The relationship of MPDATA to other high-resolution methods

Abstract

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 O(h2) dissipative term. On the other hand, MPDATA is an effective ILES method with a leading O(h2) 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.