Navier-Stokes Equation - unit problems
 

Hello.

I have a problem with interpreting results of numerical calculations. Let say, than i'm solving full 2D NS equation. Somebody asked me what is really size of the tank. And..

let: WIDTH and HEIGHT are the screen calculations

NX and NY are grid size (number of cells)

now i calculate DX and DY as WIDTH/NX and HEIGHT/NY

VIS is viscosity of the fluid

GY is grawity vector

DT is float delta time

now let:

WIDTH=320

HEIGHT=200

NX=32

NY=20

then DX = DY = 10 let:

VIS = 0.1

GY = -9.8

DT = 0.01

now im asking: from where i know what is size of my tank and other physically properties of my fluid model? is that determined by GY unit (m/s^2)??? i really dont know what are units of my calculations, and my results are only qualitate not quatitate.

Maciej Matyka,

author of Fluid NS solver - available at http://panoramix.ift.uni.wroc.pl/~maq

Re: Navier-Stokes Equation - unit problems
 

Hi Maciej. As far as I´m concerned, what really matters in such a calculation is the Reynolds number (as long as effects like surface tension are negligible). That is, once you have defined the Reynolds number (which is dimensionless) for your specific problem, the units of VIS, RHO, HEIGHT and the characteristic velocity are irrelevant (take the flow between parallel plates for instance Re=U*RHO*HEIGHT/VIS). The result will be a function of Re number only. You can prove this to yourself by writing the NS equations in dimensionless form. This can be found in any book of Fluid Mechanics.

Best regards,

Francisco.