A cell-by-cell thermally driven mushy cell tracking algorithm for phase-change problems

A thermally driven mushy cell tracking algorithm for phase-change problems with a moving boundary is presented. The equation used to track the moving boundary is based on energy balance over the mushy cell and is applied to advance a moving front in a cell-by-cell manner. The efficacy of the tracking algorithm is demonstrated on specific problems solved using the finite volume method. An implicit scheme is adopted to ensure that the numerical solution is unconditionally stable in time. A preconditioned conjugated gradient (P-CG) solver is implemented to ensure that solutions converge in a finite number of iterations. Four benchmark cases are used to validate the algorithm including solidification in one dimensional space (two-region problem), melting of pure aluminum in two-dimensional (2D) space, solidification with periodic boundary conditions, and solidification of one-region problem. The results obtained show that the current algorithm is capable of converging to accurate solutions for moving fronts and the numerical predications are in excellent agreement with corresponding analytical solutions.