Parallelization of phase-field model for phase transformation problems in a flow field

The chapter implements parallelization of a phase-field model for solidification in a flow field using OpenMP and MPI to compare their parallel performance. Phase-field models have been applied for decades to simulation of phase transformation problems. Initially most researchers focused on pure substances in the 2-D case and did not consider convection induced by a velocity field or small-scale fluctuations. The chapter presents 2-D phase-field and Navier-Stokes equations with prescribed boundary and initial conditions corresponding to lid-driven-cavity flow. Douglas & Gunn time-splitting is applied to the discrete governing equations, and a projection method is employed to solve the momentum equations. The approach taken to parallelize the algorithm is described, and results are presented for both OpenMP and MPI, with MPI being decidedly superior.