Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
Boldrini, Jose Luiz
Dias Vaz, Cristina Lucia
Southwest Texas State University, Department of Mathematics
We study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.
Phase-field, Phase transitions, Solidification, Convection, Navier-Stokes equations
Boldrini, J. L., & Dias Vaz, C. L. (2003). Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions. <i>Electronic Journal of Differential Equations, 2003</i>(109), pp. 1-25.
Attribution 4.0 International