Preconditioning of the Euler and Navier–Stokes equations in low-velocity flow simulation on unstructured grids

Low-velocity inviscid and viscous flows are simulated using the compressible Euler and Navier–Stokes equations with finite-volume discretizations on unstructured grids. Block preconditioning is used to speed up the convergence of the iterative process. The structure of the preconditioning matrix for schemes of various orders is discussed, and a method for taking into account boundary conditions is described. The capabilities of the approach are demonstrated by computing the low-velocity inviscid flow over an airfoil.