High order ADI method for solving unsteady convection–diffusion problems

We propose a high order alternating direction implicit (ADI) solution method for solving unsteady convection–diffusion problems. The method is fourth order in space and second order in time. It permits multiple use of the one-dimensional tridiagonal algorithm with a considerable saving in computing time, and produces a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable for 2D problems. Numerical experiments are conducted to test its high accuracy and to compare it with the standard second-order Peaceman–Rachford ADI method and the spatial third-order compact scheme of Noye and Tan.