Hi,Recently, we are considering the 2-D unsteady incompressible driven cavity problem,which is the most fundamental method in Computational Mathematics.Although the numerical solutions at low reynolds numbers is obtained,the acquirement at high reynolds numbers is not easy,for example,Re>5000.Now,I am reading the paper-《Fourth Order Compact Formulation of Navier-Stokes Equations and Driven Cavity Flow at High Reynolds Numbers》writen by E.Erturk. He adopted a fourth order compact formulation to resolve this problem in steady incompressible Navier-Stokes Equations.In my opinion,the key in his method is the introduction of pseudo time. Moreover,as far as I know,when the Re is larger than 10000,the periodic solution will appear.Is there a better way to find the critical value of Reynolds number.By the way,we are considering this problem at Vorticity and Streamfunction Formulation. Thank you!

have you gotten your model to solve using the 4th order equations? I used the same paper and had a good bit of trouble getting the model to converge for the cavity flow. I was also doing steady-state. I moved the equation to flow between plates (changed the boundary conditions) and was able to solve it by having two relaxation factors - one acting on the streamfunction and another acting on the velocities to control any error propogation, but I am not sure if I am allowed to do this. My results look good. It is just that the program is very dependent on the two relaxation factors,so anytime I change something I have to do a trial and error for the relaxation factors until I get satisfactory results.

critical renold number , different people have different idear?

when you use a relativly coarse grid ,you can'not get a solution under some specified Re, but when we get the grid fined, then we can get the solution of a steady N-S equation?

then how to decide whether the flow is steady or unsteady?

regards