ChrisDanger wrote:gixxer_drew wrote:F1 has been using "custom solvers" for quite some time. Unsurprisingly, I could never get any more information than that and can only guess at it might have been somehow I doubt it was this much of a departure.
Well, the full Navier Stokes equations are too complicated to solve (currently, and will be even for some time in the future), so simplifications are made where full terms may be dropped or replaced with more crude and soluble mathematical models. These simplifications vary according to the nature of the flow, so it's most likely that some have been developed by the F1 community that are more accurate than the generic models available.
Currently with the Navier-Stokes Equations (NSE), the problem that arises is due to one of the terms called the "Reynolds Stress Tensor". So the NSE as they stand default give an instantaneous view of the flow at a given point in time. One of the ways in which CFD simulations can be performed is though a common method called "Reynolds-Averaged Navier-Stokes" (RANS). To get the RANS equations, each NSE with respect to x, y and z has each "x" term replaced with "x(average)+x(fluctuation)" since at any given time, the value of "x" will be the average value for "x" plus some fluctuation at the given time. With some simplification, you are able to pull out some of the terms and get them to cancel out (for example, the average of all fluctuations is zero since they need to average out to give the average value of "x" itself) and what you are left with is a version of the NSE which have only the "x(average)" terms in it... except!! for one term which is defined (in lamans terms) as: "the total average of all the principle axis fluctuations multiplied together" (i.e. average of (x'*y'*z') ) - which in 3D space corresponds to 27 unknowns of which a few can be cancelled out.
This term, is impossible to solve; unless you know the initial conditions for the simulation... which you need to know the solution to the problem to know... and round and round it goes. There have been some methods of changing this term to other combinations of fluctuations and constants, however, in almost every case more unknowns are left to figure out and we started with.
What your k-epsilon or k-omega equations do is try to approximate this variable through the use of equations which model turbulent energy production and dissipation. The problem here is that in order for them to work, there are some constants that need to be defined... and of course, the value of these constants varies based on the geometry... So to know these exactly, you need to know the solution... and the circle begins again. Over the years, the values have changed slightly but they seem to be pretty much there for the most part in predicting flow.
In order to solve the flow over an object perfectly, you need to do something which is called a "Direct Numerical Simulation" which literally solves every single flow vortex whether large in the freestream down to the smallest scales of turbulence right in the boundary layer of the surface (called the Kolmogorov scales). This has been done for things such as flat plates and cylinders at low Reynolds number, but in terms of racing or aerospace, the Reynolds Numbers can be in the millions if not higher. There is a relationship that you can derive which tells you how many cells you need in order to perform a DNS simulation at a particular Reynolds Number which is:
The number of Cells you need must be larger than the Reynolds Number raised to the power of 9/4. So for example, if you took a 1m chord wing and flew it through normal air at about 16m/s, your Reynolds number would be about 1.06 Million. So in order to perform a DNS simulation and capture all possible flow eddies, you would need 3.6x10^13 cells (36,000,000,000,000 cells)!!!! Given that the largest simulation that I know of was solved over a million cores with a total cell count of 1.4 trillion (1.4x10^12 cells) we are still a long way off having enough computational power to know exactly what is happening...
Perhaps these new equations will get us a little closer, but if not, it sounds like an interesting new approach!!
