This paper presents an algorithm for accurately solving the full two-dimensional governing equations, along with the interface conditions that govern laminar/laminar annular/stratified internal condensing flows. The simulation approach - which can be generalized to adiabatic and evaporating flows, a 3-D level-set technique, and so on - uses a sharp-interface model, separate liquid and vapor domain computational solutions with interface conditions embedded as boundary conditions, and a moving grid technique to locate the dynamic wavy interface (in amplitude and phase) by a method of characteristics solution of the interface tracking equation. The moving grid is spatially fixed for a defined number of instants, but changes when the current marker instant advances in time.