A Coupled Level Set and Volume of Fluid (CISVOF) interface capturing method using a multi-dimensional advection algorithm for non-uniform grids has been developed for two phase flows with and without phase change for two-dimensional problems. A finite volume method with a collocated grid arrangement is used for solving the governing equations. The SIMPLE algorithm is used for velocity and pressure coupling. The piecewise linear interface calculation (PLIC) based geometrical reconstruction procedure and an Edge Matched Flux Polygon Advection (EMFPA) multi-dimensional algorithm have been implemented for the Volume of Fluid (VOF) method. For the Level Set (LS) advection equation, the convective terms are discretized using the second order accurate essentially non-oscillating (ENO) scheme. The proposed multi-dimensional advection of CLSVOF method requires interface reconstruction for the advection of VOF function and the Level Set function re-initialization only once compared to the requirement of twice interface reconstruction and Level Set re-initialization in the operator-splitting method for 2D problems. The performance of proposed CLSVOF method is evaluated for accurate mass conservation, surface tension force and interface mass transfer through various standard benchmark problems. The numerical study of two-dimensional saturated film boiling flow over a horizontal plane surface was carried out for different constant wall superheats in order to validate the implementation of boiling flow model. The present numerical results of boiling flows show better agreement with the experimental correlations. (C) 2014 Published by Elsevier Ltd.