In a fighter jet flight, a rocket launch, or even in solar winds, fluid particles can reach sufficiently high velocities that density is no longer constant within the flow. Such compressible flows exhibit features unknown to incompressible flows, such as rarefaction and shock waves. These shock waves are regions where the density changes so quickly that it becomes discontinuous, along with the velocity and pressure. They make the numerical simulations of such flows challenging as their position is not known a priori, and can in general move through the domain. These discontinuities are handled by two families of methods. On one hand, shock capturing methods do not apply special treatment to take care of the shocks, but rather diffuse it across a couple of elements. This often requires a large amount of elements, anisotropic meshes and frequent remeshing in order to maintain accuracy. On the other hand, front tracking methods follow the shock by explicitly representing its geometry within the mesh. Current implementations can, however, not handle complex changes in topology without remeshing. In this work, still in development, we propose a new front-tracking method to simulate shock waves in compressible flows at low computational cost. It is based on the eXtreme Mesh deformation approach (X-Mesh) that allows for large deformations of the mesh without changing its topology. It introduces the idea of front relaying, allowing the front to move from node to node through the mesh without remeshing.