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Table 5 Optimization of gas flow rates. Minimum objectives \(M_{J, \lambda }\) and corresponding frequencies \(\omega _{i}\), \(i\in \{1,2\}\). The last column is the number of required optimization iterations. \(\Delta t=0.025\), mesh 3

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

Objective J

λ

\(M_{J,\lambda }\)

Reduction \(M_{J,\lambda }\)

\(\omega _{1}\)

\(\omega _{2}\)

No. it

J1

0.00001

−69.27474

1.00000

0.025

0.025

17

J2

0.00001

−3.68885

0.99965

0.02558

0.02594

29

J3(1)

0.00001

0.23004

0.95145

0.03488

0.04074

34

J3(100)

0.00001

119.14479

1.00000

0.02502

0.02502

25

J1

0.0001

−68.75462

0.99999

0.02502

0.02504

23

J2

0.0001

−3.2035

0.99036

0.02773

0.02765

33

J3(1)

0.0001

0.52423

0.49829

0.09994

0.1932

28

J3(100)

0.0001

119.663

0.99998

0.02514

0.02518

22

J1

0.001

−63.58787

0.99949

0.02533

0.02533

29

J2

0.001

0.79576

0.75120

0.14665

0.14607

30

J3(1)

0.001

3.13743

0.07774

0.15003

0.15008

31

J3(100)

0.001

124.6972

0.99858

0.0264

0.02651

34

J1

0.01

−18.27467

0.91106

0.1452

0.03189

37

J2

0.01

26.98974

0.12163

0.15092

0.15044

34

J3(1)

0.01

29.30945

0.01045

0.15051

0.15031

29

J3(100)

0.01

160.6485

0.89003

0.15002

0.14975

34

J1

0.1

248.25463

0.21043

0.15047

0.14971

30

J2

0.1

288.65835

0.01293

0.15072

0.15001

38

J3(1)

0.1

290.05752

0.00157

0.15007

0.14973

39

J3(100)

0.1

421.9993

0.32359

0.15

0.15014

35