We perform simulations of the interplanetary coronal mass ejections relating to the magnetic storm on 17 March 2015. A hierarchical mesh structure is used, which is controlled by an adaptive mesh refinement technique, with fine-scale cells where it matters, the structure of the running shock waves of the coronal mass ejections and co-rotating interactive regions. The initial and the inner-boundary conditions are derived from another simulation, which uses a split dodecahedron grid. The resulting shock-wave with the models adjusted to the observed ejection speed on the sky plane show delays by 20% in the arrival time at the Earth from the observed data. By contrast, the model adjusted to the observed arrival time at the Earth needs the ejection speed 30% higher than that in the above models.