2.5. Solution Procedure in CFD

Now, what is the solution procedure? The solution procedure in general any CFD problems involves the following steps. First is we have to define the geometry of the flow, we have to discretize the domain we will come to it what defining the geometries what discretization of the domain is and then there is a solver stage. And in the end after the solution is solved, there is post processing, is after the results are obtained, we have to show it graphically or we have to find some values we have to interpret those results that we got in most of the cases plotting the results is termed as post processing.

The solution procedure in Computational Fluid Dynamics (CFD) consists of a series of necessary steps to successfully obtain results from fluid flow equations. The first step is defining the geometry, which means creating a representation of the space where fluid will flow. The second step is discretizing the domain, which involves breaking the continuous flow region into discrete parts or cells. Then, a solving stage is conducted where mathematical equations are processed to generate results. Finally, the post-processing step occurs, where these results are analyzed and visualized, allowing for interpretation of the data obtained through the simulations.

Imagine you're planning a road trip. First, you draw a map (defining the geometry) of the route you want to take, noting down cities and landmarks. Then, you break the route into manageable segments or stops (discretizing the domain). Next, you decide on the best roads (solver stage) and finally, once you've completed your trip, you gather photos and notes of interesting events to reflect on your journey (post-processing).

So now as we said that the first step is defining the geometry. So, this step includes the creation of a CAD model what is CAD computer aided design. So, you use some software is are there are even tools available within the computational fluid dynamics models where you can define the geometry or derive for example, suppose for example, there is a tank right and there is a pier. And you have to and this is open no I am just drawing it in 2d assume it is 3d and flow is coming through this right.

Defining the geometry is the first crucial step in the CFD solution process. This involves making a Computer-Aided Design (CAD) model that accurately represents the physical shape and size of the area where fluid flow is analyzed. For instance, if you’re examining water flow in a tank, you need to create a model showing the tank's dimensions and features, which will guide the simulation of how fluid behaves within that space. A precise CAD model sets the stage for accurate simulations and analysis.

Think of it like building a detailed scale model of a building before construction. Architects use CAD to ensure every inch of the design, from doors to windows, is correct. Similarly, CFD requires a precise geometry to understand how fluid will move around the modeled structures just like understanding how light will enter a room through windows.

So, the second step was discretization of the domain. So, this process is known as grid generation or mesh generation. So, the process this particular process of discretization involves developing a set of algebraic equations based on discrete points in the flow domain to be used in place of partial differential equation we told that the way that it is to be done.

Discretizing the domain involves dividing the continuous fluid flow region into smaller, manageable parts, known as a grid or mesh. This step transforms the complex equations governing fluid flow, which are differential equations, into discrete algebraic equations that can be solved numerically. By creating a grid, each small section of the flow is analyzed separately, making calculations of fluid behaviors more feasible and accurate. The goal is for the grid points to be small enough to accurately capture changes in the flow field.

Imagine slicing a large cake into many small pieces. Each slice represents a small part of the cake's overall structure, similar to how a flow domain is represented by a grid. By analyzing each slice, you can understand the entire cake better. In CFD, by analyzing each small cell of the grid, we can understand how fluid flows in the entire domain.

So, the most common discretization techniques available for the numerical solution of partial differential equations are the finite difference method. The second is finite element method and another one is finite volume method. So, we will go into small details of this, so that you have a broader idea, you will not become expert overnight and all these techniques, but will give you a very, good understanding and overall a holistic picture of what computational fluid dynamics is.

In CFD, there are several methods to discretize the governing equations, which are critical for solving fluid flow problems. The three most common methods are the Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM). The FDM approximates derivatives by differences between discrete points, while FEM breaks the domain into smaller elements and solves equations for each element, and FVM divides the flow domain into small volumes where fluxes are computed. Each method has its advantages and suitability depending on the specific type of fluid flow problem being analyzed.

Think of these methods like cooking recipes. If you want to bake a cake, you can choose different methods: you could use a standard recipe (FDM), use a mix of ingredients tailored to specific flavors (FEM), or bake individual components separately and assemble them later (FVM). Each has its advantages depending on the type of cake you want to create.

In the end after the solution is solved, there is post processing, is after the results are obtained, we have to show it graphically or we have to find some values we have to interpret those results that we got in most of the cases plotting the results is termed as post processing.

Post processing is the step that follows the calculations in CFD. This involves analyzing the data obtained from simulations and representing it in a way that can be easily understood. Common tasks include creating visual outputs such as graphs, contour plots, or animations that depict how the fluid flows in the modeled domain. This step is crucial for interpreting the results and validating them against experimental data or expected outcomes.

It's like reviewing the footage after a soccer game. Once the match is played (the simulation is run), the coach uses video to analyze player movements, strategies, and results (post processing) to improve future games. Similarly, in CFD, results are analyzed visually or numerically to draw insights about fluid behavior.

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