A fourth-order-accurate finite volume compact method for the incompressible Navier-Stokes solutions

This paper presents a finite volume fourth-order-accurate compact scheme for discretization of the incompressible Navier-Stokes equations in primitive variable formulation. The numerical method of integrating the Navier-Stokes equations comprises a compact finite volume formulation of the average convective and diffusive fluxes. The pressure-velocity coupling is achieved via the coupled solution of the resulting system of equations. The solution of the coupled set of equations is per formed with an implicit Newton-Krylov matrix-free method for stationary problems. For simulation of unsteady flows, a standard fourth-order Runge-Kutta method was used for temporal discretization and the velocity-pressure coupling was ensured at each stage also using the matrix-free method. Several incompressible viscous steady and unsteady flow problems have been computed to assess the robustness and accuracy of the proposed method. (C) 2001 Academic Press.