Stochastic convergence and the software tool W

The concept of w convergence of probability distribution functions to a probability distribution limit, also known as a Young measure, as a description of Large Eddy Simulation (LES) convergence has been proposed separately, and preliminary tests have been encouraging. Here we develop the practical side of implementation for this program. The first step is a conceptual reinterpretation of simulation data, and in this sense the idea is basically one of a post processing. In a given simulation, the grid limited information is partitioned into (a) coarse grained grid information, i.e. geometrical or space-time localization relative to a coarse grid composed of supercells, and (b) stochastic information within a supercell, giving information on random or probabilistic solution state values. The second step in a convergence study is to compare the results of the first step, i.e. to compare the probabilistic state values (with their-limited resolution-geometrical localizations). This second step, comparison of grid defined Young measures, is the subject of the present paper.