Simulating convection-coupled phase-change in enthalpy form with mixed finite elements
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Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate this convection-coupled phase-change problem on a single computational domain. The arising system of governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton's method. Previously, the monolithic approach has relied on adaptive mesh refinement to regularize local nonlinearities at phase interfaces. This contribution instead separates mesh refinement from nonlinear problem regularization and provides a robust continuation procedure to obtain accurate solutions on uniform meshes. A flexible and extensible open source implementation is provided. The code is formally verified to accurately solve the governing equations and convergence rates are shown. Simulations are presented with comparison to two experimental data sets, one for the melting of octadecane and another for the freezing of water. Furthermore, the robust solution procedure admits detailed sensitivity studies with respect to key numerical parameters. For the case of freezing water, effective reduction of numerical errors from these key parameters is successfully demonstrated.
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