Finite-difference method (FDM) is a discretization method that uses Taylor series to convert each differential term in a partial differential equation (PDE) to a linear algebraic equation (LAE), called finite-difference equation (FDE). FDM is algorithmically simple, efficient, and accurate; however, the FDM was found better suited for the simple as compared to complex geometry in a computational fluid dynamics (CFD) problem. This chapter starts with a discussion of various methods for the continuum modeling of the moving interfaces. It presents both CFD development and application aspects of the immersed boundary (IB) method. The chapter discusses two well-known phase-change problems, namely boiling and solidification. The numerical solution depends on the number of grid points for the spatial accuracy and on the magnitude of the time step for the temporal accuracy. The numerical solution results in a CFD software as a product, which is analogous to a virtual video camera.