{ FLOWSLAB.PDE}
{ *************************************************************
This problem considers the laminar flow of an incompressible, inviscid
fluid past an obstruction.
We assume that the flow can be represented by a stream function, PSI,
such that the velocities, U in the x-direction and V in the y-direction,
are given by:
U = -dy(PSI)
V = dx(PSI)
The flow can then be described by the equation
div(grad(PSI)) = 0.
The contours of PSI describe the flow trajectories of the fluid.
The problem presented here describes the flow past a slab tilted at
45 degrees to the flow direction. The left and right boundaries are held
at PSI=y, so that U=-1, and V=0.
************************************************************* }
title "Stream Function Flow past 45-degree slab"
variables
psi { define PSI as the system variable }
definitions
a = 3; b = 3 { size of solution domain }
len = 0.5 { projection of length/2 }
wid = 0.1 { projection of width/2 }
psi_far = y { solution at large x,y }
equations { the equation of continuity: }
div(grad(psi)) = 0
Boundaries
region 1 { define the domain boundary }
start(-a,-b) { start at the lower left }
value(psi)= psi_far { impose U=-1 on the outer boundary }
line to (a,-b) { walk the boundary Counter-Clockwise }
to (a,b)
to (-a,b)
to close { return to close }
start(-len-wid,len-wid) { start at upper left corner of slab }
value(psi)=0 { specify no flow on the slab surface }
line to (-len+wid,len+wid){ walk around the slab CLOCKWISE for exclusion }
to (len+wid,-len+wid)
to (len-wid,-len-wid)
to close { return to close }
monitors
contour(psi) { show the potential during solution }
plots { write hardcopy files at termination }
grid(x,y) { show the final grid }
grid(x,y) zoom(-1,0,1,1) { magnify gridding at corner }
contour(psi) as "stream lines" { show the stream function }
vector(-dy(psi),dx(psi)) as "flow" { show the flow vectors }
vector(-dy(psi),dx(psi)) as "flow" zoom(-1,0,1,1)
end