Cell-centered finite volume solution of the two-dimensional Navier-Stokes equations

Abstract

Cell-centered finite volume method with multistage time-stepping is successfully applied to two-dimensional mass-weighted, time-averaged Navier-Stokes equations for the computation of viscous flows. In the cell-centered scheme, flow quantities are associated with the center of a cell. Convective fluxes at the cell faces are evaluated by means of upwind Roe Flux Differencing Scheme (Roe FDS) with Monotone Upwind Schemes for Scalar Conservation Laws (MUSCL) approach. Green’s theorem is employed for evaluation of gradients in computation of viscous fluxes. Five stage hybrid time-stepping scheme is implemented for integration to steady state. Convergence is accelerated by utilizing local time stepping and residual smoothing. The accuracy of the present Navier-Stokes solver is verified by comparing flat-plate laminar boundary-layer solutions with theoretical solutions of Blasius and by comparing laminar airfoil solutions with those available in literature. Convergence down to machine zero attained in the computations indicates a good sign for the efficiency of the present solver. Turbulence closure for Reynolds stresses is obtained using two-layer algebraic eddy viscosity model of Baldwin and Lomax. Computed results for turbulent flows are validated with available experimental results.