Solution Of The Transient Direct Chill Casting Problem With Simultaneous Material And Interphase Moving Boundaries By The Local Radial Basis Function Collocation Technique
Free (open access)
B. Šarler & R. Vertnik
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 movement of the bottom block is approximated by the movement of the boundary condition through the computational domain. The moving 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 on the problem dimension. Realistic boundary conditions and temperature variation of material properties are included. Two-dimensional test case solution is shown at different times, verified by comparison with the finite volume method results. Keywords: direct chill casting, start-up phase, aluminium, solidification, meshless method, local radial basis function collocation method, moving boundary problem, multiquadrics.
direct chill casting, start-up phase, aluminium, solidification, meshless method, local radial basis function collocation method, moving boundary problem, multiquadrics.