Hi Dear Friends,

I have seen that stiff phenomena can occur in unstesdy flow simulation simulations. My question is this one, namely: in the context of fluid flow, what means a problem to be a stiff one?

Ferreira

Stiff Phenomena

from mathematical point of veiw, stiff sticked to problems which are not computationally tractable.

e.g. when system is ill-posed, highly non-linear systems, caotic systems, such problems are sensitive to perturbations and considering computer arithmetic limitation (impose naturally perturbation from exact solution) and also error in initial guess (considering iterative solver) we have difficulty to solve such problems.

This is just my understanding and others may have more comments !

From a numerical ODE standpoint a stiff ODE is one where you have more than 1 timescale, one of which is much smaller than the others. The smaller timescale may be of little interest but for explicit schemes the stability of the scheme is dependent on it.

See the definition in J. Blazek's Computational Fluid Dynamics: Principles and Applications book page 185. It says stiffness is the ratio of the largest to smallest time scale, or the ratio of the largest to smallest eigenvalue of Jacobian matrix. Also, from the numerics point of view, I think the system of equations that is to be solved has coefficients with some different number of magnitude.

Another example is when your roomate mixes some V1AGRA into a bowl of M&M's and you absentmindedly swallow a handful. A stiff(y) problem quickly ensues.

Dear Ferreira,

Following Peter's comments on stiffness, it is not difficult to see that problems involving reactive flows and in combustion are stiff. Turbulent flows also lead to stiffness arising from the underlying grid necessary to resolve the viscous sublayer. In the first case, the time scales of reaction are quite small compared to the flow time scales. In the second case, you need to use a smaller time scale because the grid scales close to the body is low. The second problem is overcome using a local time stepping strategy in conjunction with implicit schemes, at least for steady flows. Turbulence and combustion are inherently unsteady problems and stiffness is therefore a problem to deal with during time integration.

Hope this helps

Regards,

Ganesh