Scaling Laws for Fluid Flows
The Background Field method developd by Constantain and Doering allows one to prove rigorous bounds on how average fundamental properties of fluid flows (e.g., drag, skin friction, dissipation of kinetic energy) vary as a function of the forcing parameters of the flow (e.g., Reynolds number). A new approach to calculate optimal background flow profiles is to employ Semidefinite Programming, and can be implemented using the QUINOPT package developed in the group. We seek to couple this computational optimization approach with rigorous analytical estimates in order to prove scaling laws for hydrodynamic systems.
Related Publications
Zheng Y, Fantuzzi G, Papachristodoulou A, Goulart P, Wynn A, 2019, Chordal decomposition in operator-splitting methods for sparse semidefinite programs, Mathematical Programming.
Brackston R, Wynn A, Stumpf MPH, 2018, Construction of quasi-potentials for stochastic dynamical systems: An optimization approach, Physical Review E, Vol:98.
Fantuzzi G, Pershin A, Wynn A, 2018, Bounds on heat transfer for Benard-Marangoni convection at infinite Prandtl number, Journal of Fluid Mechanics, 837, 562-596. Link.
Fantuzzi G, Wynn A, 2017, Exact energy stability of Benard-Marangoni convection at infinite Prandtl number, Journal of Fluid Mechanics (Rapids), 822. Link.
Zheng Y, Fantuzzi G, Papachristodoulou A, Goulart P, Wynn A, 2017, Fast ADMM for homogeneous self-dual embedding of sparse SDPs, 20th IFAC World Congress
Zheng Y, Fantuzzi G, Papachristodoulou A, Goulart P, Wynn A, 2017, Fast ADMM for Semidefinite Programs with Chordal Sparsity, 2017 American Control Conference.
Fantuzzi G, Wynn A, Goulart P, Papachristodoulou A, Optimization with affine homogeneous quadratic integral inequality constraints, IEEE Transactions on Automatic Control, 62, 6221-6236 arXiv
Fantuzzi G., Wynn A., Optimal bounds with semidefinite programming: an application to stress driven shear flows, Physical Review E. 93, 043308, Link.
Fantuzzi G., Wynn A., 2015, Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming, Physics Letters A, 379, 23-32. Link.