Discretization methods for approximating the Partial Differential Equations (PDEs):
- Finite Difference (FD)
- Finite Elements (FE)
- 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