What are the reasons for solution instability?

diaw

This is an open question regarding why solutions 'blow up' at seemingly even reasonably low velocities for low-speed, viscous, incompressible flow fields.

I have noted that there are certain combinations of parameters at very low Reynold's number where solution convergence is simply impossible without the addition of solution stabilisation eg. upwinding etc.

I have looked through a number of books & references to critical cell Peclet number & critical cell Reynold's number are mentioned.

It appears to me that current theory is split into two areas , 1. Low-speed, viscous, incompressible; 2. High-speed, inviscid, compressible.

I have not been able to locate good theory for the region between these two extremes & observe that most approaches seem to use solution-stabilisation techniques eg. upwinding, to cope with the intermediate region.

I have an idea about why the solutions 'blow-up' based on new mathematical theory I have been developing, but would like to test this against existing knowledge & theory. This new theory predicts the use of very small element dimensions to overcome the 'singularity point'.

I would value feedback from the learned members of this board.

diaw...