A projection scheme for phase change problems with convection
Mireille Haddad, Youssef Belhamadia, Jean Deteix, Driss Yakoubi
Abstract
Numerical modeling of phase change problems with convection is known to be computationally expensive. The main challenge comes from the coupling between Navier–Stokes and heat energy equations. In this paper, we develop a new scheme for phase change problems based on a projection method. The proposed method reduces the size of the system by splitting the temperature, the velocity, and the pressure fields while preserving the accuracy of the simulations. A single-domain approach using a variant of the enthalpy-porosity formulation is employed. Incompressible Navier–Stokes problem with Boussinesq approximation for thermal effects in solid and liquid regions is considered. We regularize the discontinuous variables such as latent heat and material properties by a continuous and differentiable hyperbolic tangent function. The robustness and effectiveness of the proposed scheme are illustrated by comparing the numerical results with numerical and experimental benchmark.