1. A method for determining flow conditions of steady and transient flows of a multiphase mixture in a pipe positioned with respect to terrain, comprising: providing a hydrodynamic model of a drift flow type and an integrated thermodynamic model for defining properties of constituents of the multiphase mixture and solving a set of equations of mass conservation, momentum conservation and energy transfer in the multiphase mixture including an effect of gravity resulting in slugging effects due to the terrain having an irregular geometry, the model being formed with the multiphase mixture considered to be substantially at equilibrium at all times and a composition of the multiphase mixture being variable all along the pipe, mass of each constituent of the multiphase mixture being defined by a mass conservation equation for each constituent of the multiphase mixture regardless of a phase state thereof and using a time explicit numerical scheme to separate resolution of the thermodynamic model and the hydrodynamic model; and using the model to determine characteristics of flow of the multiphase mixture in the pipe.