Example

Figure 33 shows an example implementation of the polynomial identifi­cation technique. The DNS computation of a two-dimensional shear-layer, performed by Wei & Freund, is used. The pressure field is sample along the red line shown on the left of the figure. This sampled pressure field is then decomposed using Proper Orthogonal Decomposition, allowing it to be represented in terms of a set of temporal functions, ai(t), and spatial functions, ф(х). Using the polynomial identification technique, truncated to only include the linear term, the coefficients, Lij are determined. The ODE is then integrated in time and the result compared with a truncated rep­resentation (using 40 POD modes, a number found sufficient to reproduce the full DNS field with good accuracy) of the original pressure field.

The integrated ODE, a snapshot of which is shown in figure 33, was found to follow the DNS very closely for about three convective time units. After this the two solutions begin to differ, although the simplified dynamic model continues to behave in a qualitatively similar manner to the DNS.

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