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Figure 4.3 Iso-surfaces of pressure colored by the Mach number

4.1.4 Governing Equations

While we are talking about CFD, the discussion is incomplete without mentioning the governing
equations. These equations are the life blood of CFD. The famous equations of fluid dynamics are also
known as the Navier–Stokes equation. These equations were discovered independently more than
150 years ago by the French engineer Claude Navier and the Irish mathematician George Stokes.
Application of supercomputers to solve these equations introduced the field of CFD. The basis of these
equations lies in the assumption that a fluid particle deforms under shear stress. Then, using the
second law of motion and energy conservation, the dynamics of the particle is described by its mass,
momentum, and energy. In principle, all three parameters must be conserved:

1. Conservation of mass
2. Conservation of momentum
3. Conservation of energy

These set of equations constitute the Navier–Stokes equations. We will not explore the derivation of
each of these equations. Instead, the equations are mentioned and complex terms are elaborated.

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