A sixth order exponential compact ADI scheme for solving three- dimensional unsteady state convection-diffusion equation

Abstract EN

In this paper, we derive a sixth order exponential compact finite difference scheme with alternating direction implicit (ADI) scheme for solving three-dimensional unsteady convection-diffusion equation.

This scheme is sixth order for space and second order for time.

The unconditionally stability of this new version of finite difference scheme is proved with respect to initial values.

Numerical experiments are introduced to test the accuracy of the sixth order compact finite difference.

And it has high accuracy compare with the fourth order Karaa scheme and exponential fourth order compact Mahdi scheme.