Numerical modeling of convection-diffusion phase change problems

A numerical methodology is presented for the modeling of convection-diffusion controlled mushy region change problems. An efficient and accurate non-staggered control volume method, based on the momentum interpolation practice and on a high-order convection differencing scheme, is proposed for the solution of the continuum model equation. Suitable numerical techniques are implemented to overcome the numerical instability problems resulting from the strong coupling between the equations of the model. Special attention is given on the efficient treatment of the latent head evolution in the energy equation. A new numerical technique is developed which accounts for the dependence of the latent heat on the variation of temperature and concentration fields. The proposed method is applied on two phase change problems. Satisfactory agreement with previously published results is observed.