A strategy to build the next generation of fluid dynamics solvers able to fully benefit from high-performance computing is discussed. The procedure relies on a domain decomposition of unstructured meshes that is organized in two levels. The computing cells are first gathered at an elementary level in cell groups; at a second level, cell groups are dispatched over processors. Compared to the usual single-level domain decomposition, this double domain decomposition allows for easily optimizing the use of processor memory and therefore load balancing in both Eulerian and Lagrangian contexts. Specific communication procedures to handle faces, edges and nodes are associated to this double domain decomposition, which strongly reduce the computing cost; input–output times are optimized as well. In addition, any multi-level solution techniques, as deflated preconditioned conjugate gradient, are well-adapted to such mesh decomposition. This approach has been used to develop the YALES2 code, which also benefits from a non-degenerescent tessellation algorithm for tetrahedra to automatically generate high-resolution meshes on super-computers. To illustrate the capabilities of the YALES2 algorithmic, an aeronautical burner is fully simulated with a mesh of 2.6 billion cells, followed by a demonstration test over 21 billion cells.