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H-ALLEGRO is a finite difference code that solves the unsteady compressible reacting Navier-Stokes equations system on structured cartesian meshes.

It makes use of a specific "hybrid" arrangement of variables on staggered-like grids with compact high-order finite difference schemes: differentiation and interpolation rules needed to solve the Navier–Stokes equations can be Implicit (Padé) or explicit hybrid FD schemes of 6th order. The main objectives are both to improve numerical accuracy/robustness and the numerical flow solution at the boundaries.

H-ALLEGRO is a research code, mainly designed to perform DNS or highly resolved LES on thousands of processors. The adopted grid topology and procedure can be seen as an ‘hybrid colocated/staggered’ strategy.

Acoustic boundary condition treatments are then applied in a natural manner, despite the staggered character of the grid. Close to the boundaries, since the size of the stencil decreases, the scheme order is successively lowered to centred 4th order and then one-sided 3rd order.

Main features

  • High Resolution Finite difference discretization of Navier-Stokes equations
  • Compact Explicit 6th order or Implicit Padé difference schemes
  • Third-order Runge–Kutta minimal-storage integration scheme (that only requires two memory locations for each conserved property)
  • 3DNSCBC/TOM (for transverse outflow) and NSWIL (for reflecting no-slip walls) acoustic boundary treatment


The code has been designed to work on thousands of processors via the MPI protocol. Parallel communications and I/O have been optimized to achieve this goal.


A few pictures of HALLEGRO computations are available in this gallery.