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The Special Issue presents almost 40 papers on recent research in modeling of pyrometallurgical systems, including physical models, first-principles models, detailed CFD and DEM models as well as statistical models or models based on machine learning. The models cover the whole production chain from raw materials processing through the reduction and conversion unit processes to ladle treatment, casting, and rolling. The papers illustrate how models can be used for shedding light on complex and inaccessible processes characterized by high temperatures and hostile environment, in order to improve process performance, product quality, or yield and to reduce the requirements of virgin raw materials and to suppress harmful emissions.

steelmaking --- oxygen consumption --- GPR --- prediction model --- secondary refining --- water model --- mixing time --- slag entrapment --- stainless steel slag --- heating time --- Cr2O3 --- spinel --- crystal size --- processing maps --- nickel-based alloy --- flow behavior --- arrhenius equation --- hearth --- drainage --- PCA --- analysis tool --- pattern --- tapholes --- blast furnace --- coke --- carbon solution loss --- numerical simulation --- pellet pile --- Discrete Element Method --- porosity distribution --- angle of repose --- coordination number --- bubble motion --- interfacial phenomena --- entrainment --- moving path --- arsenopyrite --- arsenic removal --- mechanism --- roasting --- arsenate --- dust ash --- arsenic recovery --- titanium distribution ratio --- thermodynamic model --- ion–molecule coexistence theory --- LF refining slags --- electric arc furnace --- simulation --- process model --- COREX --- raceway zone --- gas flow --- COREX melter gasifier --- mixed charging --- burden layer structure --- burden pile width --- DEM --- burden distribution --- particle flow --- validation --- tire cord steel --- TiN inclusion --- solidification --- segregation models --- hot rolling --- TOU electricity pricing --- hot rolling planning --- genetic algorithm --- C-H2 smelting reduction furnace --- double-row side nozzles --- dimensional analysis --- multiple linear regression --- ironmaking blast furnace --- coke bed --- trickle flow --- molten slag --- liquid iron --- SPH --- charging system --- mathematical model --- radar data --- main trough --- transient fluid of hot metal and molten slag --- wall shear stress --- conjugate heat transfer --- refractory --- shape rolling --- flat rolling --- wire rod --- temperature distribution --- machine learning --- artificial intelligence --- neural network --- BOS reactor --- copper smelting --- SKS --- Shuikoushan process --- oxygen bottom blown --- gated recurrent unit --- support vector data description --- time sequence prediction --- fault detection and identification --- Lignite --- microwave and ultrasound modification --- structural characterization --- 3D molecular model --- structural simulation --- coke combustion rate --- charcoal combustion rate --- iron ore sintering process --- biomass --- quasi-particle --- quasi-particle structure --- monomer blended fuel --- quasi-particle fuel --- apparent activation energy --- coupling effect --- dynamic model --- basic oxygen furnace --- computational fluid dynamics --- CFD–DEM --- coalescence --- settling --- funneling flow --- horizontal single belt casting process (HSBC) --- computational fluid dynamics (CFD) --- double impingement feeding system --- supersonic coherent jet --- decarburization --- steel refining --- EAF --- CFD --- mass transfer coefficient --- physical modeling --- mathematical modeling --- kinetic models --- natural gas --- fuel injection --- combustion --- RAFT --- roll design --- flat-rolled wire --- strain inhomogeneity --- normal pressure --- macroscopic shear bands --- numerical model --- dual gas injection --- slag eye --- electrical energy consumption --- Electric Arc Furnace --- scrap melting --- statistical modeling --- raceway evolution --- raceway size --- flow pattern --- Eulerian multiphase flow --- blast furnace hearth --- dead man --- iron and slag flow --- lining wear --- hearth drainage --- Industry 4.0 --- copper smelter --- nickel-copper smelter --- radiometric sensors --- Peirce-smith converting --- matte-slag chemistry --- discrete event simulation --- adaptive finite differences --- n/a --- ion-molecule coexistence theory --- CFD-DEM