SUMMARYThis work aims at developing/combining numerical tools adapted to the simulation of the near field of highly underexpanded jets. An overview of the challenging numerical problems related to the complex shock/expansion structure encountered in these flows is given and an efficient and low-cost numerical strategy is proposed to overcome these, even on short computational domains. Based on common upwinding algorithms used on unstructured meshes in a mixed finite-volume/finite-element approach, it relies on an appropriate utilization of zonal anisotropic remeshing algorithms. This methodology is validated for the whole near field of cold air jets issuing from axisymmetric convergent nozzles and yielding various underexpansion ratios. In addition, the most usual corrections of the k-model used to take into account the compressibility effects on turbulence are precisely assessed.