Numerical Solution of Phase Change Problems: An Eulerian-Lagrangian Approach

The problem of solid-liquid phase change is tackled from art Eulerian-Lagrangian kinematic point of view. The theory is first presented for a one-dimensional space and then generalized to a two-dimensional space. The irregular shape of the phase front is treated with generalized curvilinear coordinates. A feature of the resulting finite-difference scheme is that the current field values and front position are solved simultaneously. As a result, numerical solutions show excellent agreement with the analytical solution for the one-dimensional melting problem and with experimental data for a two-dimensional buoyancy-driven phase-change problem.