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Table 6 Optimization of nozzles’ positions. Computed weighted centers (equation (9)) for the used objective functionals on level 3. The labels correspond to the configurations in Fig. 9

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

Objective

\(x_{n1,c}\)

\(y_{n1,c}\)

\(x_{n2,c}\)

\(y_{n2,c}\)

Label

\(J_{1}^{\mathrm{opt},3}\)

−0.11144

0.11144

0.08788

−0.12436

\(J_{2}^{\mathrm{opt},3}\)

−0.11515

0.11515

0.0167

−0.10072

\(J_{3}^{\mathrm{opt},3}(1)\)

−0.11694

0.11694

0.07203

−0.12565

\(J_{3}^{\mathrm{opt},3}(10)\)

−0.12457

0.12457

0.09542

−0.13819

\(J_{3}^{\mathrm{opt},3}(25)\)

−0.12246

0.12246

0.03319

−0.14931