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The solar wind is an ionized gas built mostly of hydrogen nuclei and energized electrons. These particles are constantly ejected by the Sun. During the period of high solar activity, the plasma ejections become more intense, and extreme events can occur, such as intense coronal mass ejections (CMEs) and solar flares, which can result in severe magnetic storms. The interaction between a super magnetosonic solar wind plasma and the Earth’s magnetosphere creates a bow shock that deflects and decelerates the plasma. During fast CMEs or high-speed streams, the bow shock is compressed and, in consequence, compresses the magnetopause. The study of the magnetopause location is of utmost importance since it protects the Earth and satellite equipment orbiting near space. With the magnetopause compression, the possibility of energized particles, mass, and momentum transfer into the inner magnetosphere may impact the Earth's plasma convection. This study has the goal to analyze the solar wind parameters and the response of the magnetopause during the severe geomagnetic storm of May 2024, by using a magnetohydrodynamic computational simulation (MHD) available on the CCMC-NASA website. In addition, we calculate the magnetopause location obtained by Shue et al., (1998) empirical model and compare those results with the magnetopause nose position given by the simulation. The Dst and Sym-H indices were analyzed to classify the storm phases, and the behavior of the magnetopause as a function of the storm phases was analyzed. Our work demonstrates that during the sudden impulse commencement and main phase of the geomagnetic storm, the most intense compression of the magnetopause occurs. Due to the arrival of the solar structures, the magnetopause gets closer to the Earth. A high degree of similarity was observed between the magnetopause position calculated by the simulation and the Shue empirical model, except for some discrepancies arising from the distinct calculation methods: namely, the Shue model relies on the interplanetary magnetic field (Bz) and the dynamic pressure (Pd), whereas the simulation is based on the peak of current density (J). The results obtained allowed the understanding of the scientific fundamentals of space weather, with an emphasis on learning about the processes resulting from the interaction between the solar wind and the Earth's magnetosphere during extreme events.