Solution of transient direct-chill aluminium billet casting problem with simultaneous material and interphase moving boundaries by a meshless method.

*(English)*Zbl 1195.76325Summary: This paper uses a recently developed upgrade of the classical meshless Kansa method for solution of the transient heat transport in direct-chill casting of aluminium alloys. The problem is characterised by a moving mushy domain between the solid and the liquid phase and a moving starting bottom block that emerges from the mould during the process. The solution of the thermal field is based on the mixture continuum formulation. The growth of the domain and the movement of the bottom block are described by activation of additional nodes and by the movement of the boundary nodes through the computational domain, respectively. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented by the multiquadrics radial basis function collocation on a related sub-set of nodes. Time stepping is performed in an explicit way. The governing equation is solved in its strong form, i.e. no integrations are performed. The polygonisation is not present and the method is practically independent of the problem dimension. Realistic boundary conditions and temperature variation of material properties are included. An axisymmetric transient test case solution is shown at different times and its accuracy is verified by comparison with the reference finite volume method results.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76T99 | Multiphase and multicomponent flows |

80A22 | Stefan problems, phase changes, etc. |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

##### Keywords:

direct-chill casting; start-up phase; aluminium; solidification; meshless method; local radial basis function collocation method; moving boundary problem; multiquadrics
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\textit{R. Vertnik} et al., Eng. Anal. Bound. Elem. 30, No. 10, 847--855 (2006; Zbl 1195.76325)

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