Modeling binary alloy solidification by a random projection method

Abstract

This paper addresses the numerical modeling of the solidification of a binary alloy that obeys a liquidus-solidus phase diagram. In order to capture the moving melting front, we introduce a Lagrange projection scheme based on a random sampling projection. Using a finite volume formulation, we define accurate numerical fluxes for the temperature and concentration fields which guarantee the sharp treatment of the boundary conditions at the moving front, especially the jump of the concentration according to the liquidus-solidus diagram. We provide some numerical illustrations which assess the good behavior of the method: maximum principle, stability under CFL condition, numerical convergence toward self-similar solutions, ability to handle two melting fronts. KEYWORDS binary alloy, finite volume method, Lagrange projection scheme, random sampling projection, sharp model, solidification, Stefan problem 1 Numer Methods Partial Differential Eq. 2019;35:733-760. wileyonlinelibrary.com/journal/num

Explicit solutions related to the Rubinstein binary-alloy solidification problem with a heat flux or a convective condition at the fixed face

“…Therefore, we obtain (4) and (5). Similarly, considering the equalities ix-xii from (1), we deduce that…”

“…A study of binary-alloy problems can be seen in [2,5,8,12,16,17,24,25]. Recent works on the solidification of a binary alloy are [1,3,5,6,7,9,10,11,12,14,21,22,23,28].…”

“…A study of binary-alloy problems can be seen in [2,5,8,12,16,17,24,25]. Recent works on the solidification of a binary alloy are [1,3,5,6,7,9,10,11,12,14,21,22,23,28]. The heat flux condition (1.v) imposed at the fixed face was first considered in [18] for a two-phase Stefan problem for a semi-infinite homogeneous material.…”

Explicit solutions related to the Rubinstein binary‐alloy solidification problem with a heat flux or a convective condition at the fixed face

“…A study of binary-alloy problems can be seen in [5][6][7][8][9][10][11][12]. Recent works on the solidification of a binary alloy are [6,8,[13][14][15][16][17][18][19][20][21][22][23][24]. The heat flux condition (1.v) imposed at the fixed face was first considered in [25] for a two-phase Stefan problem for a semi-infinite homogeneous material.…”

“…A study of binary-alloy problems can be seen in [5][6][7][8][9][10][11][12]. Recent works on the solidification of a binary alloy are [6,8,[13][14][15][16][17][18][19][20][21][22][23][24].…”