No abstract

Although climate models have been improving in accuracy and efficiency over the past few decades, it now seems that these incremental improvements may be slowing. As tera/petascale computing becomes massively parallel, our legacy codes are less suitable, and even with the increased resolution that we are now beginning to use, these models cannot represent the multiscale nature of the climate system. This paper argues that it may be time to reconsider the use of adaptive mesh refinement for weather and climate forecasting in order to achieve good scaling and representation of the wide range of spatial scales in the atmosphere and ocean. Furthermore, the challenge of introducing living organisms and human responses into climate system models is only just beginning to be tackled. We do not yet have a clear framework in which to approach the problem, but it is likely to cover such a huge number of different scales and processes that radically different methods may have to be considered. The challenges of multiscale modelling and petascale computing provide an opportunity to consider a fresh approach to numerical modelling of the climate (or Earth) system, which takes advantage of the computational fluid dynamics developments in other fields and brings new perspectives on how to incorporate Earth system processes. This paper reviews some of the current issues in climate (and, by implication, Earth) system modelling, and asks the question whether a new generation of models is needed to tackle these problems.

Cut-cell meshes present an attractive alternative to terrain-following coordinates for the representation of topography within atmospheric flow simulations, particularly in regions of steep topographic gradients. In this paper, we present an explicit twodimensional method for the numerical solution on such meshes of atmospheric flow equations including gravitational sources. This method is fully conservative and allows for time steps determined by the regular grid spacing, avoiding potential stability issues due to arbitrarily small boundary cells. We believe that the scheme is unique in that it is developed within a dimensionally split framework, in which each coordinate direction in the flow is solved independently at each time step. Other notable features of the scheme are: (i) its conceptual and practical simplicity, (ii) its flexibility with regard to the one-dimensional flux approximation scheme employed, and (iii) the well-balancing of the gravitational sources allowing for stable simulation of near-hydrostatic flows. The presented method is applied to a selection of test problems including buoyant bubble rise interacting with geometry and lee-wave generation due to topography.

In this article the interaction of a shock wave with a rectangular block of sulphur hexafluoride ͑SF 6 ͒, occupying part of the test section of a shock tube, is studied by experimental and numerical means. The difference between the ratios of the specific heats of the two gases ͑air and SF 6 ͒ gives rise to numerical problems ͑generation of spurious waves at their interface͒. This necessitated the development of a multifluid algorithm ͑augmented Navier-Stokes formulation͒. The governing equations are based on a thermodynamically consistent and fully conservative formulation. A Riemann-problem-based scheme ͑the weighted average flux method͒ is used to integrate the hyperbolic part of the system. To this end, a new approximate Riemann problem solver has been formulated to account for the variable ratio of specific heats. The resulting algorithm was implemented in an adaptive mesh refinement code, which allowed high-resolution simulations to be performed on desktop computers. The evolution of the flow is well captured by the two-dimensional numerical solution, up to the point at which dimensionality effects become significant. The experimental evidence and numerical solutions complement each other to allow the time-evolving features present to be accurately identified and tracked, and the resulting flow physics to be discussed. Where possible, quantitative geometric comparison is made between both sets of results and good agreement demonstrated.

This paper presents a simplified reactive multi-gas model for the numerical simulation of detonation waves. The mathematical model is formulated based on a thermodynamically consistent and fully conservative formulation, and is extended to model reactive flow by considering the reactant and product gases as two constituents of the system and modelling the conversion between these by a simple one-step reaction mechanism. This simplified model allows simulations using more appropriate chemico-thermodynamic properties of the combustible mixture and yields close Chapman-Jouguet detonation parameters from detailed chemistry. The governing equations are approximated using a high-resolution finite volume centred scheme in an adaptive mesh refinement code, permitting high-resolution simulations to be performed at flow regions of interest. The algorithm is tested and validated by comparing results to predictions of the one-dimensional linear stability analysis of the steady detonation and through the study of the evolution of two-dimensional cellular detonation waves in gaseous hydrogen-based mixtures.