Parallel-in-time methods for the propagation of uncertainties in wind-farm simulations

Large eddy simulations (LES) of turbulence resort to coarse-grained models of the small scales of motion for which numerical resolution is not available.

LES can be applied for the aerodynamic analysis of wind farms at sea. However, the model that describes the nonlinear unresolved-resolved interactions is a major source of uncertainty. Therefore, we aim to study the nonlinear propagation the uncertainties in LES of wind farms.

To start, a comparative study of Polynomial Chaos, Gaussian process and Karhunen-Loeve based surrogate models for uncertainty propagation (UP) is performed and the best method is tailored to turbulence. The number of cores needed for this UP is so large that a space-only parallelization does not suffice; hence parallel-in-time (PinT) algorithms are applied.

Basically, multiple time steps are introduced and the serial dependencies are shifted to the largest time step. Parareal is a prime example which has been applied with success to many problems. For turbulent flows, however, parareal suffers from convergence problems and artificial dissipation. Both problems are addressed by improving the coarse-time operator. The PinT-software is set up such that it can be used for Navier-Stokes solvers; the software may also be (re)used for the time integration of similar pde’s.