periodic_map

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periodic_map

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{ PERIODIC_MAP.PDE

 This example is a modification of PERIODIC.PDE, and shows the use of the MAP facility in applications with periodic boundaries.

 ( Only FlexPDE versions 7.16 or later support this facility. )

 

 The PERIODIC (or ANTIPERIODIC) statement presets the behavior of all variables.

 A statement MAP() = 1 or MAP() = -1 may then appear for any number of variables,

 to independently set the behavior of that variable.

 MAP(.)=1 means PERIODIC,  MAP(.)=-1 means ANTIPERIODIC

 

}

 

title 'MAPPED PERIODIC BOUNDARY TEST'

 

variables

    u,v

 

definitions

   k = 0.1

   h=0

   x0=0.5  y0=-0.2

   x1=1.1  y1=0.2

   offset = sqrt(5)-2

 

select

  debug(periodics)

 

equations

   u : div(K*grad(u)) + h = 0

   v : div(K*grad(v)) + h = 0

 

boundaries

  region 1

    start(-1,-1)

    value(u)=0 value(v)=0   line to (0.9,-1) to (1,-1)

 

    { The following boundary is required to be a periodic image of the boundary

       two units to its left. (This image boundary has not yet been defined.) }

    periodic(x-2,y)

    { The variable U is declared PERIODIC, and the variable V is declared ANTIPERIODIC: }

    map(u)=1 map(v)=-1

    { the boundary is declared to be an arc: }

    arc(center=-1,0) to (1,1)

 

    value(u)=0 value(v)=0 line to (-1,1)

 

    { The following arc provides the required image boundary for the previous

       periodic statement }

    nobc(u) nobc(v) { turn off the value BC }

    arc(center= -3,0) to close

 

  { an off-center heat source provides the asymmetric conditions to

     demonstrate the periodicity of the solution }

  region 2  h=10 k=10

    start(x0,y0) line to (x1,y0) to (x1,y1) to (x0,y1) to close

 

monitors

    grid(x,y)

    contour(u)

    contour(v)

 

plots

    grid(x,y)

    contour(u)

    contour(v)

    elevation(u,v) from(-1+offset,0) to (1+offset,0)

 

end