Over the last few years direct numerical simulation (DNS) of turbulence have achieved, in extreme cases, spatial resolutions of 32K squared collocation points in 2D and 4K cubed points in 3D. In the past it was deemed not necessary in DNS simulations to exceed double precision (roughly 16 significant decimal places). As higher resolutions become accessible, higher precision may also be required. This is not just because higher resolution increase the number or floating point operations and thus the accumulation of rounding errors. Indeed, recent results by Joris van der Hoeven and others indicate that in order to obtain a reasonable precision on scaling exponents (say, a precision of 3-4 digits) the floating point operations - in particular the FFTs - must be performed in much higher than double precision. This has to do with the presence of subdominant corrections involving small parameters such as the viscosity.
Uriel Frisch (Laboratoire Lagrange, Observatoire de la Cote d'Azur Universite de Nice-Sophia Antipolis)
Date & Time
12 December 2011, 16:00 to 17:00
Faculty Hall, IISc, Bangalore