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 performed 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.