Fundamentals of Computational Fluid Dynamics

1.0 Fluid Mechanics versus Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is a branch of Fluid Mechanics, which primarily deals with solving the governing partial differential equations of fluid flow using numerical techniques such as the Finite Difference Method (FDM), Finite Volume Method (FVM), Finite Element Method (FEM), Lattice Boltzmann Method (LBM), Smoothed Particle Hydrodynamics (SPH), etc.

During the solution process, the governing partial differential equations are discretised into a large system of linear equations (the size of the linear system depends upon the mesh considered for the CFD simulation), which are then solved using computers as the size of the linear system is too large to be solved by hand for practical flow problems encountered in real life scenarios.

In a broader sense, a CFD solution process typically involves the transformation of a physical problem into a mathematical model, which comprises of certain key components such as

• ($i$) a discretised computational domain, composed of numerous small control volume cells or computational stencils,
• ($ii$) the governing partial differential equations of fluid flow, which describe the behaviour of the fluid within the computational domain,
• ($iii$) the boundary conditions, which sets some constraints as to how the fluid should behave near the computational domain boundaries so that the formulated mathematical model depicts a real-life scenario as closely as possible, and
• ($iv$) the initial conditions; these are the values assumed by the field variables (variables that we solve for using CFD such as the velocity, pressure, etc., which are a function of both space and time) at the start of a CFD simulation process. Alternately, the initial conditions can be construed as something that is required to advance the solution forward in time for the time-marching problems such as the unsteady flows.

Before delving deeper into the topic of CFD, it is important to familiarise oneself with some common concepts and terminologies from Fluid Mechanics, which form the foundational base for Computational Fluid Dynamics.

The distinction between Fluid Mechanics and Computational Fluid Dynamics is generally made in the context that Fluid Mechanics, in general, refers to the principles of Mechanics applied to fluid flow phenomena that govern and describe the fluid motion, which encompasses ($i$) Theoretical Fluid Mechanics ($ii$) Computational Fluid Mechanics as well as the ($iii$) Experimental Fluid Mechanics, whereas when we talk about CFD, we are primarily referring to the theoretical/computational aspect of Fluid Mechanics.

In this tutorial, we begin our study of computational fluid dynamics by first reviewing some of the very fundamental concepts and key terminologies from Fluid Mechanics. Then, we take a closer look at the governing partial differential equations describing fluid flows. In future tutorials, we will delve deeper into practical CFD and the tools we use to simulate fluid flow.

In CFD, a physical system is often modelled as an Open System (or a Control Volume) whereas the fundamental conservation laws are usually described using the System (Closed System) approach. So, it is first important to distinguish and differentiate between the Closed and the Open systems.