Abstract
We propose and develop a new finite volume method for a one-pressure model of two-phase flows in one and two dimensional, where the first phase is vapor, which is compressible, and the second phase referred to as the liquid phase. This model has complex characteristic values, which poses a numerical difficulty. This scheme consists of a predictor stage and corrector stage. Numerical results are presented for two-phase flows model in one and two dimensions. It is found that the proposed finite volume scheme offers a robust and accurate approach for solving this model, and this scheme reveals to be robust and efficient for non-hyperbolic and non-conservative systems and our scheme does not need complicated Jacobian fields decomposition.