Résumé
The partial differential equations that describe two-phase flows in pipes are highly non-linear due to the strong dependence between pressure and wave celerity. The possible appearance of shock waves makes Godunov schemes very attractive, for they can handle such discontinuities automatically. Fluxes at the cell interfaces are computed by solving a Riemann problem. To do so, an approximate state, non-iterative solver designed in a previous study is used. The treatment of boundary conditions uses an iterative procedure. Existing approximations for the sound celerity under the isothermal assumption are generalized to other situations. A comparison between the isothermal and the adiabatic assumptions shows that such assumptions play an important role in the behaviour of the solution. Finally, numerical results obtained using the first-order Godunov method on representative test cases are presented and the need for higher-order reconstruction techniques is acknowledged.