Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer-Meshkov instability

Both experiments and computations are naturally constrained by boundary conditions. In fundamental problems such as homogeneous decaying turbulence (HDT) or shock-induced mixing layers, a size constraint naturally limits the growth of the large scales in the problem, modifying the physics observed. This paper explores through Large Eddy Simulation (LES) the integral properties using computations from 1283 to 10243 for HDT and 1283 to 5123 for the Richtmyer-Meshkov instability (RMI). Kinetic energy decay rates in both cases are shown to be relatively insensitive to the domain size until the spectral peak is at the first wave number. The integral length is significantly more sensitive, showing substantial discrepancies once it is greater than 10% of the domain size. However, the key error is shown to be due to a lack of statistical averaging once the integral length is greater than 5% of the box size, thus appearing earlier than the length scale saturation. This highlights that a single computation at modes...

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