A new family of (5,5)CC-4OC schemes applicable for unsteady Navier-Stokes equations
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes which are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter are then applied to unsteady Navier-Stokes system. The proposed schemes, where transport variable and its first derivatives are carried as the unknowns, combine virtues of compact discretization and Pade scheme for spatial derivative. These schemes which are based on a five point stencil with constant coefficients, named as "(5,5) Constant Coefficient 4th Order Compact'' [(5,5)CC-4OC], give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods. These schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable. They efficiently capture both transient and steady solutions of linear and nonlinear convection-diffusion equations with Dirichlet as well as Neumann boundary conditions. Subsequently the proposed schemes are applied to problems governed by the incompressible Navier-Stokes equations. The results obtained are in excellent agreement with analytical and available numerical results in all cases, establishing efficiency and accuracy of the proposed schemes. (C) 2013 Elsevier Inc. All rights reserved.
navier-stokes equations unsteady convection-diffusion equation high order compact scheme