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

Journal of Mathematics in Industry

Table 3 Optimization of gas flow rates. Reductions of the objective functionals, level 2 vs. level 3

Δt	\(C_{S}\)	λ	Level	\(J_{1}\)	\(J_{2}\)	\(J_{3}(1)\)	\(J_{3}(100)\)
0.025	0.01	0.00001	2	1.000	0.999	0.987	1.000
0.025	0.01	0.00001	3	1.000	0.997	0.968	1.000
0.025	0.01	0.0001	2	1.000	0.935	0.708	1.000
0.025	0.01	0.0001	3	1.000	0.941	0.594	1.000
0.025	0.01	0.001	2	0.970	0.275	0.126	0.998
0.025	0.01	0.001	3	0.995	0.336	0.110	0.999
0.025	0.01	0.01	2	0.258	0.032	0.014	0.859
0.025	0.01	0.01	3	0.497	0.042	0.012	0.874
0.025	0.01	0.1	2	0.030	0.003	0.004	0.351
0.025	0.01	0.1	3	0.069	0.004	0.002	0.362