Dear Mr. Fadaei,

Sorry about the ambiguity. This very "large" value is campared to the small value for creeping flow. I have tried to simulate the laminary flow in porous media. Any idea about determining the critical Re values for the transition from laminary to turbulent flow in COMSOL?

Thank you.

Regards,

Bill

It is not clear what equations are used to model porous media flow that include the Reynolds number. I will assume some form of steady Navier-Stokes equations are involved.

In principle the stability of the steady solution of the Navier-Stokes equations can be controlled by monitoring the right-most pair of eigenvalues and checking when they cross into the right half-plane (a Hopf-bifurcation occurs). To do this in practice, see e.g. Elman-Meerbergen-Spence-Wu, SIAM J Sci Comput 34(3):A1585-A1606. 2012.

It should be noted that numerical stability is not the same as actual stability, e.g. certain numerical stabilization methods may result in stable steady-state numerical solutions far beyond the range of actually stable solutions. There is quite a bit of confusion in the CFD literature about the range of stable steady-state solution even for simple test problems, such as lid-driven cavity flow in 2D.

Dear Dr. Lassila,

Thank you for your suggestion and recommendation. I totally agree with you on the confusion about the range of stable steady-state solution.

I used the dimensionless Navier-Stokes equation and the mass conservation equation to model the flow, thus the Re number is included in the steady  simulations.

Could you please recommend some references on numerical simulations about finding the transition from steady to unsteady flow, especially for porous medium?

Thank you in advance.

Best Regards,

Bill