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{ 1D_SPHERE.PDE

 

 This problem demonstrates the use of 1D spherical coordinates.

 

}

title '1D Sphere Test -- Gaussian'

 

coordinates

   sphere1 { default coordinate name is "R" }

 

variables

   u

 

definitions

   k = 1

   w=0.1

  { assume a gaussian solution }

   u0 = exp(-r^2/w^2)

  { apply the correct analytic source for spherical geometry

      (we could use div(k*grad(u0)) here, but that would not test the 1D Sphere expansions) }

   s = -(2/w^2)*(2*r^2/w^2-3)*u0

 

   left=point(0)

   right=point(1/10)

 

equations

   U:  div(K*grad(u)) +s = 0

 

boundaries

  region 1

      start left     point value(u)=u0

      line to right   point load(u)=(-2*k*r*u0/w^2)

 

monitors

  elevation(u) from left to right

 

plots

  elevation(u,u0) from left to right

  elevation(u-u0) from left to right as "Error"

  elevation(-div(grad(u)),s) from (0.01) to right

 

end