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Figure 7 | Journal of Mathematics in Industry

Figure 7

From: Optimal control of buoyancy-driven liquid steel stirring modeled with single-phase Navier–Stokes equations

Figure 7

Optimization of nozzles’ positions. Results obtained for levels 2 (top) and 3 (bottom), \(J_{1}\) (left), and \(J_{2}\) (right). The reduction of the functionals is depicted in accordance with the legend, i.e., the size of the circles represents \(1-R_{i}\) with the corresponding reduction \(R_{i}\) from equation (8). The red crosses are the computed weighted centers, see equation (9). The black plus signs indicate the default positions of the nozzles as given in Table 1

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