# Introduction to CFD

Many, especially students wouldn’t be having a clear picture about the master of fluid dynamics software, CFD (Computational Fluid Dynamics). Hope my article helps you out.

In this real world, most of the practical problems are related to fluid problems. The study of forces and moment in the moving fluid is called fluid dynamics. Firstly, study or investigation can be classified into two types. They are

• Theoretical FD
• Experimental CFD

In theoretical FD, we would be able to express the physical behavior of any fluid in terms of mathematical expression. And in experimental FD, we would be able to see the flow behavior with the help of smoke generation, followed by the calculation of forces and moment on any geometry exerted by the moving fluid.

After some explainable development in both theoretical and experimental FD approach, the third approach has been introduced, which is a combo pack of high speed computer and accurate numerical algorithm called computational fluid dynamics which helps in solving physical problems.

The CFD is today an equal partner with pure theory and pure experiment in the field of analysis and providing solutions for FD problems.

# Strategy of CFD:

The strategy begins with the philosophy of fluid dynamics. There are three fundamental physical principles upon which all of fluid dynamics is based on. Those principles are conservation of mass, momentum and energy. The conservation equation speaks physics.

The conservation equations are expressed in the form of mathematical statements. Those mathematical expressions/statements are in the form of continuous partial differential equation. Many would have known the meaning of continuous function; in the solution, we would extract all the points in that function which is expressed by limits.

E.g.  p=p(x) in 1D problem; (0<x<1)

Here we could extract all point of pressure within the limits, which is continuous function. In continuous domain, each flow variable is defined at every point in the domain.

Mathematical behavior of partial differential equation can be classified as hyperbolic, elliptic, parabolic or mixed. We’ll discuss about the PDE equations later.

### Grid Generation:

Splitting a whole single volume into small number of volume with defined shapes like pyramid, cuboid, tetrahedral, hexahedral, triangle, quadrilateral, etc., is called grid generation. In this grid generation, the small numbers of volumes are called as elements which consist of node, face and edge.

Finite Volume Method will be carried out for solving fluid flow problems. If that CFD technique is applied to any domain, the flow variables can be calculated using interpolation because of the continuous function. But flow separation, boundary layer, shock waves and all cannot be computed fully over the geometry which is inside the domain. So, it is necessary to split the domain into pieces that means into N number of grid points as well as elements.

### Discretization:

Now the gap between geometry and domain (fluid flow volume) is fully covered with mesh elements depending on the type of simulation. But now the partial differential equation is a continuous function. So there is a need to convert the continuous thing into discrete thing. The process of converting continuous partial differential equation into algebraic difference equation by using FDM or (FVM, FEM) is called discretization. The algebraic difference equation gives the flow variables only at the discrete points or node points. From that, we could interpolate the intermediate points between two grid points.

Then the transformation is made to communicate between algebraic difference equation and generated grid. After the transformed combination combined with developed numerical algorithms or techniques and then after computing it will yield the flow results over geometry in high speed computers.

Here grid generation meant, splitting the virtual domain using soft wares like ANSYS-ICEMCFD, T-Grid, STAR-CCM, etc. And Discretization meant splitting the PDE equations into Algebraic Difference Equation.

## Process involved in CFD:

Basically it can be segregated into 3 steps.

• Pre-Processing
• Solving
• Post processing.

In pre-processing, the grid generation would be there, because generated mesh quality is the primary consideration. If the element lacks quality, then there is a possibility of disturbance in the stability of solution and it will start diverging, instead of converging. The stability of solution will be discussed later in large view to enjoy the magic of mathematics in CFD.

In solving part, the boundary conditions and initial conditions will be defined to initialize the solving process. If you choose turbulence model, time variant/invariant term, the solvers like ANSYS-Fluent, ANSYS-CFX, CFD++, STAR-CCM, etc., will be started and  it runs until the residual criteria reaches or converges the solution.

In post-processing process, the processed data of control volume (discrete domain) which is needed for flow variables to predict the physics behind the geometry can be viewed.