The alternating group explicit (AGE) iterative method for solving a Ladyzhenskaya model for stationary incompressible viscous flow

Abstract

In this paper, the alternating group explicit (AGE) iterative method is applied to a nonlinear fourth-order PDE describing the flow of an incompressible fluid. This equation is a Ladyzhenskaya equation. The AGE method is shown to be extremely powerful and flexible and affords its users many advantages. Computational results are obtained to demonstrate the applicability of the method on some problems with known solutions. This paper demonstrates that the AGE method can be implemented to approximate solutions efficiently to the Navier–Stokes equations and the Ladyzhenskaya equations. Problems with a known solution are considered to test the method and to compare the computed results with the exact values. Streamfunction contours and some plots are displayed showing the main features of the solution.

Keywords:

• Alternating Group Explicit (AGE) method
• Ladyzhenskaya equations
• Navier–Stokes equations

Acknowledgements

This research work was undertaken while the first author was on sabbatical leave from King Fahd University of Petroleum and Minerals. The first author wishes to express his gratitude to the University for providing the financial support while on research attachment at Univesiti Tenaga Nasional, Malaysia, where some of this work was done. Also he would like to thank M.S. Sahimi for introducing him to the subject.

Additional information

Notes on contributors

M. S. Sahimi

Email: [email protected]