FIRST, ENCOUNTER, CFD: The Samurai Way

My first encounter with CFD was with the beautiful RANS equation, in this blog I would be sharing few insights into it.
RANS term which stands for Reynolds Averaged Navier stokes equation.
The RANS includes 4 terms(speaking in terms of heat transfer):

1)The local time derivative

2)The diffusion term-> which is the divergence term of the temperature

3)The convection term->which is the divergence term of the scalar product of velocity and temperature

4)The additional source terms

The Navier stokes equation is analogous to Newton’s Second law of motion which states that the rate of change of momentum that is equal to the sum of the forces acting on it.
The Navier stokes equation is used to find the velocity of the fluid.
There are 2 ways about linear interpolation which could be used to solve CFD problems about heat transfer:

1)Central Difference Scheme: We calculate the difference in the temperature between the centroids of the adjacent cells.

2)Upward Difference Scheme: We calculate the difference in the temperature between the centroid and the adjacent cell faces.

The choice between the two schemes is dependant on another quantity which is called the Peclet number.
The Peclet number is defined as the ratio of a convective transfer of the quantity to the diffusive transfer of the quantity.
If the Peclet number is high we prefer going with the Upward difference scheme.
Though the upward difference scheme has a lower accuracy than the central difference scheme.
CFD is mainly used to understand the fluid-structure interaction.
The equations governing are mostly partial differential equations.
The key thing to notice is that whenever an element has meshed there are mainly 2 types of cells which are boundary cells and interior cells.
So whenever the flow moves from left to right the convection term is negative and the diffusive term on the left face is zero.
and vice -versa concerning the sign and zero terms when the flux is from right to left face.
The finite volume method is generally used to solve the CFD equations where the body is divided into several cells and the boundary cells act as a connecting link with one face attached to a support and the other face is connected to the face of the adjacent interior cell.
We can avail the solution by calculating the coefficients of the PDE and then the partial differential equation can be solved.
These were few aspects I learned with my first encounter with CFD
Hoping to share more encounters with everyone.