Sphere1D

title '1D Sphere Test - Gaussian'

coordinates

sphere1

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)

equations

    div(K*grad(u)) +s = 0

boundaries

    Region 1

       start left  point value(u)=u0

       line to right  point value(u)=u0

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