Adjoint linearised Euler solver in the frequency domain for jet noise modelling

The paper is devoted to extending the new efficient frequency-domain method of adjoint Green's function calculation to curvilinear multi-block RANS domains for middle and farfield sound computations. Numerical details of the method such as grids, boundary conditions and convergence acceleration are discussed. Two acoustic source models are considered in conjunction with the method and acoustic modelling results are presented for a benchmark low-Reynolds-number jet case.

The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

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.

Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads

The paper deals with the static analysis of pre-damaged Euler-Bernoulli beams with any number of unilateral cracks and subjected to tensile or compression forces combined with arbitrary transverse loads. The mathematical representation of cracks with a bilateral behaviour (i.e. always open) via Dirac delta functions is extended by introducing a convenient switching variable, which allows each crack to be open or closed depending on the sign of the axial strain at the crack centre. The proposed model leads to analytical solutions, which depend on four integration constants (to be computed by enforcing the boundary conditions) along with the Boolean switching variables associated with the cracks (whose role is to turn on and off the additional flexibility due to the presence of the cracks). An efficient computational procedure is also presented and numerically validated. For this purpose, the proposed approach is applied to two pre-damaged beams, with different damage and loading conditions, and the results so obtained are compared against those given by a standard finite element code (in which the correct opening of the cracks is pre-assigned), always showing a perfect agreement. © 2013 Elsevier Ltd. All rights reserved.

CFD study of a sudden-expanding coal combustor using Euler-Euler and Euler-Lagrange models

In this study, the Euler-Euler (E-E) and Euler-Lagrange (E-L) models designed for the same chemical mechanism of heterogeneous reactions were used to predict the performance of a typical sudden-expanding coal combustor. The results showed that the current E-E model underestimated the coal burnout rate because the particle temperature fluctuation on char combustion is not adequately considered. A comparison of the E-E and E-L simulations showed the underestimation of heterogeneous chemical reaction rates by the E-E model. (C) 2010 Elsevier Ltd. All rights reserved.

Volcanic air pollution and mortality in France 1783?1784

Grattan J.P., Rabartin, R., Self, S. & Thordarson, Th. 2005. Volcanic air pollution and mortality in France 1783-84. Comptes Rendu Geosciences. 641-651 This item is available in both English and French in the PDF file.

Acid damage to vegetation following the Laki Fissure eruption in 1783 - an historical review

Grattan, John and Pyatt, Brian. 'Acid damage to vegetation following the laki fissure eruption in 1783 - an historical review' The Science of the Total Environment. 26 August 1993. 151 pgs 241-247

El problema de Rencontre

A mediados del siglo XVIII el prolífico y genial matemático suizo leonhard Euler analizó y resolvió un juego de probabilidad con cartas llamado Rencontre. Como otros problemas probabilísticos, el enunciado es fácilmente comprensible, su análisis no es elemental y el resultado parece contrario a la intuición o, cuando menos, sorprendente. Euler utiliza, para la resolución del problema, la combinatoria y la suma de ciertas sucesiones. En este artículo se pretende llegar a la misma conclusión recurriendo a unas matemáticas más cercanas al alumno de bachillerato.

Recta de Euler en cuadriláteros

El circuncentro (O), baricentro (G) y ortocentro (H) de todo triangulo estan alineados en la recta de Euler y verifican la relación mGH = 2 · mOG. En el presente artıculo se define baricentro (G) y ortocentro (H) de un cuadrilátero inscriptible de circuncentro (O) y se demuestra que dichos puntos están alineados y verifican la relación mGH = 3 · mOG.

On the coupling of Navier–Stokes and linearised Euler equations for aeroacoustic simulation

Aerodynamic generation of sound is governed by the Navier–Stokes equations while acoustic propagation in a non-uniform medium is effectively described by the linearised Euler equations. Different numerical schemes are required for the efficient solution of these two sets of equations, and therefore, coupling techniques become an essential issue. Two types of one-way coupling between the flow solver and the acoustic solver are discussed: (a) for aerodynamic sound generated at solid surfaces, and (b) in the free stream. Test results indicate how the coupling achieves the necessary accuracy so that Computational Fluid Dynamics codes can be used in aeroacoustic simulations.

[Lecture review] 4. 'Three great mathematicians: Euler', 6 March 2002

Tony Mann provides a review of the lecture: 'Three great mathematicians: Euler' held on 6 March 2002 as the fourth and last lecture of the Gresham College History of Mathematics season.

[Book review] Reviews

Review of biography of Leonhard Euler - Andreas K Heyne and Alice P Heyne (text) and Elena S Pini (illustrations), Leonhard Euler: a man to be reckoned with, translated from the German by Alice P Heyne and Tahu Matheson, Birkhauser, 2007, 45 pp, £14.50, ISBN 3-7643-8332-9.