Ilya Timofeyev (University of Houston, USA) is granted a Mercator-Fellowship within the SPP 2410.
This fellowship is associated with the SPP 2410 project “Stochastic subgrid scale modeling and structure-preserving flux limiting for hyperbolic systems”under the project leadership of Prof. Dr. Dmitri Kuzmin.
Talk
Ilya Timofeyev holds his talk with the title
Stochastic Sub-Grid Flux Parametrization for Turbulent PDEs Using Stochastic Homogenization
on Monday, July 22, 2024.
Abstract:
We present a systematic approach for deriving the subgrid parametrization in finite-volume discretization of turbulent PDEs using the stochastic homogenization (aka mode-reduction) approach.
First, we introduce coarse variables by applying a box filter to a fine-mesh discretization and decompose all dynamic variables into large-scales and small-scale fluctuations. Next, we interpret this decomposition as the slow and fast variables in the system. We then modify the equation for the fast variables and introduce a multiscale parameter to emphasize the scale separation between the fast and slow variables. The reduced stochastic model is derived in the limit of infinite scale separation and includes additional subgrid terms such as cubic nonlinearity and multiplicative noises. We discuss two examples - the forced and damped Burgers and the 1D Shallow-Water models and demonstrate numerically good agreement in the statistical sense between the Direct Numerical Simulations and reduced dynamics.