Moving boundary-moving mesh analysis of freezing process in water-saturated porous media using a combined transfinite interpolation and PDE mapping methods

This paper couples the grid generation algorithm with the heat transport equations and applies them to simulate the thermal behavior of freezing process in water-saturated porous media. Focus is placed on establishing a computationally efficient approach for solving moving boundary heat transfer problem, in two-dimensional structured grids, with specific application to an undirectional solidification problem. Preliminary grids are first generated by an algebraic method, based on a transfinite interpolation method, with subsequent refinement using a partial differential equation (PDE) mapping (parabolic grid generation) method. A preliminary case study indicates successful implementation of the numerical procedure. A two-dimensional solidification model is then validated against available analytical solution and experimental results and subsequently used as a tool for efficient computational prototyping. The results of the problem are in good agreement with available analytical solution and experimental results.