NUMERICAL APPROXIMATION OF RIEMANN PROBLEMS FOR A LIQUID–GAS TWO-PHASE ISENTROPIC FLOW MODEL: COMPUTATIONAL ASSESSMENT OF THREE EXPLICIT NUMERICAL SCHEMES

Abstract

This paper revisits the numerical solution of Riemann problems for a one-dimensional liquid-gas two-phase isentropic flow model. The main purpose is to provide a corrected and reproducible comparison of three classical finite-volume schemes: Lax-Friedrichs, two-step Lax-Wendroff, and FORCE. The numerical solutions are compared with a model-specific Riemann reference, using the same mesh, CFL condition, boundary treatment, and admissibility checks for all three methods. For the baseline parameters k = 0.6 and γ = 0.8, the first test problem contains two rarefaction waves separated by a contact discontinuity, whereas the second contains two shocks with a contact in between. At N = 400, Lax-Wendroff gives the smallest integral errors in both test problems, although small oscillations appear near discontinuities. Lax-Friedrichs is more diffusive, while FORCE gives intermediate errors and wave resolution. A separate smooth translating-contact test gives observed convergence orders of 0.991, 2.000, and 0.997 for Lax-Friedrichs, Lax-Wendroff, and FORCE, respectively. Additional tests involving left-moving waves, mixed wave patterns, and positive low-density states were also carried out. Across the benchmark calculations, no non-positive accepted phase masses were observed, and the conservation residual remained close to machine precision. These results provide a verified numerical baseline for further work on higher-resolution methods for this reduced two-phase model.