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Modular Data Assimilation for Flow Prediction
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DOI：10.1002/num.70066.png)
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Abstract
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Modular nudging algorithms (inspired by Kalman filters) are presented. Forecast v(n+1) -v(n) / k + v(n) . del v(n+1) - v triangle(n+1) + del q(n+1) = f(x) If data at t(h+1): Analysis v(n+1) -v(n+1)/ k - chi I-H(u(t(n+1)) - v(n+1)) = 0. There are 3 main results. 1. If I-H(2). I-H, analysis has implicit stability and explicit complexity: v(n+1 =) v(n+1) + k chi/1+ k chi [I(H)u(t(n+1)) - I(H)v(n+1)]. 2. For H small and chi large, predictability horizons are infinite. 3. For any H and chi, errors decrease and predictability horizons increase. Numerics confirm the method's effectiveness.
Keywords:
data assimilation
Navier Stokes
nudging
predictability
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