1.1. Computational fluid dynamics (Contd.)

So, we talked about grids so, there are actually 2 types of grids. One is a structured grid and the structured grid means the grids are regular and coherent structure to the mesh layer. These are the simplest the structured grid and they are generally uniform rectangular grid those are called the structured grids. So, the structured grids look like this one here. So, you see they have a uniform rectangular grid. So these all the small shapes are rectangular. Structured grids are not limited to rectangular grids only.

In computational fluid dynamics, the grids used to simulate fluid flow can be classified into two categories: structured and unstructured grids. Structured grids are organized in a regular pattern, often as uniform rectangular shapes. They are easy to work with because their orderly arrangement allows for simple calculations. However, structured grids can take on various shapes beyond rectangles, allowing for more flexibility in modeling complex geometries.

Imagine arranging books on a shelf. If you line them up neatly, all facing the same way, that's like a structured grid. But, if you randomly stack books of different sizes and orientations, that represents an unstructured grid—less orderly but potentially easier for fitting into irregular spaces.

The second one are the unstructured grids. So, the grid cell arrangement is irregular and has no symmetry pattern if you see in the last one, there was a symmetry pattern here. If you consider this one you see symmetry cause this and here it is completely symmetry this one in the unstructured grids, the cell arrangement is irregular and has no symmetric pattern something like this, so, see the triangles, these are off, no specific, same type.

Unstructured grids differ from structured grids in that their cell arrangements are highly irregular. This lack of symmetry allows for better modeling of complex geometries, like those found in natural environments or intricate mechanical structures. While they can be more difficult to manipulate computationally compared to structured grids, their flexibility makes them crucial for many applications.

Think of a modern city plan where streets curve and shape according to natural landscapes, as opposed to the grid layout of a planned neighborhood with straight, symmetrical roads. Just as a city may grow in a complex layout, unstructured grids can adapt to fit complex fluid flow environments.

So, now after this regeneration we comes to the solver stage. So, in this stage that the governing differential equations are solved by an approximate numerical technique after specifying the boundary and the initial conditions. So, the actual real solution of those differential equations is done at this stage called the solver stage and in post processing, the extraction of results and visualization how the results appear is done.

Once a grid has been established, the next step in computational fluid dynamics is called the solver stage. Here, the governing equations that describe fluid motion, such as the Navier-Stokes equations, are addressed using numerical methods. This involves defining initial and boundary conditions, which set the parameters for the simulation. After solving these equations, results are extracted and visualized to analyze fluid behavior.

Consider baking a cake: first, you gather ingredients (initial conditions) and choose a recipe (boundary conditions). As you mix and bake, you’re running a process (the solver stage) that transforms raw ingredients into a finished cake. The final cake is like the visualized results of your fluid dynamics simulation.

Therefore, due to the no slip condition the tangential component of the velocity at a stationary wall is set to 0.

Boundary conditions are critical in CFD because they define how the fluid interacts with physical boundaries. For instance, the no-slip condition means that at a stationary wall, the fluid touching the wall has zero velocity relative to the wall. This simulates how real fluids adhere to surfaces, affecting flow characteristics.

Imagine a river flowing past a steep shore. The water right against the shore moves very slowly due to friction. This is like the no-slip condition in CFD, where the velocity of the fluid at the wall (the shore) is effectively zero.

Now, as I said I mentioned about being closed and you know being open there is a wall at the boundary these wall and other concepts you have read in your previous lectures of hydraulic engineering. So, we are going to talk about the wall boundary condition, since fluid cannot pass through a wall the normal component of the velocity relative to the wall is set to 0 and this is what is this called this is called no slip condition.

Inflow and outflow conditions specify how fluid enters or exits a computational domain. For inflow boundaries, certain velocities or pressures are defined, indicating how quickly and in what manner fluid enters the system. Conversely, outflow boundaries determine how fluid exits, ensuring accurate representation of fluid behavior at the edges of the simulation.

Think of a water park slide. The entrance (inflow) has a certain flow of water, while the exit (outflow) must allow for water to flow out without backing up. The water's behavior at these points must be carefully controlled, just like the boundary conditions in CFD.

So first important information that we have is that it is 2 dimensional in nature. So, the unknowns, you can start guessing the unknowns first is going to be velocity you which is along X direction. Secondly, the velocity V, which is along Y direction.

During the solver stage, identifying the unknown variables is essential. In a two-dimensional fluid flow problem, the key unknowns are typically the velocities in the x and y directions, as well as pressure. These variables are interconnected and must be solved together using the corresponding equations, like continuity and momentum equations.

Think of playing a video game where you control a character (representing our unknowns) that moves in a 2D space (like a plane). As they navigate through obstacles, factors like speed (velocity) and power (pressure) are constantly changing based on where the character is and what’s around them.

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