GEOMETRIC CONSERVATION LAW FOR FINITE VOLUME DISCRETIZATION OF STEFAN PROBLEM ON BOUNDARY-FITTED GRIDS

The conservative finite volume scheme for heat transfer problem in two-dimensional region with moving boundaries is presented. The two-phase Stefan problem is considered as an example. To track the moving interface between solid and liquid, the front-fixing technique is applied. The time varying physical domain is mapped to a fixed computational space with regular boundaries. Finite volume approximation of governing equations is constructed in computational domain on fixed rectangular grid. The geometric conservation law is incorporated into the numerical scheme. The Jacobian and the grid velocities of the control volume are evaluated to satisfy the discrete form of the Jacobian transport equation. This procedure guarantees the enforcing of space conservation law in the physical domain. The numerical scheme inherits the basic properties of the original differential problem.