4 papers
An Artificial-Compressibility Physics-Informed Neural Network for the Unsteady Incompressible Navier--Stokes Equations
Aytekin Çibik
We study a physics-informed neural network (PINN) for the unsteady, two-dimensional incompressible Navier--Stokes equations in which the stiff divergence-free constraint is replace…
Data assimilation for slightly compressible flow
Aytekin Ãıbık, Rui Fang
Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus p…
Modular data assimilation for flow prediction
Aytekin Ãıbık, Rui Fang, William Layton
This report develops several modular, 2-step realizations (inspired by Kalman filter algorithms) of nudging-based data assimilation $$Step \ 1 \quad \frac{\widetilde {v}^{n+1}-v^{n…
Data assimilation with model errors
Aytekin Ãibik, Rui Fang, William Layton +1
Nudging is a data assimilation method amenable to both analysis and implementation. It also has the (reported) advantage of being insensitive to model errors compared to other assi…