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Using the boundary-fitted coordinate system, we calculate the unsteady solidification problem.
Numerical results are generated for a specific melting and solidification problem.
Our work proves that the application of the precipitation modeling framework for the solidification problem is successful.
This simple numerical solution method can be easily applied to any arbitrary shape and the unsteady solidification problem.
A three-dimensional melting and solidification problem is solved in which a second layer of solid is added at variable rates.
A 2D axisymmetric formulation for the solution of a directional solidification problem using an inverse finite-element method (IFEM) is presented.
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Convergence under grid refinement is demonstrated for dendritic solidification problems.
Thus, our extended formulation encompasses a wider class of solidification problems than previous IFEM methods.
The resulting meshless front tracking method is tested on sample solidification problems in one and two dimensions.
In this framework, the enthalpy-porosity model for multiphase flow in melting and solidification problems can be employed.
Error analysis and grid refinement studies are performed for test problems involving the diffusion and convection diffusion equations, and for stable solidification problems.
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