Numerical method for heat transfer, fluid flow, and stress analysis in phase-change problems

This work presents a finite-volume method for simultaneous prediction of physical phenomena occurring during a solid/liquid phase change, including buoyancy-driven flow in the liquid, deformation and stresses in the solid, and heat transfer in both the liquid and solid parts of the solution domain. The liquid is treated as a Newtonian incompressible fluid and it is assumed that the solid behaves as a thermoelastic body, although other constitutive equations for liquid and/or solid could easily be incorporated. The method solves integral equations of mass, momentum, and energy balance discretized on numerical meshes consisting of cells of arbitrary polyhedral shape. The method is validated by comparing numerical results with analytical solutions and available measurement data.