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 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


       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"  



  psi             { define PSI as the system variable }  



  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: }  

  psi : div(grad(psi)) = 0  



  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 }  



  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)