Two High Order Compact Difference Schemes For Solving Burgers Equations

The Burgers equations are simplified as the incompressible Navier-Stokes equation,and study of the numerical solution method for them are focused by many researchers.And finite difference method is one the most widely applicated methods for solving these equtions.So far,many high accurate schemes have been developed.However,many of them need to transform the nonlinear Burgers equations into linear equations,or the solving Burgers equations of derived schemes are system of nonlinear equations,and the iterative method is used to solve even the one dimensional Burgers equations.Very few schemes exist without using transformation or system arising from them are linear.Two two-level high order compact finite difference implicit schemes are proposed for solving the one dimensional Burgers equations.Where,derivative type high order compact finite difference scheme(DHOC)is constructed by using the four order compact difference formulas and the Taylor se-ries expansion method,and equation type high order compact difference scheme is obtained by using the error correction method.The local truncation error of two kinds of schemes is O(?2 + ?h2 + h4),i.e.two kinds of schemes are the fourth order accuracy for space when ? = O(h2).And the two kinds of schemes are all system of linear equations,which can be obtained by Thomas algorithm.At the same time,the stability of the two schemes are analyzed by using the Fourier analysis method.Next,the two high accurate compact finite difference schemes are extended to solving two dimensional and three di-mensional Burgers equations.Then,numerical experiments are conducted to verify the accuracy and the reliability of solving one,two and three dimensional Burgers equations.Then,for the one-dimensional,two-dimensional and three-dimensional Burgers equation,numerical experiments are conducted to verify the reliability and accuracy of the two schemes.The numerical results show that the numerical results of the two schemes are identical with the exact solution of problems.This fully show the accuracy and reliability of the methods in this paper.