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The travelling slice approximation of continuous casting process is widely used in industrial practice to model the heat transfer and solidification. Short computational times that are possible due to the reduction from three to two dimensions compensate for lower accuracy introduced by the approximation. In the same spirit, the travelling slice approximation is also used for the thermomechanical model in the present paper. The model includes contributions from metallostatic pressure, thermal contraction and viscoplastic deformation to describe the stress in the material slice. It incorporates simple models to predict the hot tearing and cracking. The model is solved with a novel strong-form meshless method. It allows flexible adaptive node distribution to accurately describe the behaviour in the solidifying region. In this paper we focus on the two-way coupling of the heat transfer and deformation of the strand to model the air-gap formation in the initial stage of the casting process and to study the emergent behaviour that is the result of this coupling. We find that the inclusion of the air-gap model significantly changes the stress distribution in the corners of the strand because of the reheating caused by the reduced heat-transfer.

Purpose This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method. Design/methodology/approach A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case. Findings The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented. Originality/value A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.