Error analysis of SES, a mixed-dynamics model to capture all turbulent scales

Direct numerical simulations of high Reynolds number turbulent flows are computationally expensive owing to the large number of modes that need to be resolved. Selected Eddy Simulation (SES) is a mixed-dynamics approach consisting of solving a subset of modes and modeling the rest using simple dynamics. Since only a fraction of the modes are solved at every step, this can reduce the computational cost associated with high Reynolds number simulations. We have previously applied SES to study isotropic turbulence and shown that one can capture the dynamics of turbulence with just 10% of modes. This reduced computational cost comes at the cost of accuracy.

We study this mixed-dynamics approach in model PDEs and show how error changes with time-step size, percentage of resolved modes and equation parameters. The analytical analysis offers insight into how probability affects results and, thus, how to choose a probability distribution for a particular flow configuration and condition. Since each model differential equation represents a process in real turbulent flows, our study sheds light on the effect of this mixed-dynamics approach on individual turbulent processes. Analytical results are compared with numerical results.