Comparison of high-order accurate schemes for solving the nonlinear viscous burgers equation

In this paper, a comparison between higher order schemes has been performed in terms of numerical accuracy. Four finite difference schemes, the explicit fourth-order compact Pade scheme, the implicit fourth-order Pade scheme, flowfield dependent variation (FDV) method and high order compact flowfie ld dependent variation (HOC-FDV) scheme are tes ted. The FDV scheme is used for time disc retization and the fourth-order compact Pade scheme is used for spatial derivatives. The solution procedures consist of a number of tri-diagonal matrix operations and produce an efficient solver. The comparisons are performed using one dimensional nonlinear viscous Burgers equation to demonstrate the accuracy and the convergence characteristics of the high-resolution schemes. The numerical results show that HOC-FDV is highly accurate in comparison with analytical and with other higher order schemes