A VMS Finite Element Formulation for the Numerical Simulation of Phase Change Problems with Variable Density
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The understanding of liquid-solid phase change problems is a critical step in applied engineering design in several industry areas. Because density changes affect the dynamics of the process, the mathematical model considered is formed by the density-variable Navier-Stokes coupled with a modified diffusion-convection type equation for energy conservation, including the latent heat required to produce the phase-change process. The mathematical model is solved by a numerical algorithm based on the Variational Multiscale finite element method introduced by Hughes in 1995. The proposed method perform a dynamic term-by-term stabilized formulation capable of solving thermally coupled incompressible flows using equal order interpolations and convective dominant scenenarios. Numerical simulations involving water freezing and alloy solidification are presented to demonstrate and compare with other numerical approaches the robustness and the efficiency of the proposed strategy.