Computationally efficient generation of gaussian conditional simulations over regular sample grids

The generation over two-dimensional grids of normally distributed random fields conditioned on available data is often required in reservoir modeling and mining investigations. Such fields can be obtained from application of turning band or spectral methods. However, both methods have limitations. First, they are only asymptotically exact in that the ensemble of realizations has the correlation structure required only if enough harmonics are used in the spectral method, or enough lines are generated in the turning bands approach. Moreover, the spectral method requires fine tuning of process parameters. As for the turning bands method, it is essentially restricted to processes with stationary and radially symmetric correlation functions. Another approach, which has the advantage of being general and exact, is to use a Cholesky factorization of the covariance matrix representing grid points correlation. For fields of large size, however, the Cholesky factorization can be computationally prohibitive. In this paper, we show that if the data are stationary and generated over a grid with regular mesh, the structure of the data covariance matrix can be exploited to significantly reduce the overall computational burden of conditional simulations based on matrix factorization techniques. A feature of this approach is its computational simplicity and suitability to parallel implementation.     

Can simulations reproduce the observed temperature–mass relation for clusters of galaxies?

It has become increasingly apparent that traditional hydrodynamical simulations of galaxy clusters are unable to reproduce the observed properties of galaxy clusters, in particular overpredicting the mass corresponding to a given cluster temperature. Such overestimation may lead to systematic errors in results using galaxy clusters as cosmological probes, such as constraints on the density perturbation normalization σ ₈. In this paper we demonstrate that inclusion of additional gas physics, namely radiative cooling and a possible pre-heating of gas prior to cluster formation, is able to bring the temperature–mass relation in the innermost parts of clusters into good agreement with recent determinations by Allen, Schmidt & Fabian using Chandra data.     

Assessing the credibility of a series of computational fluid dynamic simulations of open channel flow

Recent developments in numerical algorithms have enabled the construction of three‐dimensional models for the prediction of flows in open channels. These advances encompass improvements in both numerical solutions and the process representation required for an accurate system definition. However, to date, there is still little agreement on how to assess systematically and report the credibility of these simulations. This paper addresses this problem by adopting a Grid Convergence Index approach. The results indicate, for two simple hypothetical cases, a zero‐degree confluence and a meander bend, that the numerical code can be verified to an acceptable numerical standard. However, it is shown that this does not mean that verification is complete, as the literature implies, as whilst the discretization resolution may be sufficient to verify one of the model variables it does not imply that every variable has converged. Furthermore, the scheme may still be insufficient to capture all the processes of interest that are operating within the chosen environment. Copyright © 2003 John Wiley & Sons, Ltd.