"The high Reynolds number flow is not difficult to compute, the problem is we simply don't know how.
Is it a truth? A joke? A feeling? Or just a contradiction?
If a theoretic(exact) solution for the high Reynolds number flow is no longer required, how do you think to get just an engineering solution for it(maybe within a 2% tolerance error as comparing to the theoretical one).
Will we know how to solve it nowadays?
Re: "The high Reynolds number flow is not difficult to compute, the problem is we simply don't know how.
A difficult task is something like finding a cure for cancer. Knowing that there are many commercial codes around, many research institutes exist, many CFD papers published, many guru created, It is hard to say that the high Reynolds number flow is difficult to compute. It is not a truth, not a joke, not a feeling, not a contradiction, but a FACT. The other night, I was still thinking about the FD vs FV vs FE, I told myself that life would be easier if they had invented the Navier-Stokes solutions instead of Navier-Stokes equations. In the last night's TV program, there was a program about the music lessons and the kid's math performance. Appearantly, there is a positive relationship between the music and the ability to solve the math problem. So, I try to look at the forum here as a place to play music. Maybe in this way, I will be able to pick up some hints to solve the high Reynolds number flows. There are three (or more) schools of thinking about how to solve Navier-Stokes equations:(1). reverse the Newton's approach to turn the derivatives into finite difference approximation, (2). integrate the equations over a small volume, make whatever assumptions necessary to satisfy the conservation law, (3). assume that the solution will behave in certain ways , multiply the equations with some functions and go through minimization processes. The first one is royal to the original spirit of governing equations, the second one feels that the solution should be hidden inside the conservation law, and the third one thinks that every solution is a consequence of the mathematical operation only. In the days when people were solving boundary layer equations using "shooting method", the initial slope has to be very accurate in order to satisfy the boundary conditions on the other side. A 2 % error is definitely not adequate to give you a solution in that method. Upwind method was created as a consequence of coarse mesh ( or cell Reynolds number) problem. But soon the Journals decided that solutions obtained from the first-order upwind method are not acceptable for publication. The Navier-Stokes solutions are so easy to obtain that they think the solution is not good enough to withstand the time. They were probably right, we have to keep looking for the real solution just as if we are looking for cancer cure. Your question really is very important because with the Navier-Stokes solution of high Reynolds number flows everywhere, the CFD field is dead. ( get a commercial code and you have the solution. Many companies are doing just that as if they have found the magic drug of Viagra.) I have to stop now, to keep it short.
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