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From: John Peterson <jwpeterson@gm...>  20110627 14:43:56

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 