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Numerical analysis of data assimilation for slightly compressible flow
Aytekin Çıbık, Rui Fang
Continuous data assimilation improves flow predictions by continually nudging a model toward available observational data. For slightly compressible flow, a recent model addresses…
Data assimilation for slightly compressible flow
Aytekin Çıbık, 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 Çıbık, 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 Çibik, 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…
Adaptive Parameter Selection in Nudging Based Data Assimilation
Aytekin Çıbık, Rui Fang, William Layton +1
Data assimilation combines (imperfect) knowledge of a flow's physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of…
The Ramshaw-Mesina Hybrid Algorithm applied to the Navier Stokes Equations
Aytekin Çibik, Farjana Siddiqua, William Layton
In 1991, Ramshaw and Mesina proposed a novel synthesis of penalty methods and artificial compression methods. When the two were balanced they found the combination was 3-4 orders m…