# Computational Fluid Dynamics (CFD)

Navier-Stokes + Incompressible + Finite difference method

Discretization methods for approximating the Partial Differential Equations (PDEs):

1. Finite Difference (FD)
2. Finite Elements (FE)
3. Finite Volume (FV)

#### Finite Difference (FD)

Taylor’s polynomial

#### Incompressible 2D

3 equations , ,

We obtain by transposing the equation and we obtain the explicit form of the equation:

is obtained by multiplying the Navier Stokes equations by , then we sum them:

We have a Poisson equation:

An iterative method can solve this equation:

There are several algorithms that were designed to solve Poisson equation, it can be discretised as a tridiagonal block matrix:

• Thomas algorithm
• Successive overrelaxation
• Fast Furier transforms
• multigrid methods