Hi All Just a few questions ! I am modelling liquid motion in a U tube. Reynolds number is of the order of about 3000.

I am looking at mesh and time step independance studies and suitability of turbulence models.

Is there any systematic way of looking at timestep and mesh size independance. I am not sure wheteher I should look at halfing and doubling my mesh with fixed time steps, and then look at the effect that a variable time step has on my solution, or should I be looking at maintaining a fixed CFL number with my mesh refinement (and hence changinging time step).

I also have found that my Y+ values are extremely low as a result of very small shear stresses. Y plus is of the order of 0.9 which is well below the 10-300 range. I am using the low reynolds number k-e model, but have found similar problems with other turbulent models and am not sure of how to remedy this. I also have tried changing the mesh density since Y plus is a function of y from the wall ?

I would also appreciate any references discussing the above further.

thanks in advance

eugenio

Hi eugenio

I dont know about the independence question, but for the low Reynolds number ke model, you need Y+ to be around or under 1, so that is not a problem. I think Y+ should be relatively independent of the model you use. No Doubt others will shed more light on the subject.

(1). I think, the mesh independent solution issue is an issue of responsibility. You don't want to cheat yourself or others about the solution obtained which is depends on the particular mesh used. (2). If you consider the time variable similar to the spatial variable, then the time step should be treated in the same way as the mesh size. Both are independent variables. (3). When using the wall function treatment with a turbulence model, the range of the validity of the law of the wall must be observed. This is the condition of using the wall function. The range of matching location is a function of the pressure gradient (or adverse pressure gradient), and Reynolds number. So, the matching location is problem dependent. (4). The use of a low Reynolds number turbulence model does not require any special condition, as long as the mesh independent practice is followed. (but based on the equilibrium boundary layer profile, the sublayer profile is always U+=Y+, the value of near wall Y+=<1 is suggested. But this is not the condition required to get mesh independent solution. It is simply a ball park number to begin with. (5). The issue of CFL is solution algorithm related, it is more or less a stability issue when using a particular algorithm.

There is no doubt that mesh and time step independence study is essential for numerical modelling. It is a good practice to seek mesh and time step-independent solutions by halving the mesh resolution and time step simultaneously and keeping the CFL number constant. If only minor variation of the solution is detected, then you have shown that the solution is mesh and time step independent. However, it is usually very expensive to do so.