Geodesic
On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials
Applications of Mathematics, Tome 56 (2011) no. 1, pp. 117-136.

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We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the balance of the momentum of the system influences significantly the numerical solution and is necessary in order to get a better match with the experimental observations. Here an up-to-date list of the most meaningful mathematical models and numerical simulations of this test is discussed and the need is shown of an accurate revision of the numerical simulations of melting/solidification processes of pure materials (e.g. artificial crystal growth) produced in the last thirty years and not accounting for the solid phase mechanics.
DOI : 10.1007/s10492-011-0012-5
Classification : 35Q35, 35Q99, 35R37, 74S20, 76M20, 78M20, 80A22
Keywords: liquid/solid phase change; deformation; convection; numerical simulation; finite differences 
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     title = {On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials},
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Mansutti, Daniela; Bucchignani, Edoardo. On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials. Applications of Mathematics, Tome 56 (2011) no. 1, pp. 117-136. doi : 10.1007/s10492-011-0012-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0012-5/

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