# Computational Fluid Dynamics

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The Governing Equations

1

CHAPTER 1

THE GOVERNING EQUATIONS

1.1

INTRODUCTION

C – Computational F – Fluid D – Dynamics CFD (Computational Fluid Dynamics) may be defined as follows:

“The science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena by solving the mathematical equations which govern these processes by means of computer based simulations.” (Versteeg and Malalasekara, 2007)*

Analysis of fluid dynamics using CFD can be based on either Lagrangian or Eulerian approach. In the Lagrangian approach (Figure 1.1), the fluid is considered comprising of a large number of finite sized fluid particles which has mass, momentum, internal energy and other properties. Then the mathematical equations are derived for each fluid particle. A major drawback of this approach is that, it is restrictively time consuming when considering even a very small volume of fluid. Even when a gas is being considered where there are fewer molecules and a larger time-step can be used, because of the longer mean free path of the molecules, the number of molecules that can be considered is severely limited. Smooth Particle Hydrodynamics is the currently famous CFD technique based on the Lagrangian approach.

* An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition), Longman Scientific & Technical, 2007

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2 An Introduction to the Computational Fluid Dynamics

Streamlines Streakline Fluid particle

Control volume

Figure 1.1 Lagrangian (left) and Eulerian (right) description of a flowing fluid

In the later approach, it considers how the flow properties change at a fluid element as function of space and time. From this method, the information about the flow is obtained in terms of what happened at fixed points in space as the fluid flows through those points. In this book, we only consider the Eulerian based CFD...