Parallel solution of multiphase transport problem

Abstract

In this paper we tackle solidification of a binary alloy that is modelled by fluid flow in free and porous media, heat and mass transport, phase change modelled by eutectic phase diagram, and microscopic species transport. The model is formulated through four tightly coupled Partial Differential Equations describing conservation laws, namely Navier Stokes equation, Darcy equation, and two convective-diffusive equations for describing heat and solute transport. The PDEs are supported by constitutive relations, contributing additional information regarding the diffusion transport, stresses, interfacial forces and buoyancy forces. The solution of the problem at hand is addressed from computational point of view, i.e. the numerical solution procedure is formulated in a way suitable for parallel execution, especially for multi and many core architectures. Results are presented in terms of macrosegregation maps, and parallel efficiency analyses.