Next Article in Journal
Microstructure–Property Relationships in Thermomechanically Processed Medium-Mn Steels with High Al Content
Next Article in Special Issue
Laboratory Experimental Setup and Research on Heat Transfer Characteristics during Secondary Cooling in Continuous Casting
Previous Article in Journal
Impact of Warm Rolling Process Parameters on Crystallographic Textures, Microstructure and Mechanical Properties of Low-Carbon Boron-Bearing Steels
Previous Article in Special Issue
Simulation of Crack Initiation and Propagation in the Crystals of a Beam Blank
Article Menu
Issue 11 (November) cover image

Export Article

Open AccessArticle

Applied Mathematical Modelling of Continuous Casting Processes: A Review

Division of Processes, Department of Materials Science and Engineering, Brinellvägen 23, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
Current address: Department of Applied Mathematics and Statistics, Institute of Mathematical and Computer Sciences, University of São Paulo at São Carlos, P.O. Box 668, São Carlos 13560-970, São Paulo, Brazil.
Metals 2018, 8(11), 928;
Received: 21 October 2018 / Revised: 31 October 2018 / Accepted: 2 November 2018 / Published: 9 November 2018
(This article belongs to the Special Issue Continuous Casting)
PDF [5994 KB, uploaded 9 November 2018]


With readily available and ever-increasing computational resources, the modelling of continuous casting processes—mainly for steel, but also for copper and aluminium alloys—has predominantly focused on large-scale numerical simulation. Whilst there is certainly a need for this type of modelling, this paper highlights an alternative approach more grounded in applied mathematics, which lies between overly simplified analytical models and multi-dimensional simulations. In this approach, the governing equations are nondimensionalized and systematically simplified to obtain a formulation which is numerically much cheaper to compute, yet does not sacrifice any of the physics that was present in the original problem; in addition, the results should agree also quantitatively with those of the original model. This approach is well-suited to the modelling of continuous casting processes, which often involve the interaction of complex multiphysics. Recent examples involving mould taper, oscillation-mark formation, solidification shrinkage-induced macrosegregation and electromagnetic stirring are considered, as are the possibilities for the modelling of exudation, columnar-to-equiaxed transition, V-segregation, centreline porosity and mechanical soft reduction. View Full-Text
Keywords: asymptotic analysis; numerical simulation; continuous casting asymptotic analysis; numerical simulation; continuous casting

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Vynnycky, M. Applied Mathematical Modelling of Continuous Casting Processes: A Review. Metals 2018, 8, 928.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Metals EISSN 2075-4701 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top