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Implicit LES methods are numerical methods that capture the energy-containing and inertial ranges of turbulent flows, while relying on their own intrinsic dissipation to act as a subgrid model. We present a scheme-dependent Kolmogorov scaling analysis of the solutions produced by such methods. From this analysis we can define an effective Reynolds number for implicit LES simulations of inviscid flow. The approach can also be used to define an effective Reynolds number for under-resolved viscous simulations. Simulations of maintained homogeneous isotropic turbulence and the Taylor-Green vortex are presented to support this proposal and highlight similarities and differences with real-world viscous fluids. Direct comparison with data from high resolution DNS calculations provides validation of the effective viscosity and effective Kolmogorov length scale.

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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.

We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic equations. These systems of equations are usually solved by coupling finite element and CFD models. Here we solve them simultaneously, by recasting all the equations in the same, hyperbolic form and solving them on the same grid with the same finite-volume numerical schemes. The proposed compressible, multiphase, hydrodynamic formulation can employ a hierarchy of five reactive and non-reactive flow models, which allows simple to more involved applications to be directly described by the appropriate selection. The communication between the hydrodynamic and elastoplastic systems is facilitated by means of mixed-material Riemann solvers at the boundaries of the systems, which represent physical material boundaries. To this end we derive approximate mixed Riemann solvers for each pair of the above models based on characteristic equations. The components for reactive flow and elastoplastic solid modelling are validated separately before presenting validation for the full, coupled systems. Multi-dimensional use cases demonstrate the suitability of the reactive flow-solid interaction methodology in the context of impactdriven initiation of reactive flow and structural response due to violent reaction in automotive (e.g. car crash) or defence (e.g. explosive reactive armour) applications. Several types of explosives (C4, Deetasheet, nitromethane, gaseous fuel) in gaseous, liquid and solid state are considered.In this work, we present the coupling of fuel/explosive formulations with fluid and solid models suitable for a range of automotive and defence applications. We use the terms fluid and hydrodynamic interchangeably as well as the terms solid and elastoplastic. The complete explosive-inert fluid-solid system is represented in an Eulerian frame and both the hydrodynamic (for fuel/explosive and inert fluid) and elastoplastic systems of equations are solved with finite volume techniques, employing high-resolution, shock-capturing methods. The communication between the different systems is achieved by employing the Riemann ghost fluid method and the mixed-material Riemann solvers presented here.The mathematical description of the elastoplastic system has been traditionally done in a Lagrangian framework. The original Lagrangian form of the solid equations has been reformulated into a conservative form of equations in the Eulerian frame by Godunov and Romenskii [1], Kondaurov [2] and Plohr and Sharp [3]. This has the advantage of allowing the solution of the elastoplastic solid formulation in the same framework as the explosives hydrodynamic formulation, using the same (or the same family of) highresolution, shock-capturing methods. This led to the development of high-order, shock capturing schemes for the numerical solution of such systems. For example, Miller and Colella [4] and Barton...

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