Sample Problems > Usage > Periodicity > two-way

{ TWO-WAY_PERIODIC.PDE

This example shows the use of FlexPDE in applications with two-way periodic boundaries.

Starting in version 7, two-way periodcity is fully supported at a single point.

Prior to version 7, this was not supported and a small segment with no

periodicity needed to be inserted near the two-way periodic point.

}

title 'TWO-WAY PERIODIC BOUNDARY TEST'

variables

definitions

k = 1

h=0

x0=0.4 x1=0.9 { right box x-coordinates }

x2=-0.5 x3=0.0 { left box x-coordinates }

y0=-0.7 y1 = -0.3 {y-coordinates for both boxes }

equations

u : div(K*grad(u)) + h = 0

boundaries

region 1

{ Periodic bottom boundary }

start(-1,-1)

periodic(x,y+2) line to (1,-1)

{ Periodic right boundary }

periodic(x-2,y) arc(center=-1,0) to (1,1)

{ Image of periodic bottom boundary }

line to (-1,1)

{ Image of periodic right boundary }

arc(center= -3,0) to close

{ off-center hot box }

start(x0,y0)

value(u)=1 line to (x1,y0) to (x1,y1) to (x0,y1) to close

{ off-center cold box }

start(x2,y0)

value(u)=-1 line to (x3,y0) to (x3,y1) to (x2,y1) to close

monitors

grid(x,y)

contour(u)

plots

grid(x,y)

contour(u)

end

two-way_periodic