A high-order ADI method for parabolic problems with variable coefficients

Abstract

A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman–Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier–Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.

Keywords:

• high-order compact scheme
• ADI method
• 2D incompressible Navier–Stokes equations
• driven cavity flow

2000 AMS Subject Classification :

• 65M06

Acknowledgement

This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.