Do you really think it's a stability problem? I am running delta_t to the order of 10^-6. Even then I have problems. Morover it's an implicit scheme. It shoudl be running at delta_t less than an explicit scheme. The same set of equation for the explicit Mccormack's scheme run at delta_t of 10^-4. Do you have any other suggestions? Thanks

(1). It's nothing new! I have the same problem for over a year now (with a commercial code). (2). I am not complaining about it, because I think it is a combination of many things. (3). For coarse mesh with wall function, it is normally not a problem. (4). It becomes a nightmare when I need very fine mesh for the low Re model (actually, it is a two layer model, not quite a low Re model yet). (5). In my case, I know that the initial guess of the flow field is always a problem. That is, the sharp velocity gradient next to the wall behaves just like a shock wave. At the wall, the velocity is zero. Then in the flow field, the velocity is finite. The spacing is Y+=1. or something like that. (6). Then there is this single precision and double precision math problem. And Even higher gradient for the k and epsilon, etc. (7). So, I would say, the coupled, implicit does not always lead to stable solution. The other way to do is to let the initial flow field equal to zero. But then somewhere there will be a discontinuity in boundary conditions. You can't make the boundary conditions uniform everywhere. The inlet is always different from the exit conditions. (8). If you are using someone's code, it is not easy. (9). I have been using the time step equal to or less than 1.0E-06. One trick is to set the method to upwind first until you have nearly converged solution. Then you can switch to the higher order method. But, there is no guarantee that it will work. (10). The same is true for switching between different turbulence models. And there is this mesh quality problem, which is hard to control in 3-D. (1). SO, I think, it is all right to say that cfd is not for everybody. (11). I am not saying that codes are useless. What I am trying to say is: it is hard to get a solution, and it is even harder to get the reasonable solution. (12). And in principle, if the initial solution (or flow field) is close to the final solution , then, the coupled, implicit, higher-order method could be advantageous. The question is: with several hundred thousands cells, how do you come up with a good initial solution? Not easy.