zbMATH — the first resource for mathematics

Solution of transient direct-chill aluminium billet casting problem with simultaneous material and interphase moving boundaries by a meshless method. (English) Zbl 1195.76325
Summary: 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.

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)
Full Text: DOI
[1] Altenpohl, D.G., Aluminium: technology, applications, and environment: a profile of a modern metal, (1998), Aluminium Association & TMS Warrendale
[2] Beckermann, C., Modelling of macrosegregation, Int mater rev, 47, 243-261, (2002)
[3] Williams, A.J.; Croft, T.N.; Cross, M., Modelling of ingot development during start-up phase of direct chill casting, Metall mater trans, 34B, 727-734, (2003)
[4] Liu, G.R., Mesh free methods, (2003), CRC Press Boca Raton, FL
[5] Šarler, B., Meshless methods, (), [Chapter 9] · Zbl 1297.80015
[6] Buhmann, M.D., Radial basis function: theory and implementations, (2003), Cambridge University Press Cambridge · Zbl 1038.41001
[7] Kansa, E.J., Multiquadrics—a scattered data approximation scheme with applications to computational fluid dynamics—II. solutions to parabolic, hyperbolic and elliptic partial differential equations, Comput math appl, 19, 147-161, (1990) · Zbl 0850.76048
[8] Šarler B, Vertnik R. Meshfree explicit local radial basis function collocation method for diffusion problems. Comput Math Appl, in print. · Zbl 1168.41003
[9] Vertnik R, Šarler B. Meshless local radial basis function collocation method for convective diffusive solid – liquid phase change problems. Int J Numer Methods Heat Fluid Flow, in print. · Zbl 1121.80014
[10] Kovačević, I.; Šarler, B., Solution of a phase-field model for dissolution of primary particles in binary aluminium alloys by an r-adaptive mesh-free method, Mater sci eng A, 413-414, 423-428, (2005)
[11] Fic, A.; Nowak, A.J.; Białecki, R., Heat transfer analysis of the continuous casting process by the front tracking BEM, Eng anal boundary elements, 24, 215-223, (2000) · Zbl 0942.80002
[12] Šarler, B.; Mencinger, J., Solution of temperature field in DC cast aluminium alloy billet by the dual reciprocity boundary element method, Int J numer methods heat fluid flow, 9, 267-297, (1999) · Zbl 0962.76567
[13] Šarler, B.; Perko, J., DRBEM solution of temperatures and velocities in DC cast aluminium slabs, (), 357-369
[14] Šarler, B.; Kovačević, I.; Chen, C.S., A mesh-free solution of temperature in direct-chill cast slabs and billets, (), 271-280
[15] Vertnik, R.; Šarler, B.; Perko, J., Solution of temperature field in DC cast aluminium alloy billet by the diffuse approximate method, Mater technol, 38, 257-261, (2004)
[16] Šarler, B.; Vertnik, R.; Perko, J., Application of diffuse approximate method in convective – diffusive solidification problems, Comput mater continua, 2, 77-83, (2005) · Zbl 1160.76383
[17] Mencinger J. Calculation of transient temperature field during semicontinuous casting of aluminium. In: Škerget L, Marn J, editors. Proceedings Kuhljevi dnevi ‘02, Ribno pri Bledu, September 26-27, 2002, Slovenian Society for Mechanics, Ljubljana, 2002, p. 81-8.
[18] Roache, P.J., Verification and validation in computational science and engineering, (1998), Hermosa Albuquerque
[19] Divo E, Kassab AJ. An efficient localized RBF meshless method applied to fluid flow and conjugate heat transfer. ASME J Heat Transfer, in print.
[20] Divo E, Kassab AJ. Modeling of convective and conjugate heat transfer by a third order localized RBF meshless collocation method. In: Nowak AJ, Białecki RA, Weçel G, editors. Eurotherm 82: Numerical heat transfer, September 13-16, 2005, Gliwice-Krakow, Poland, Zaklad Graficzny Politehniki Śląskiej, Gliwice, 2005, p. 357-66.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.