| A three-dimensional Navier-Stokes flow solver for structured grids is developed using a Newton-Krylov algorithm. Turbulence is modelled using the Spalart-Allmaras one-equation model. Spatial derivatives are approximated using centered-differences with second and fourth-difference dissipation. The equations are transformed into curvilinear coordinates and linearized using Newton's method. The reverse Cuthill-McKee method is applied to reorder the equations, and a preconditioner is formed based on an incomplete lower-upper factorization of a first-order approximate Jacobian. The linear system at each Newton iteration is then solved using a generalized minimal residual method. An approximate-Newton startup phase is followed by a Jacobian-free inexact-Newton phase.;Various aspects of the code are studied in this work. A parametric study attempting to optimize the performance of the code was performed on the following variables: ILU fill-levels, inexact-Newton convergence parameter, residual reduction tolerance parameter for switching to the inexact-Newton phase, and a preconditioning parameter used in the formation of the approximate Jacobian. The solver was validated by comparing with a well-validated flow solver, OPTIMA2D, and a grid convergence study is presented for laminar and turbulent flows about the ONERA M6 wing. |
