The generation and propagation of waves in a viscous flow solver are indispensable part of naval computational fluid dynamic (CFD) applications. This paper presents numerical simulations of two-dimensional wave propagation in the framework of two-phase finite volume method (FVM) with different temporal discretization schemes. Implicit Euler, Crank-Nicolson (CN) and second-order backward temporal discretization schemes are compared by using viscous flow solver based on the open source library OpenFOAM. The combinations of each temporal discretization scheme and explicit limiter are used for the formulation of the Volume Of Fluid (VOF) field convection equation. A new formulation using the second-order backward temporal discretization scheme with explicit limiter are investigated. Two-dimensional periodic domains are considered to compare different time-stepping methods. Also, five different refinement levels of meshes are used to study the convergence properties of each method. The non-linear wave is generated with stream function wave theory using ‘foamStar’, which is a specialized OpenFOAM library package developed by Bureau Veritas in collaboration with École Centrale de Nantes.