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Above: CFD simulations are often associated with RANS models solved on a so-called ‘grid’ where the fluid space is cut into many little boxes. This is a cut through a RANS grid around two sails together with streamlines and pressure surfaces used to analyse the results. But RANS is not the only kind of CFD. There are plenty of other possibilities as well as many different flavours of RANS itself. Left: in F1, as elsewhere, there have been plenty of cases of relying too much on simulation and wind tunnel testing then finding the results corrupted by issues such as scaling and calibration. On track the car is never in a steady state, constant motion generating aero-instability that may not be evident in the tunnel; hence the prevalence of aero rakes (basically a large suite of pitot tubes) on view during early season testing… and bitten fingernails among the design teams. In the America’s Cup the cause of tank testing was set back years after Britt Chance’s disastrous 12 Metre Mariner (inset) launched with her chopped-away bustle which proved great at 1/8th scale… not so great on the waters of Rhode Island. The story famously goes that skipper Ted Turner realised things were badly wrong during the tow from the yard to her base, when he threw a banana skin over the stern and was horrified to see it still there an hour later, rolling and flipping in Mariner’s wretched wake as the design of the future tried to drag Long Island Sound to Connecticut


stick with it! So, for the purpose of this article, let us consider the Navier-Stokes equation simply as an exquisite piece of fine art and turn back to the essence. While this Navier-Stokes equation may


not look too crazy there still exists no general solution to it for most practical cases, despite it having been around for almost 200 years. And even worse: mathe- maticians are still not even sure if a general solution is guaranteed at all. A big part of the reason for that lack of


a solution is due to the power of the equa- tion: it describes the flow at every point in space and every instance in time. We are thus required to solve it simultaneously for space and time – everywhere, for ever. This makes physical sense. In the flow


everything is connected. A tiny disturbance, like a bee flapping its wing, can cause insta- bilities that grow and grow and become rel- evant on a large scale. Hence the Navier- Stokes equation must see (and connect) the tiniest piece of turbulence, for example from a micro-scratch at the top of the mast, as well as the wind shadow behind this Superyacht five minutes to weather. Solving all of this is obviously not a trivial task. Luckily over the decades genius physi-


cists and engineers came up with tricks to obtain simplified solutions. These solu- tions are all based on more or less severe assumptions, and each particular set of simplification constitutes what I called earlier a CFD ‘incarnation’. All incarna- tions come from the same Navier-Stokes equation, but all rely on different sets of assumptions for their simplifications. To


distinguish them, each is given a specific name: RANS, VLM, SPH… Of course, each set of simplifications


comes with a set of advantages and disad- vantages, powers and limitations. If the simplifications are chosen wisely, very accurate results are obtained efficiently. If not, well… it means at best wasted effort. However, inappropriate simplifications can also lead to results that may look


Choosing the wrong assump- tions may lead to a set of beautiful results that are nothing more than colourful pictures – a very dangerous outcome for the innocent


reasonable but are wrong by virtue of their inherent assumptions. Unfortunately, it is often difficult to obtain valid CFD results with the right simplifications (simply because the underlying problem described through Navier-Stokes is just not simple), while it can be much easer to obtain (wrong!) results from inadequate simplifi- cations. Choice and judgement are left to the user. To guide us through the ancestry of different CFD methods, their simplifica- tions and the implications that come with them, the graphic on the following page gives a simplified genealogy narrowed down to a few selected methods.


So divide and conquer The first step towards making the Navier-


Stokes equation solvable is the same for every CFD method: ‘divide et impera’, as the ancient Romans taught us. Instead of solving the equation everywhere and for every time, we set ourselves limits, the so- called domain (eg 100m around the boat for the next 60 seconds). Then we break the domain down into little chunks of time, the time step, and little parcels in space. Within each parcel at each time step we


assume the flow does not change (or is of a known shape – but better ignore that for now). This immediately reduces the com- plexity of the task from finding a solution everywhere and at every time to only solv- ing the interaction between the parcels in space and time. This step is called discreti- sation. The amount of discretisation varies from method to method and can usually be adjusted somehow by the modeller. For example, whether we deal with


chunks of 10 seconds or 10 milliseconds, blocks of 1m or 1mm, that is our choice. Due to some fancy maths (which we promised not to talk about) the discretised flow simulation now becomes solvable. We could now feed the discretised


Navier-Stokes equation to a computer. But the effort would be immense and not very stable. To get consistent results a few more steps are necessary. First, we look at how the domain can best be discretised.


Grid-based vs grid-free The way the simulation domain is discre- tised into space parcels is a big simplifica- tion that separates two fundamentally dif- ferent kinds of CFD methods. First, there 


SEAHORSE 51


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