Preconditioned Newton-Method for Computing Supersonic and Hypersonic Nonequilibrium Flows

Preconditioned Krylov subspace methods and a Jacobi line relaxation method are tested in an implicit scheme to solve the three-dimensional Navier-Stokes equations for nonequilibrium supersonic and hypersonic flows. Special attention has been paid to the development of vectorizable preconditioners. In the numerical scheme the Jacobian of the fluxes is computed using the first-order inviscid fluxes and a thin shear-layer approximation of the viscous fluxes. In the second part, the influence of these approximations of the Jacobian is examined. Starting from a matrix-free implicit method, the scheme is developed to an exact Newton method without approximations in the Jacobian.