Call for contributions to a numerical benchmark problem for 2D columnar solidiﬁcation of binary alloys M. Bellet a , H. Combeau b , Y. Fautrelle c , D. Gobin d, * , M. Rady e , E. Arquis e , O. Budenkova c , B. Dussoubs b , Y. Duterrail c , A. Kumar b , C.A. Gandin a , B. Goyeau d , S. Mosbah a , M. Zalo  znik b a CEMEF, CNRS, Ecole des Mines de Paris-ParisTech, BP 207, 06904 Sophia Antipolis Cedex, France b Institut Jean Lamour, CNRS, Nancy-Universite´, UPV-Metz, 54042 Nancy Cedex, France c SIMAP, CNRS, INPG, Universite´ Joseph Fourier, 38402 St Martin d’He`res Cedex, France d FAST, CNRS, Universite´ Pierre et Marie Curie, 91405 Orsay Cedex, France e TREFLE, CNRS, Universite´ de Bordeaux, Arts et Me´tiers ParisTech, ENSCPB, 33607 Pessac Cedex, France article info Article history: Available online 26 August 2009 Keywords: Benchmark Solidiﬁcation Columnar growth Binary mixture Thermosolutal convection abstract This call describes a numerical comparison exercise for the simulation of ingot solidiﬁcation of binary metallic alloys. Two main steps are proposed, which may be treated independently: 1. The simulation of the full solidiﬁcation process. First a speciﬁed ‘minimal’ solidiﬁcation model is used and the contributors are provided with the corresponding sets of equations. The objective is to verify the agreement of the numerical solutions obtained by different contributors. Then different physical solidiﬁcation models may be compared to check the features that allow for the best possible prediction of the physical phenomena. 2. A separate preliminary exercise is also proposed to the contributors, only concerned with the convective problem in the absence of solidiﬁcation, in conditions close to those met in solidiﬁcation processes. Two problems are considered for the case of laminar natural convection: transient thermal convection for a pure liquid metal with a Prandtl number on the order of 10 2 , and double-diffusive convection in an enclosure for a liquid binary metallic mixture with a Prandtl number on the order of 10 2 and a Lewis number on the order of 10 4 . Ó 2009 Elsevier Masson SAS. All rights reserved. This call for contribution aims at proposing a set of comparison exercises for the sake of veriﬁcation and validation of mathematical models and numerical codes concerned with ingot solidiﬁcation of binary metallic alloys. This exercise consists of two main steps, which may be treated independently. 1. The main phase concerns the simulation of the full solidiﬁca- tion process, in two different stages:  A stage of veriﬁcation [4]: comparison of the numerical results obtained by different codes using a speciﬁed «minimal» solid- iﬁcation model resulting from the volume averaging technique. The contributors are provided with the corresponding sets of equations and the objective is to verify the degree of agreement of the numerical solutions of the contributors.  A stage of validation: comparison of the different physical solidiﬁcation models of the contributors. The objective of this stage is the best possible prediction of the physical phenomena. This exercise is closely linked to experiments that are being developed within the present project and it will be treated later. 2. A separate preliminary exercise is also proposed to the contributors, which deals only with the convective aspect of the problem in the absence of solidiﬁcation, in conditions close to those met in solidiﬁcation processes. Two problems are considered for the case of laminar natural convection:  Transient thermal convection for a pure liquid metal with a Prandtl number on the order of 10 2 , referring to the initial thermal transient period in a solidiﬁcation process with initial liquid superheat,  Double-diffusive convection in an enclosure for a liquid binary metallic mixture with a Prandtl number on the order of 10 2 and a Lewis number on the order of 10 4 , to simulate ther- mo-solutal convective ﬂows in the bulk liquid zone during solidiﬁcation. The main features of the comparison exercise are described hereafter, but the complete details (problem description, system of equations, parameters, initial and boundary conditions, thermo- physical properties and format of outputs) may be found on the * Corresponding author. E-mail address: gobin@fast.u-psud.fr (D. Gobin). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts 1290-0729/$ – see front matter Ó 2009 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2009.07.024 International Journal of Thermal Sciences 48 (2009) 2013–2016