A finite volume nodal point scheme for solving two dimensional Navier-Stokes equations

Abstract

A finite volume nodal point spatial discretization scheme for the computation of viscous fluxes in two dimensional Navier-Stokes equations has been presented here. The present scheme gives second order accurate first derivatives and at least first order accurate second derivatives even for stretched and skewed grid. It takes almost the same numerical efforts to solve full Navier-Stokes equations as that for using thin layer approximation. The scheme has been implemented to solve laminar viscous flows past NACA0012 aerofoil. To advance the solution in time a five stage Runge-Kutta scheme has been used. To accelerate the rate of convergence to steady state, local time stepping, residual averaging and enthalpy damping have been employed. Only a fourth order artificial dissipation has been used here for global stability of the solution. A comparative study of the results obtained by the present scheme for full Navier-Stokes equations and for thin layer approximation have been made with other numerical methods developed earlier.