Numerical solution of the incompressible Navier–Stokes equations with exponential type schemes

Abstract

A new exponential type finite-difference scheme of second-order accuracy for solving the unsteady incompressible Navier–Stokes equation is presented. The driven flow in a square cavity is used as the model problem. Numerical results for various Reynolds numbers are given, and are in good agreement with those presented by Ghia et al. (Ghia, U., Ghia, K.N. and Shin, C.T., 1982, High-Re solutions for incompressible flow using the Navier–Stokes equations and a multi-grid method. Journal of Computational Physics, 48, 387–411.).

Keywords:

• Exponential type
• Navier–Stokes equations
• Driven cavity
• Velocity profile

Acknowledgements

X.F.F. would like to thank Dr Yong-Bin Ge for helpful suggestions and encouragement. The project was jointly supported by the National Natural Science Foundation of China (Grant No. 19702008), the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P. R. China, and the Science Research Foundation of Ningxia University.