In the search of WHY Computational Fluid Dynamics...

I am of the opinion that when we plan to delve into a subject, we must have a clear cut purpose - why we are doing it. This is what I say - first What - then Why - and then only How.

Purpose of learning a subject is essential to fall in love with the subject.

So here we go...

My exploration continues.

Why We Need CFD (Computational Fluid Dynamics)

We need CFD because the governing equations of fluid motion — such as the Navier-Stokes equations — are continuous, nonlinear partial differential equations (PDEs) that describe how fluid velocity, pressure, temperature, and density evolve over time and space.

These equations are derived based on:

- Conservation of mass (Continuity equation)

- Conservation of momentum (Newton’s second law → Navier-Stokes equations)

- Conservation of energy (First law of thermodynamics)

The Core Challenge...

These governing equations are defined in a continuous domain — meaning:

They assume infinitely small control volumes,

Variables like velocity and pressure change smoothly and continuously,

Solutions require solving PDEs over an infinite number of points in space and time.

But this is not possible to compute directly on a computer because:

Computers can only work with discrete data — finite points and numbers.

How CFD Helps...

CFD bridges the gap by:

Discretizing the continuous equations into a finite form (e.g., using finite volume, finite difference, or finite element methods),

Breaking the domain into small control volumes or grid cells (called meshing),

Approximating the continuous functions and derivatives using numerical methods,

Solving the resulting algebraic equations using iterative solvers.

We need CFD because the fundamental equations governing fluid flow, like the Navier-Stokes equations, are defined in continuous form and cannot be solved analytically for most real-world problems. CFD allows us to discretize these equations, making them solvable using numerical methods on computers.

CFD exists because real fluids follow continuous laws, but computers need discrete data. CFD translates the language of calculus into the language of algorithms.