Development of a 2-D algorithm to simulate convection and phase transition efficiently

We develop a Jacobian-Free Newton–Krylov (JFNK) method for the solution of a two-dimensional convection phase change model using the incompressible Navier–Stokes equation set and enthalpy as the energy conservation variable. The SIMPLE algorithm acts as a physics-based preconditioner to JFNK. This combined algorithm is compared to solutions using SIMPLE as the main solver. Algorithm performance is assessed for two benchmark problems of phase change convection of a pure material, one melting and one freezing. The JFNK-SIMPLE method is shown to be more efficient per time step and more robust at larger time steps. Overall CPU savings of more than an order of magnitude are realized.