The relationship of MPDATA to other high‐resolution methods

High‐resolution methods have produced the ability to conduct large eddy simulations without the benefit of an explicit subgrid model. This capability is known as implicit large eddy simulation (ILES). A number of high‐resolution methods have been shown to have this property. There are notable exceptions where high‐resolution method do not work as ILES, particularly methods that have a leading ( h 2 ) dissipative term. On the other hand, MPDATA is an effective ILES method with a leading ( h 2 ) dissipative term. This dichotomy has played a key role in the discovery of the key role of conservation or control volume form in producing ILES results. In the process of this analysis, I describe a variant of the method leading to a useful alternative form of sign‐preserving limiters. This form is proposed as an extension of the basic MPDATA methodology allowing some flexibility in the choice of effective high‐order methods. This multistage version of the algorithm removes the leading order nonlinear dissipative error. I rediscover the recursive form of the MPDATA iteration through modified equation analysis (MEA). Finally, returning to the original purpose of the analysis, I describe how the different principles used in MPDATA have been an important contributor to the recent theoretical understanding of ILES. MPDATA is compared with monotone high‐resolution methods both analytically and computationally. The numerical comparison focuses on the validation of ILES methods for high Reynolds number decaying isotropic turbulence. Copyright © 2005 John Wiley & Sons, Ltd.