Time averaging of instantaneous quantities in HYDRA

For turbulent flow the evaluation of direct numerical simulations (DNS) where all scales are resolved and large-eddy simulation (LES) where only large-scales are resolved is difficult because the results are three-dimensional and transient. To simplify the analysis, the instantaneous flow field can be averaged in time for evaluation and comparison to experimental results. The incompressible Navier-Stokes flow code HYDRA has been modified for calculation of time-average quantities for both DNS and LES. This report describes how time averages of instantaneous quantities are generated during program execution (i.e., while generating the instantaneous quantities, instead of as a postprocessing operation). The calculations are performed during program execution to avoid storing values at each time step and thus to reduce storage requirements. The method used in calculating the time-average velocities, turbulent intensities, <{ital u}{sup ``}{sup 2}>, <{ital va}{sup ``}{sup 2}>, and <{ital w}{sup ``}{sup 2}>, and turbulent shear, <{ital u}{sup ``}{ital v}{sup ``}> are outlined. The brackets <> used here represent a time average. the described averaging methods were implemented in the HYDRA code for three-dimensional problem solutions. Also presented is a method for taking the time averages for a number of consecutive intervals and calculating the time average for the sum of the intervals. This method could be used for code restarts or further postprocessing of the timer averages from consecutive intervals. This method was not used in the HYDRA implementation, but is included here for completeness. In HYDRA, the running sums needed fro time averaging are simply written to the restart dump