Three-dimensional high-resolution compressible Navier-Stokes solver

Abstract EN

The implicit schemes provide considerable economy in terms of computer resources, compared to explicit ones; and thus are more appropriate for the investigation of unsteady flows where long CPU times are required.

The paper presents the development of a high-resolution scheme for solving the three-dimensional compressible Navier-Stokes equations in conjunction with a fully implicit-unfactored method.

The implicit-unfactored solution of the time-dependent equations is obtained via Newton-type sub-iterations, Ganss-Seidel relaxation and matrix preconditioning.

The scheme utilizes the low-Reynolds k-e turbulence model.

The high-order flux reconstruction is combined with a characteristic-based method.

It is a flux averaging procedure in which the flow variables and, subsequently the fluxes, are calculated at the cell faces by an upwind Godunov-type scheme.

The characteristic values at the cell faces are calculated by a five-point upwind extrapolation scheme accompanied by sensor functions to deteot shocks.

The implicit-unfactored solver is validated for subsonio and transonic flows around NACA 0012 airfoil.

The numerical results arc found to be in good agreement with the past experimental and numerical results.