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{ SPACE_CHARGE.PDE
This problem describes the electric field in an insulated cardioid-like
chamber due to an electrode at the tip of the cardioid and a localized
space charge near the center of the body.
Adaptive grid refinement detects the space charge and refines
the computation mesh to resolve its shape.
}
title "Electrostatic Potential with probe and space charge"
select errlim = 1e-4
definitions bigr = 1 smallr = 0.4 x0 = sqrt(bigr^2/2) y0 = x0 r = sqrt(x^2+y^2) { define the electrode center } xc = sqrt((bigr-smallr)^2/2) yc = xc { A space charge source at -xc } source = x/((x+xc)^2 + y^2 + 0.001) k=0.1
variables V
equations V : div(k*grad(V)) + source = 0
boundaries region 1 start(xc,yc-smallr) |
natural(V) = 0 { -- insulated outer boundary }
arc(center=xc,yc) to (x0,y0)
arc(center=0,0) angle 270
arc(center=xc,-yc) to (xc,smallr-yc)
value(V)=1 { -- applied voltage = 1 on tip }
arc(center=xc,0) angle -180 to close
plots
grid(x,y)
contour(V) as "Potential"
contour(V) zoom(0.2,-0.2,0.4,0.4)
surface(V) viewpoint (0,10,30)
surface(V) zoom(-0.6,-0.2,0.4,0.4)
surface(source) zoom(-0.6,-0.2,0.4,0.4)
end