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A code is developed to simulate incompressible free surface flo ws using the Roeu0027s flux- difference splitting scheme. An interface of two fluids is considered as a moving contact discontinuity. The continuities of pressure and normal velocity across the interface are enforced by the conservation law in the integral sense. The fluxes are computed using the Roeu0027s flux-difference splitting scheme for two incompressible f luids. The interface can be identified based on the computed density distribution. However, no additional treatment is required along the interface during the whole computations. Complicated time evolution of the interface including topological change can be captured without any difficulties. The developed code is applied to simulate the Rayleigh-Taylor instability of two incompressible fluids in the density ratio of 7.2:1 and the broken dam problem of water-air. The present results are compared with other available results and good agre ements are achieved for the both cases. ※Keywords: Free surface(), Contact discontinuity( ), Rayleigh-Taylor instability(Rayleigh-Taylor ), Broken dam( ), Incompressible fluids( )

Numerical Simulation of Free Surface Flows Using the Roe's Flux-difference Splitting Scheme