Flowslab

{ 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