On the physical inadmissibility of ILES for simulations of Euler equation turbulence

Abstract: We present two main results. The first is a plausible validation argument for the principle of a maximal rate of entropy production for Euler equation turbulence. This principle can be seen as an extension of the second law of thermodynamics. In our second main result, we examine competing models for large eddy simulations of Euler equation (fully developed) turbulence. We compare schemes with no subgrid modeling, implicit large eddy simulation (ILES) with limited subgrid modeling and those using dynamic subgrid scale models. Our analysis is based upon three fundamental physical principles: conservation of energy, the maximum entropy production rate and the principle of universality for multifractal clustering of intermittency. We draw the conclusion that the absence of subgrid modeling, or its partial inclusion in ILES solution violates the maximum entropy dissipation rate admissibility criteria. We identify circumstances in which the resulting errors have a minor effect on specific observable quantities and situations where the effect is major. Application to numerical modeling of the deflagration to detonation transition in type Ia supernova is discussed.