Modeling the Effects of Round-off Error in Chaotic Dynamical Simulations

The majority of computational fluid dynamics simulations, including for turbulent flows, use double precision arithmetic. Using lower-precision (e.g., single) could reduce the computational cost of such calculations, however, larger round-off errors potentially compromise solution accuracy. Our objective is to understand the effect of round-off error on simulations of chaotic systems. We solve the 1D Kuramoto-Sivashinsky equation using finite differences with an IMEX Runge-Kutta scheme. The solutions obtained using different precisions are analyzed by examining the statistics, including velocity structure functions, spatial and temporal energy spectra, and the Lyapunov exponent. The results show that the spatial and temporal energy spectra are not particularly sensitive to the precision. However, the velocity structure function is different for single precision, and the growth rate of small perturbations is orders of magnitude larger for single precision.