Essentially, the strategy of CFD is to replace the continuous problem domain with a discrete domain using a grid domain with a discrete domain using a grid.
In a continuous domain, each flow variable is defined at every point in the domain. For instance, the velocity u in the continuous 1D domain shown below would be given as
u = u(x), 0 < x < 1 u u(x), 0 x 1
In the discrete domain, each flow variable is defined only at the grid points. So, in the discrete domain shown below, the velocity would be p, , y defined only at the N grid points.
ui= u(xi), i = 1, 2, . . . ,N
Let's keep things simple by using a 1D illustration (and using a finitedifference approach):