A detailed sharp interface level set method (SI-LSM) based CFD development methodology as well as its implementation and application to the various types of Stefan problem is not found and reported here. The methodology and code-validation are presented in-detail for heat and/or mass transfer induced Stefan flow, 2D Cartesian as well as axi-symmetric coordinate system and Dirichlet as well as jump boundary conditions at the interface. For the Dirichlet BC, a higher order extrapolation methodology is presented - for the computation of ghost fluid value across the interface. Whereas, for the jump BC, a generic finite volume method based discretized equation is proposed - consisting of additional source term and modification in diffusion coefficient for the control-volumes adjoining the interface. An excellent agreement between the present and published results are shown separately for Stefan flow problems induced by heat transfer (melting as well as solidification), mass transfer (isothermal evaporation) and heat as well as mass transfer (non-isothermal evaporation). Finally, a performance study is presented demonstrating a superior performance of the present sharp as compared to diffused interface level set method. The performance study is also presented for two different methods of computation of normal gradient across the interface, with regard to numerical oscillations in the results.The present work involving localized fluid flow and heat as well as mass transfer in the two-phase domain - will be extremely useful to CFD developer on multi-phase flow. (C) 2016 Elsevier Ltd. All rights reserved.