Fourth Order Compact Formulation of Navier-Stokes Equations and Driven Cavity Flow at High Reynolds Numbers

Abstract

A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can also be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601x601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.

References in corpus (1)

• Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers

Cited by in corpus (7)

• Discussions on Driven Cavity Flow
• Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Skewed Cavity
• Fine Grid Numerical Solutions of Triangular Cavity Flow
• Multiple-distribution-function lattice Boltzmann method for convection-diffusion-system based incompressible Navier-Stokes equations
• Comparison of Wide and Compact Fourth Order Formulations of the Navier-Stokes Equations
• Time dependent simulation of the Driven Lid Cavity at High Reynolds Number
• Numerical Performance of Compact Fourth Order Formulation of the Navier-Stokes Equations