# On the Efficiency of the Iterative Techniques for Solving Incompressible Navier-Stokes Equations

## TL;DR

This paper compares various iterative methods for solving incompressible Navier-Stokes equations, highlighting the multigrid method's superior efficiency in terms of computational time and iteration count.

## Contribution

It provides a detailed numerical comparison of multiple iterative techniques, demonstrating the effectiveness of the multigrid method for these equations.

## Key findings

- Multigrid method outperforms other iterative methods in speed.
- Multigrid requires fewer iterations to converge.
- Jacobi and Gauss-Seidel are less efficient than multigrid.

## Abstract

It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible Navier-Stokes equations. The numerical approaches implemented in the solver include Jacobi, Gauss-Siedel, Successive Over Relaxation, Alternating Direct Implicit and Multigrid methods. The results reveal that multigrid method is the most powerful iterative method among all other methods investigated in terms of the computational time and the number of iterations.