A study of multigrid method to solve the incompressible Navier-Stokes equation

Abstract

Incompressible fluid in the square cavity which is governed by 2-Dimensional Navier-Stokes equation has been a popular example for testing and comparing numerical methods and there are already many numerical results about this subject. This paper deals with mathematical multigrid theory as well as implementation of multigrid methods to accelerate convergence speed and to reduce computational time of the square cavity problem. Some iterative algorithms including conjugate gradient method are tested and i give the numerical results with the primitive variable formulation of 2-Dimensional incompressible Navier-Stokes equation.