Fluid-structure interaction: Extended-FEM approach to solidification

The extended finite element method (XFEM) and the level set method (LSM) are applied to simulate the solidification phenomenon and the behavior of the liquid-solid phase transition. The temperature-based energy equation is loosely-coupled with the incompressible Navier-Stokes (INS) equations and solved by XFEM using the Stefan condition to express the energy conservation law for phase change. The INS equations are additionally supplemented with the Boussinesq approximation for the buoyancy force that drives the ensuing melt flow. The temperature, pressure, and fluid velocity are discontinuous at the interface, and the LSM implicitly captures its location. A modified abs-enrichment scheme (where abs stands for the absolute value function) is used for the weakly-discontinuous temperature field, and a sign-enrichment scheme is employed for the strongly-discontinuous pressure field. The penalty method imposes the interface temperature and velocity and allows for fluid-structure interactions. The numerical model is verified with several benchmark tests: 1D solidification, infinite corner solidification, Frank sphere, flow over a cylinder, as well as tin melting with non-constant density. Once the simulation results have been shown to be in good agreement with analytical solutions and results obtained with other methods, the present methodology is applied to a melting ice cylinder at a high Reynolds number. •XFEM and the level set method simulate the behavior of liquid-solid phase transition.•A modified abs-enrichment scheme is used for weakly-discontinuous temperature field.•Penalty method imposes the interface temperature and velocity and allows for FSI.•Level sets are advected using a second-order Taylor-Galerkin VMS stabilization method.•Validated methodology is applied to a melting ice cylinder at a high Reynolds number.