NONLINEAR IMPLICIT SCHEME USING NEWTONS METHOD FOR THE NUMERICAL-SOLUTION OF THE NAVIER-STOKES EQUATIONS

We study a family of upwind numerical fluxes for the Euler equations, the so-called extrapolated fluxes, depending on a parameter k. The mai n dispersive and dissipative terms of the truncation error are present ed as functions of k for the steady state scheme. A numerical flux for the Navier-Stokes equations is defined by adding a centred viscous fl ux to the extrapolated flux. Unless the implicit operator is factored, an unconditionally stable scheme is obtained when associating such a flux to a classical implicit stage for a scalar equation. For unsteady flow, we introduce two schemes with Newton algorithms for nonlinear e quations. Accuracy, dissipative and dispersive behaviour are discussed according to the number of iterative-steps. Steady and unsteady two-d imensional flows in a compressor stage and around a bump in a channel are computed. The present results are compared with experimental data and computational results obtained with a centred scheme with artifici al viscosity and Runge-Kutta time stepping. (C) Elsevier, Paris.