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From: Saumil Patel <saumil.patel134@gm...>  20110628 14:04:04

Thank You, John. This makes sense. I was able to get results for Re 100. I have been trying to get results for Re = 1000. I've tried two approaches: 1) to multiply the diffusion term by 1/Re and 2) Change the boundary condition to U=1000. BC's are still based on the Penalty formulation. In both cases I'm using a refined mesh of 500 by 500. I'm having trouble getting accurate results so I was wondering if the Kmatrix is becoming illconditioned when I multiply the diffusion term by .001 (1/Re)? Do you have any suggestions on getting around it this issue? Thanks for your help, Saumil On Mon, Jun 27, 2011 at 10:43 AM, John Peterson <jwpeterson@...>wrote: > On Sun, Jun 26, 2011 at 1:37 PM, Saumil Patel <saumil.patel134@...> > wrote: > > Hello, > > > > I am getting familiar with the LIBMESH code and I was wondering if the > FEM > > formulation for the Unsteady NSE in example 13 are in a nondimensional > > form? If so, I would just need to multiply the diffusion terms in the > Kuu > > and Kvv submatrices by the inverse Reynolds number factor, correct? > > Well the *dimensional* incompressible NS equations typically contain > only a single parameter: "nu", the kinematic viscosity, anyway. > > So if you multiply the diffusion terms in ex13 by some parameter, you > can think of it as a dimensional viscosity or an inverse Reynold's > number. > > > Furthermore, I wouldn't need to change the B.C. condition for the top > lid, > > correct? > > The velocity on the top lid, the size of the domain, and the timestep > will all take on different physical meaning depending on whether the > value multiplying the diffusion terms is thought of as the Reynolds > number or the kinematic viscosity. Consider: > > The default values for ex13 are domain size = "1", lid velocity="1". > > If the number multiplying the diffusion terms is thought of as the > kinematic viscosity (in SI units of m^2/s, say) then the domain size > is 1 meter, the lid velocity 1 m/s. > > On the other hand, if the number multiplying the diffusion terms is > thought of as 1/Re, then setting the lid velocity="1" just means the > lid velocity is equal to the "characteristic velocity used in defining > the Reynold's number" and does not imply any particular units. In > this case, one can always assign a physical value to, for example, the > lid velocity "U" by specifying particular values for the Re, the > kinematic viscosity of the fluid, and the domain size "L": > > Ex1, air @ 300K (nu=15.68e6 m^2/s) in a L=1cm enclosure, Re=1: U = Re > * (nu/L) ~ 0.15 cm/s > > Ex2, water @ 50C (nu=0.553e6 m^2/s) in a L=1m enclosure, Re=1: U ~ .55 > micron/s > > That is, the same Re=1 solution could represent either of the two > physical situations (and infinitely many others!) above. > >  > John > 