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