•Algorithms to compute a three-phase flow model with immiscible phases.•Verification test cases of a three-phase flow model.•Simulation of Chauvin’s shock tube experiment.•Preliminary simulations of vapour explosion. This paper is devoted to the simulation of the three-phase flow model 20, in order to account for immiscible components. The whole model is first recalled, and the main properties of the closed set are given, with particular focus on the Riemann problem associated with the convective subset that contains non-conservative terms, and also on the relaxation process. The model is hyperbolic, far from resonance occurrence, and a physically relevant entropy inequality holds for smooth solutions of the whole system. Owing to the uniqueness of jump conditions, specific solutions of the one-dimensional Riemann problem can be built, and these are useful (and mandatory) for the verification procedure. The fractional step method proposed herein complies with the continuous entropy inequality, and implicit schemes that are considered to account for relaxation terms take their roots on the true relaxation process. Once verification tests have been achieved, focus is given on the simulation of the experimental setup 8, 9, in order to simulate a cloud of droplets that is hit by an incoming gas shock-wave. Finally, the study of a three-phase flow setup involving thermal effects is presented, it is based on the KROTOS experiment 25 which focuses on vapour explosion simulation.