Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries

Long-lasting adverse effects after short-term low-dose treatment with metoclopramide for vomiting

Metoclopramide is commonly used to treat vomiting caused by seasickness and acute gastroenteritis on cruise ships and serious adverse effects have not been reported from use at sea. We report severe long-lasting adverse effects in a young female seafarer following short-term, low-dose use of metoclopramide. During rough seas a 25-year-old female musician on a cruise vessel presented with nausea and vomiting. She was given intramuscular metoclopramide 10 mg and diphenhydramine 25 mg. Vomiting stopped after the injections, but she felt tired, confused and dizzy. She then had been taking metoclopramide 5–10 mg a day, but stopped after a total per oral dose of 30 mg as she developed disturbing symptoms that she related to the medication, including dizziness, anxiety, fatigue, depression and involuntary movements (twitches, jerks, ticks, and tremors of the eyelids, tongue, neck, fingers, arms and legs). Neurological examination, blood tests, electrocardiography and magnetic resonance imaging of the brain were all normal. Although gradually reduced in strength and frequency, the adverse effects were very disturbing for about 10 months, but at 13 months she was almost fully recovered. For many years numerous vomiting sea travellers have been successfully treated with a single parenteral 10 mg dose of metoclopramide. There are no obvious reasons why our previously healthy patient experienced such serious and long-lasting side effects after low-dose, short-term metoclopramide administration. Until more is known, metoclopramide should be reserved for debilitating cases — and only be given after other remedies have been tried and found ineffective

Improving Information and Performance in Grain Marketing: an Assessment of Current Market Information Systems, and Recommendations for Developing a Public Grain MIS

This paper focuses on one dimension which is at the core of all modern economies: how to provide private and public agents with timely and accurate information regarding current and expected future market conditions. Its objective is to show the need for a public market information system for agricultural markets in Ethiopia, and to present concrete proposals that can be reviewed, debated, and modified as necessary by the relevant Ethiopian authorities in collaboration with Food Security Research Project (FSRP) personnel.food security, food policy, Crop Production/Industries, Marketing, Q18,

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all

Accuracy Analysis for Finite-Volume Discretization Schemes on Irregular Grids

A new computational analysis tool, downscaling test, is introduced and applied for studying the convergence rates of truncation and discretization errors of nite-volume discretization schemes on general irregular (e.g., unstructured) grids. The study shows that the design-order convergence of discretization errors can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all. The downscaling test is a general, efficient, accurate, and practical tool, enabling straightforward extension of verification and validation to general unstructured grid formulations. It also allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are several new findings arising from the use of the downscaling test analysis. It is shown that the discretization accuracy of a common node-centered nite-volume scheme, known to be second-order accurate for inviscid equations on triangular grids, degenerates to first order for mixed grids. Alternative node-centered schemes are presented and demonstrated to provide second and third order accuracies on general mixed grids. The local accuracy deterioration at intersections of tangency and in flow/outflow boundaries is demonstrated using the DS tests tailored to examining the local behavior of the boundary conditions. The discretization-error order reduction within inviscid stagnation regions is demonstrated. The accuracy deterioration is local, affecting mainly the velocity components, but applies to any order scheme

A Critical Study of Agglomerated Multigrid Methods for Diffusion

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts

Development and Application of Agglomerated Multigrid Methods for Complex Geometries

We report progress in the development of agglomerated multigrid techniques for fully un- structured grids in three dimensions, building upon two previous studies focused on efficiently solving a model diffusion equation. We demonstrate a robust fully-coarsened agglomerated multigrid technique for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A signi cant speed-up in computer time is demonstrated for a model diffusion problem, the Euler equations, and the Reynolds-averaged Navier-Stokes equations for 3D realistic complex geometries

Varicella at sea: a two-year study on cruise ships

Background. Being highly contagious by person-to-person transmission, varicella can easily spread within the multinational population of a cruise ship and into communities ashore. The aim of the study was to report the prevalence of varicella infections in a fleet of cruise ships during a twoyear period and to discuss measures to prevent and contain shipboard outbreaks. Material and methods. All probable varicella cases among passengers and crew on 34 cruise ships were registered for 2 years by the medical facilities onboard. Patients remained isolated until 6 days after rash onset. Susceptible contacts were identified and offered post-exposure prophylaxis. Crew nationality, number of vaccinated contacts, and direct vaccination costs were registered. Results. During two years 187 varicella cases (36 passengers, 151 crew) were registered and 2,685 varicella vaccinations were administered at an estimated direct vaccination cost of US $ 283,832. Of the 34 ships, only 3 reported no cases of varicella. There were 8 clusters (′outbreaks′) of ≥ 5 varicella cases presenting less than 42 days apart, comprising a total of 89 patients. While > 130 nations were represented among the crew, the 151 crew cases came from 26 countries, and 88 (58%) of them came from 5 sub-tropical/tropical countries. Conclusions. All cruise vessels must expect to encounter varicella cases or outbreaks onboard every few years. Every varicella case can start an outbreak and thus trigger several time-consuming and expensive containment measures, including isolation and mass vaccination of susceptible contacts. Mandatory pre-contract evidence of varicella immunity from all seafarers or from subgroups according to position or nationality might be worth considering. Seafarers known to be immune to varicella should always carry valid documentation while traveling