A high-order finite difference discretization strategy based on extrapolation for convection diffusion equations

We propose a new high-order finite difference discretization strategy, which is based on the Richardson extrapolation technique and an operator interpolation scheme, to solve convection diffusion equations. For a particular implementation, we solve a fine grid equation and a coarse grid equation by using a fourth-order compact difference scheme. Then we combine the two approximate solutions and use the Richardson extrapolation to compute a sixth-order accuracy coarse grid solution. A sixth-order accuracy fine grid solution is obtained by interpolating the sixth-order coarse grid solution using an operator interpolation scheme. Numerical results are presented to demonstrate the accuracy and efficacy of the proposed finite difference discretization strategy, compared to the sixth-order combined compact difference (CCD) scheme, and the standard fourth-order compact difference (FOC) scheme.