Parallelizable block diagonal preconditioners for the compressible Navier-Stokes equations (Q1913120)

We propose a new block diagonal preconditioner for solving the Navier-Stokes equations for compressible two-dimensional flows, using finite element methods on unstructured grids, and discuss the parallelization of this method. The core of the Navier-Stokes solver is the coupled solution of the nonlinear equations at each time step by a preconditioned nonlinear GMRES algorithm. Special attention is paid to the partitioning strategy, which is easily generalizable to three-dimensional problems. Numerical results are presented for several transonic and supersonic calculations around a NACA 0012 aerofoil.