exercices_cimlib/Exercices_Binaire_SolidifDirige/FrontTracking_1D

Same methodology as the one presented in the section 3 of paper https://www.sciencedirect.com/science/article/pii/S1359645400000707 with the Landau transforms.
matlab code
Numerical informations:

• 1D
• Implementation using the Finite difference method
• Thermic equation expressed using the implicit method
• Resolution of the matrix equation using the tridiagonal matric algorithm

Hypotheses: Same density for all phases

Velocity of the interface of the mushy domain (dendritic front): v_d=2.9e^-6ΔT^2.7 [m.s^-1].
Velocity of the interface of the fully solid domain (eutectic front): v_eut=3e^-5ΔT² [m.s^-1].

Outputs

Outputs on the temperature field on sensors

Outputs on the solid fraction field on sensors

Interfaces velocities have a generic expression v_int=AΔTⁿ. To decrease interfaces undercoolings, we increase coefficients A.
Velocity of the interface of the mushy domain (dendritic front): v_d=2.9e^-6ΔT^2.7 [m.s^-1].
Velocity of the interface of the fully solid domain (eutectic front): v_eut=3e^-5ΔT² [m.s^-1].

Outputs

Outputs on the temperature field on sensors

Outputs on the solid fraction field on sensors