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## Numerical Resolution (numerical + resolution)
## Selected Abstracts## Modelling of cement suspension flow in granular porous media INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2005Z. SaadaAbstract A theoretical model of cement suspensions flow in granular porous media considering particle filtration is presented in this paper. Two phenomenological laws have been retained for the filtration rate and the intrinsic permeability evolution. A linear evolution with respect to the volume fraction of cement in the grout has been retained for the filtration rate. The intrinsic permeability of the porous medium is looked for in the form of a hyperbolic function of the porosity change. The model depends on two phenomenological parameters only. The equations of this model are solved analytically in the one-dimensional case. Besides, a numerical resolution based on the finite element method is also presented. It could be implemented easily in situations where no analytical solution is available. Finally, the predictions of the model are compared to the results of a grout injection test on a long column of sand. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Finite element of slender beams in finite transformations: a geometrically exact approach INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2004Frédéric BoyerAbstract This article is devoted to the modelling of thin beams undergoing finite deformations essentially due to bending and torsion and to their numerical resolution by the finite element method. The solution proposed here differs from the approaches usually implemented to treat thin beams, as it can be qualified as ,geometrically exact'. Two numerical models are proposed. The first one is a non-linear Euler,Bernoulli model while the second one is a non-linear Rayleigh model. The finite element method is tested on several numerical examples in statics and dynamics, and validated through comparison with analytical solutions, experimental observations and the geometrically exact approach of the Reissner beam theory initiated by Simo. The numerical result shows that this approach is a good alternative to the modelling of non-linear beams, especially in statics. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A simple method for compressible multiphase mixtures and interfaces INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003Nikolai AndrianovAbstract We develop a Godunov-type scheme for a non-conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial differential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and non-equilibrium thermodynamics (two pressures, two temperatures, two densities, etc.).Its numerical resolution poses several difficulties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non-conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Modeling for simulation of fluidized-bed incineration process AICHE JOURNAL, Issue 6 2001F. MariasA mathematical model for the fluidized-bed incineration process was developed using the waste composed of wood, cardboard and polyvinyl chloride. It is based on heat and mass balances of the gas held within the five zones representing both the bubbling bed and freeboard and including heat transfer with sand and reacting particles of char (pyrolysis residue). The mixture fraction concept and assumption of chemical equilibrium are used to compute temperature and species concentration fields resulting from volatile combustion. These fields are affected by char combustion, which relies, in turn, on a model based on surface reaction and a full population balance. The formation of pollutants (NOx, SOx ) was also taken into account. The main steps involved by the numerical resolution of the model are discussed, and some results are shown for a 1 MW unit. [source] ## Generalized MRI reconstruction including elastic physiological motion and coil sensitivity encoding MAGNETIC RESONANCE IN MEDICINE, Issue 6 2008Freddy OdilleAbstract This article describes a general framework for multiple coil MRI reconstruction in the presence of elastic physiological motion. On the assumption that motion is known or can be predicted, it is shown that the reconstruction problem is equivalent to solving an integral equation,known in the literature as a Fredholm equation of the first kind,with a generalized kernel comprising Fourier and coil sensitivity encoding, modified by physiological motion information. Numerical solutions are found using an iterative linear system solver. The different steps in the numerical resolution are discussed, in particular it is shown how over-determination can be used to improve the conditioning of the generalized encoding operator. Practical implementation requires prior knowledge of displacement fields, so a model of patient motion is described which allows elastic displacements to be predicted from various input signals (e.g., respiratory belts, ECG, navigator echoes), after a free-breathing calibration scan. Practical implementation was demonstrated with a moving phantom setup and in two free-breathing healthy subjects, with images from the thoracic-abdominal region. Results show that the method effectively suppresses the motion blurring/ghosting artifacts, and that scan repetitions can be used as a source of over-determination to improve the reconstruction. Magn Reson Med, 2008. © 2008 Wiley-Liss, Inc. [source] ## Ionization-induced star formation , I. The collect-and-collapse model MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007J. E. DaleABSTRACT We conduct smoothed particle hydrodynamics simulations of the ,collect-and-collapse' scenario for star formation triggered by an expanding H ii region. We simulate the evolution of a spherical uniform molecular cloud with an ionizing source at its centre. The gas in the cloud is self-gravitating, although the cloud is prevented from globally collapsing. We find that the shell driven by the H ii region fragments to form numerous self-gravitating objects. We repeat our calculations at four numerical resolutions to ensure that they are converged. We compare our results to the analytical model of Whitworth et al. and show that our simulations and the predictions of Whitworth et al. are in good agreement in the sense that the shell fragments at the time and radius predicted by Whitworth et al. to within 20 and 25 per cent, respectively. Most of the fragments produced in our two highest resolution calculations are approximately half the mass of those predicted by Whitworth et al., but this conclusion is robust against both numerical resolution and the presence of random noise (local fluctuations in density of a factor of ,2) in the initial gas distribution. We conclude that such noise has little impact on the fragmentation process. [source] ## Simulations of strong gravitational lensing with substructure MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006Adam AmaraABSTRACT Galactic-sized gravitational lenses are simulated by combining a cosmological N -body simulation and models for the baryonic component of the galaxy. The lens caustics, critical curves, image locations and magnification ratios are calculated by ray shooting on an adaptive grid. When the source is near a cusp in a smooth lens' caustic, the sum of the magnifications of the three closest images should be close to zero. It is found that in the observed cases this sum is generally too large to be consistent with the simulations, implying that there is not enough substructure in the simulations. This suggests that other factors play an important role. These may include limited numerical resolution, lensing by structure outside the halo, selection bias and the possibility that a randomly selected galaxy halo may be more irregular, for example, due to recent mergers, than the isolated halo used in this study. It is also shown that, with the level of substructure computed from the N -body simulations, the image magnifications of the Einstein cross-type lenses are very weak functions of source size up to 1 kpc. This is also true for the magnification ratios of widely separated images in the fold and cusp,caustic lenses. This means that selected magnification ratios for the different emission regions of a lensed quasar should agree with each other, barring microlensing by stars. The source size dependence of the magnification ratio between the closest pair of images is more sensitive to substructure. [source] ## Populating dark matter haloes with galaxies: comparing the 2dFGRS with mock galaxy redshift surveys MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2004Xiaohu YangABSTRACT In two recent papers, we developed a powerful technique to link the distribution of galaxies to that of dark matter haloes by considering halo occupation numbers as a function of galaxy luminosity and type. In this paper we use these distribution functions to populate dark matter haloes in high-resolution N -body simulations of the standard ,CDM cosmology with ,m= 0.3, ,,= 0.7 and ,8= 0.9. Stacking simulation boxes of 100 h,1 Mpc and 300 h,1 Mpc with 5123 particles each we construct mock galaxy redshift surveys out to a redshift of z= 0.2 with a numerical resolution that guarantees completeness down to 0.01L*. We use these mock surveys to investigate various clustering statistics. The predicted two-dimensional correlation function ,(rp, ,) reveals clear signatures of redshift space distortions. The projected correlation functions for galaxies with different luminosities and types, derived from ,(rp, ,), match the observations well on scales larger than ,3 h,1 Mpc. On smaller scales, however, the model overpredicts the clustering power by about a factor two. Modelling the ,finger-of-God' effect on small scales reveals that the standard ,CDM model predicts pairwise velocity dispersions (PVD) that are ,400 km s,1 too high at projected pair separations of ,1 h,1 Mpc. A strong velocity bias in massive haloes, with bvel,,gal/,dm, 0.6 (where ,gal and ,dm are the velocity dispersions of galaxies and dark matter particles, respectively) can reduce the predicted PVD to the observed level, but does not help to resolve the overprediction of clustering power on small scales. Consistent results can be obtained within the standard ,CDM model only when the average mass-to-light ratio of clusters is of the order of 1000 (M/L), in the B -band. Alternatively, as we show by a simple approximation, a ,CDM model with ,8, 0.75 may also reproduce the observational results. We discuss our results in light of the recent WMAP results and the constraints on ,8 obtained independently from other observations. [source] ## High resolution in z -direction: The simulation of disc-bulge-halo galaxies using the particle-mesh code SUPERBOX ASTRONOMISCHE NACHRICHTEN, Issue 9-10 2008R. BienAbstract SUPERBOX is known as a very efficient particle-mesh code with highly-resolving sub-grids. Nevertheless, the height of a typical galactic disc is small compared to the size of the whole system. Consequently, the numerical resolution in z direction, i. e. vertically with respect to the plane of the disc, remains poor. Here, we present a new version of SUPERBOX that allows for a considerably higher resolution along z. The improved code is applied to investigate disc heating by the in-fall of a galaxy satellite. We describe the improvement and communicate our results. As an important application we discuss the disruption of a dwarf galaxy within a disc-bulge-halo galaxy that consists of some 106 particles. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Ionization-induced star formation , I. The collect-and-collapse model MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007J. E. DaleABSTRACT We conduct smoothed particle hydrodynamics simulations of the ,collect-and-collapse' scenario for star formation triggered by an expanding H ii region. We simulate the evolution of a spherical uniform molecular cloud with an ionizing source at its centre. The gas in the cloud is self-gravitating, although the cloud is prevented from globally collapsing. We find that the shell driven by the H ii region fragments to form numerous self-gravitating objects. We repeat our calculations at four numerical resolutions to ensure that they are converged. We compare our results to the analytical model of Whitworth et al. and show that our simulations and the predictions of Whitworth et al. are in good agreement in the sense that the shell fragments at the time and radius predicted by Whitworth et al. to within 20 and 25 per cent, respectively. Most of the fragments produced in our two highest resolution calculations are approximately half the mass of those predicted by Whitworth et al., but this conclusion is robust against both numerical resolution and the presence of random noise (local fluctuations in density of a factor of ,2) in the initial gas distribution. We conclude that such noise has little impact on the fragmentation process. [source] ## Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 582 2002A. R. BrownAbstract Large-eddy simulations of the development of shallow cumulus convection over land are presented. Many characteristics of the cumulus layer previously found in simulations of quasi-steady convection over the sea are found to be reproduced in this more strongly forced, unsteady case. Furthermore, the results are shown to be encouragingly robust, with similar results obtained with eight independent models, and also across a range of numerical resolutions. The datasets produced are already being used in the development and evaluation of parametrizations used in numerical weather-prediction and climate models. © Royal Meteorological Society, 2002. A. R. Brown's, A. P. Lock's and M. K. MacVean's contributions are Crown copyright. [source] |