## 1D viscous flow with gravity

General discussions about how to formulate a script for FlexPDE.

### 1D viscous flow with gravity

I have viscous fluid flowing upwards.
I want to obtain steady velocity profile u(x).
To compare it with inviscid velocity profile u(x) = sqrt(u0² - 2gx).

I define domain from x=0 to u0²/2g (i.e. achieved height in the inviscid case).
I think mistakes are in boundary conditions, but I don't see what it should be.
Also I don't understand why Initial value section must be there in my problem, but the script worked even less without it.
Thank you for any hint!

COORDINATES
cartesian1

VARIABLES
u

DEFINITIONS
gravity = 9.87
dens = 1000
visc = staged(0.000000001, 0.001, 0.01)
u0 = 1
height = u0^2/(2*gravity)

INITIAL VALUES
u=u0

EQUATIONS
u: div(visc*grad(u)) - dens*gravity = dens*u*dx(u)

BOUNDARIES
REGION 1
START(0) point value(u)=u0
Line to (height) point load(u)=0

PLOTS
ELEVATION(u) FROM (0) to (height)
END
s0050506

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Joined: Sat Nov 22, 2014 7:46 pm