Hi Vincent, why dont you post this into the wiki.

the force term problem
if there are force term in the NS equation, how to deal with it??
for example, when use the immersed boundary method to solve the flow past fixed circular, what should i do with the force term nondimension??? 
In the case of an additional body force (like gravity) the equation changes to include an additional term.
Again dividing by yields this term indeed as an acceleration . If we then substitute in the following way: We end up with the following equation: So for instance if we want to simulate gravity where . Then we first determine by multiplying by H and dividing by . For instance, let's say we took H = 0.4 m and V = 2 m/s, this gives that is equal to 9.8*0.4/4 is 0.98. Good luck! Regards, Vincent 
A simple immersed boundary method can be implemented in the following way. The philosophy behind the idea is that we will determine the fluid flow without the obstacle and the in a next step force the fluid flow to zero using a body force.
Introducing a phase indicator function that can either be one (solidphase) or zero (fluidphase). By multiplying our body force with this phase indicator function we only imply a force where our obstacle is. However we can't use a simple constant for the forcing term since we want this opposing force to set the velocity exactly to zero and not a positive or negative value. So we need a parametrization for our body force. The forcing in a certain cell can be expressed in the following form: Here is our phase indicator function as defined above. is our numerical timestep the velocity in a certain cell at the current timestep before forcing. Our desired velocity is which is equal to zero in the case of a solid. Combining these elements gives that our full equation: Now we need to supply a geometry field () and the desired velocity field (which for simple cases will be zero everywhere). Good luck! Regards, Vincent 
Dimensionless NaviorStoks in cylindrical coordinate :
http://i49.tinypic.com/24o66wn.jpg nondimensional parameters which we use here: http://i47.tinypic.com/5cbmuv.jpg for rcomponent we have: http://i49.tinypic.com/21oaid4.jpg http://www.cfdonline.com/Forums/dat...AAAElFTkSuQmCC 
for thetacomponent, we have:
http://i47.tinypic.com/av6879.jpg and finally for zcomponent, we have: http://i48.tinypic.com/2q19gcy.jpg 
Hi VincentD, could you tell me how to choose V and H ???

Hi,
I need to non dimensionalize energy equation of navier stokes. Can you help me out 
Nondimensionalization of NV equations in cylindrical coordinates
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theta is not dimensionally homogeneous to a lenght that needs to be nondimensionalized but it is an angle position (rad).

Thank You! but what will be wrong with the below dimensionless parameters?
I considered theta as a reference variable to dimensionalize the tangential coordinate I also expressed the tangential dimensionless velocity considering the angular velocity as a reference variable. http://s10.postimg.org/72y0uw6t5/dim...parameters.png 
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No, theta ranges from 0 to 2*pi is already a nondimensional number, furthermore, the velocity reference is unique 
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I can see now how theta is already dimensionless. I am still a little bet confused about how the tangential velocity can be expressed in terms of a the unique reference velocity (Vr) which has [ L / T ] dimensions while omega r have a dimension [ T ^1] ? Thank you so much 
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It should be noted this seems to be a derivation for an incompressible flow.

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