Same goal different solutions
 The term Computational Fluid Dynamics is used to cover a large and diverse group of solution techniques, all of which to some degree solve for the flow around or inside a body.
In FLUID, I will focus on providing you with enough broad knowledge to distinguish these methods; recognise their strengths and limitations and understand the best option for a particular problem.
Navier-Stokes – the basis of CFD
Most CFD methods can be related back to the Navier-Stokes equation:
Looks complicated? But in essence the Navier-Stokes equation is Newton’s 2nd law, F=ma, applied to fluid motion. The terms on the right hand side of the equation above relate to the inertia of the fluid and those on the left relate to the stresses on the fluid, the pressure gradient, viscosity and outside forces.
To solve the Navier-Stokes equations directly, the equations would need to be applied to microscopic portions of the fluid, an unrealistic task for the foreseeable future even with the rapid power increase in modern computers. So the solution must be simplified, the various forms of CFD can be related back to the physics omitted in their simplification of the Navier-Stokes equations.
Navier-Stokes - What to solve?
The first simplification is applied to turbulence. To solve the navier-stokes equations directly for all scales of turbulence in a fluid would require mesh resolution too fine to be practical. To get around this time, averaged equations such as RANS (Reynolds-averaged navier-stokes) are used in conjunction with turbulence models. Turbulence modeling is complicated but in its simplest form model the energy dissipated through small scales of turbulence as a transportable quantity that can be resolved throughout the fluid and likewise be affected by and effect the flow.
An even bigger simplification is to ignore viscosity entirely. With the Navier-Stokes equation simplifies to the Euler equation. Euler codes are unpopular primarily due to the difficulty getting stable results in practical geometries.
CFD demystified: A further simplification – Potential Flow
 From an Euler solution, the next simplification is to ignore vorticity in the flow. This allows the velocity field to be represented as the gradient of a scalar function – f the velocity potential. A solution can then be calculated for the potential that describes the flow around a body. This is generally achieved numerically by using panels on the surface hence many potential methods are known as panel codes.
For a Naval Architect, potential flow can be a very useful tool but it is important to recognise its limitations. As it ignores vorticity it does not give good results in areas of turbulent flow and has no capability for solving boundary layer effects although many potential solutions use adjustments account for these limitations. A lack of viscosity, both real and numeric does mean that wave patterns are propagated away from the hull surface so a potential method will be far superior for wash studies. Potential codes are also an order of magnitude faster than RANS so a potential solution so can generally generate a result in a relatively quick time on a standard pc.
CFD demystified: Michell – thin ship potential theory
 Another method that needs to be mentioned in any discussion of CFD in Naval Architecture is the Michell integral for the wave resistance of thin ships. First published in 1898 by Australian mathematician J.H Michell, it uses a centreplane source distribution proportional to the rate of change of local beam to represent the potential flow field. It assumes that the change in local beam must be small, an assumption that only holds true for thin ships, hence it is often known as thin ship theory.
While it does have limitations the Michell integral is a very useful tool particularly in multihull design and wash studies.
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