by industry; however, these techniques tend to suffer in capturing accurately line dynamic response and so reproducing peak tensions. In an attempt to improve credibility of model test data the proposed truncation procedure sets up the truncated model, based on line dynamic response rather than quasi-static system stiffness. Vibration decay of transverse elastic waves due to fluid drag forces is assessed and it is found that below a certain length criterion, the transverse vibrational characteristics for each line are inertia driven, hence with respect to these motions the truncated model can assume a linear damper whose coefficient depends on the local line properties and vibration frequency. Initially a simplified taut string model is assumed for which the line is submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a general guideline for the truncation length criterion, which is suitable for any kind of line with any top motion. The focus of this paper is to extend this work to a more complex line configuration of a conventional deepwater mooring line and so enhance the generality of the truncation guideline. The paper will close with an example case study of a spread mooring system, applying this method to create an equivalent numerical model at a reduced depth that replicates exactly the static and dynamic characteristics of the full depth system. Copyright © 2012 by ASME.

Unbiased Linear Property Estimation For Spheres From Sections Exhibiting Overprojection And Truncation

In the biological sciences, stereological techniques are frequently used to infer changes in structural parameters (volume fraction, for example) between samples from different populations or subject to differing treatment regimes. Non-homogeneity of these parameters is virtually guaranteed, both between experimental animals and within the organ under consideration. A two-stage strategy is then desirable, the first stage involving unbiased estimation of the required parameter, separately for each experimental unit, the latter being defined as a subset of the organ for which homogeneity can reasonably be assumed. In the second stage, these point estimates are used as data inputs to a hierarchical analysis of variance, to distinguish treatment effects from variability between animals, for example. Techniques are therefore required for unbiased estimation of parameters from potentially small numbers of sample profiles. This paper derives unbiased estimates of linear properties in one special case—the sampling of spherical particles by transmission microscopy, when the section thickness is not negligible and the resulting circular profiles are subject to lower truncation. The derivation uses the general integral equation formulation of Nicholson (1970); the resulting formulae are simplified, algebraically, and their efficient computation discussed. Bias arising from variability in slice thickness is shown to be negligible in typical cases. The strategy is illustrated for data examining the effects, on the secondary lysosomes in the digestive cells, of exposure of the common mussel to hydrocarbons. Prolonged exposure, at 30 μg 1−1 total oil-derived hydrocarbons, is seen to increase the average volume of a lysosome, and the volume fraction that lysosomes occupy, but to reduce their number.

Biosynthesis and structure of the Burkholderia cenocepacia K56-2 lipopolysaccharide core oligosaccharide:truncation of the core oligosaccharide leads to increased binding and sensitivity to polymyxin B

Burkholderia cenocepacia is an opportunistic pathogen that displays a remarkably high resistance to antimicrobial peptides. We hypothesize that high resistance to antimicrobial peptides in these bacteria is because of the barrier properties of the outer membrane. Here we report the identification of genes for the biosynthesis of the core oligosaccharide (OS) moiety of the B. cenocepacia lipopolysaccharide. We constructed a panel of isogenic mutants with truncated core OS that facilitated functional gene assignments and the elucidation of the core OS structure in the prototypic strain K56-2. The core OS structure consists of three heptoses in the inner core region, 3-deoxy-d-manno-octulosonic acid, d-glycero-d-talo-octulosonic acid, and 4-amino-4-deoxy-l-arabinose linked to d-glycero-d-talo-octulosonic acid. Also, glucose is linked to heptose I, whereas heptose II carries a second glucose and a terminal heptose, which is the site of attachment of the O antigen. We established that the level of core truncation in the mutants was proportional to their increased in vitro sensitivity to polymyxin B (PmB). Binding assays using fluorescent 5-dimethylaminonaphthalene-1-sulfonyl-labeled PmB demonstrated a correlation between sensitivity and increased binding of PmB to intact cells. Also, the mutant producing a heptoseless core OS did not survive in macrophages as compared with the parental K56-2 strain. Together, our results demonstrate that a complete core OS is required for full PmB resistance in B. cenocepacia and that resistance is due, at least in part, to the ability of B. cenocepacia to prevent binding of the peptide to the bacterial cell envelope.

Host Defence Peptide LL-37; Effects of truncation on antimicrobial activity

Background: The oral cavity is an ideal environment for colonisation by micro-organisms. A first line of defence against microbial infection is the secretion of broad spectrum host defence peptides (HDPs). In the current climate of antibiotic resistance, exploiting naturally occurring HDPs or synthetic derivatives (mimetics) to combat infection is particularly appealing. The human cathelicidin, LL-37 is one such HDP expressed ubiquitously by epithelial cells and neutrophils. LL-37 exhibits the ability to bind lipopolysaccharide (LPS) and displays broad spectrum activity against a wide range of bacteria. The current study focuses on truncation of LL-37 and defining the antimicrobial and LPS binding activity of the resultant mimetics. Objectives: To assess the antimicrobial and LPS binding activity of LL-37 and three truncated mimetics (KE-18, EF-14 and KR-12). Methods: Peptides were synthesised in-house by Fmoc solid phase peptide synthesis or obtained commercially. Antimicrobial activity was determined using a radial diffusion assay and ability to bind LPS was determined by indirect ELISA. Results: LL-37 and mimetics displayed antimicrobial activity against Streptococcus mutans and Enterococcus Faecalis. KE-18 and KR-12 were shown to possess antimicrobial activity against both pathogens whereas EF-14 was the least antimicrobial. In terms of LPS binding, KE-18 and KR-12 were both effective whereas EF-14 showed the least activity of the three mimetics. Conclusion: Truncation of LL-37 can yield peptides which retain antimicrobial activities and have the ability to bind LPS. Interestingly in some cases the truncation of LL-37 produced mimetics with greater potency than the parent molecule in terms of antimicrobial activity and LPS binding. This work was funded by DEL and the Diabetes Wellness Foundation.