Résumé
Godunov-type algorithms are very attractive for the numerical solution of discontinuous flows. The reconstruction of the profile inside the cells is crucial to scheme performance. The non-linear generalization of the discontinuous profile method (DPM) presented here for the modelling of two-phase flow in pipes uses a discontinuous reconstruction in order to capture shocks more efficiently than schemes using continuous functions. The reconstructed profile is used to define the Riemann problem at cell interfaces by averaging of the components of the variable in the base of eigenvectors over their domain of dependence. Intercell fluxes are computed by solving the Riemann problem with an approximate-state solver. The adapted treatment of boundary conditions is essential to ensure the quality of the computational results and a specific procedure using virtual cells at both extremities of the computational domain is required. Internal boundary conditions can be treated in the same way as external ones. Application of the DPM to test cases is shown to improve the quality of computational results significantly.