A finite-volume/Newton method for a two-phase heat flow problem using primitive variables and collocated grids

A finite-volume/Newton's method is presented for solving the incompressible heat flow problem in an inclined enclosure with an unknown melt/solid interface using primitive variables and collocated grids. The unknown melt/solid interface is solved simultaneously with all of the field variables by imposing the weighted melting-point isotherm. In the finite-volume formulation of the continuity equation, a modified momentum interpolation scheme is adopted to enhance velocity/pressure coupling. During Newton's iterations, the ILU (0) preconditioned GMRES matrix solver is applied to solve the linear system, where the sparse Jacobian matrix is estimated by finite differences. Nearly quadratic convergence of the method is observed. The robustness of the method is further enhanced with the implementation of the pseudo-arclength continuation. The effects of the Rayleigh number and gravity orientation on flow patterns and the interface are demonstrated. Bifurcation diagrams are also constructed to illustrate flow transition and multiple steady states. 42 refs., 13 figs., 5 tabs