<< Click to Display Table of Contents >>

Navigation:  Sample Problems > Usage > 3D_domains >


Previous pageReturn to chapter overviewNext page



 This problem constructs two non-coplanar spheres inside a box by constructing  

 a single dividing surface  to delimit both spheres.


 The domain consists of three layers.

   layer 1 is the space below the spheres

   layer 2 contains the sphere bodies, and is of zero thickness outside the spheres

   layer 3 is the space above the spheres

 The sphere interiors are Void, and are thus excluded from analysis. You could  

 just as well fill them with material if you wanted to model the insides.


 The bounding surfaces of layer 2 are specified as a slope perpendicular to the  

 centerline of the spheres and over-ridden by regional expressions within  

 the (X,Y) extent of each sphere.


 Click "Controls->Domain Review" to watch the mesh construction process.


 See TWOZ_PLANAR.PDE, TWOZ_EXPORT.PDE and TWOZ_IMPORT.PDE for other methods of  

 treating spheres with centers on differing Z coordinates.




title 'Two Spheres in 3D - direct surface matching'  









    K = 1               { dielectric constant of box filler (vacuum?) }  

    box = 1 { bounding box size }  


    { read sphere specs from file, to guarantee that they are the same as those in surfgen }  

    #include ""  


    { sphere shape functions }  

    sphere1_shape = SPHERE ((x1,y1,0),R1)  

    sphere2_shape = SPHERE ((x2,y2,0),R2)  


    { construct an extrusion surface running through both sphere diameters

          by building an embankment between the spheres }  

    Rc = sqrt((x2-x1)^2+(y2-y1)^2)-R1-R2  

    Rx = Rc*(x2-x1)/Rc/4  

    Ry = Rc*(y2-y1)/Rc/4  

    xm = (x1+x2)/2  

    ym = (y1+y2)/2  

    xa = xm - Rx  

    ya = ym - Ry  

    xb = xm + Rx  

    yb = ym + Ry  

    xc = xm + Ry  

    yc = ym - Rx  

    slope = PLANE((xa,ya,z1), (xb,yb,z2), (xc,yc,0))  

    zbottom = min(z2,max(z1,slope))  

    ztop = zbottom  




   U: div(K*grad(u))  = 0  



  surface "box_bottom"  z=-box  

  surface "sphere_bottoms"  z = zbottom  

  surface "sphere_tops"  z = ztop  

  surface "box_top" z=box  



    surface "box_bottom" natural(u) = 0 {insulating boundaries top and bottom }  

    surface "box_top" natural(u) = 0  


    Region 1 { The bounding box }  

start(-box,-box) line to (box,-box) to (box,box) to (-box,box) to close  


  limited region 2 { sphere 1 }  

      mesh_spacing = R1/5   { force a dense mesh on the sphere }  

       zbottom = Z1-sphere1_shape { shape of surface 2 in sphere 1}  

       ztop = Z1+sphere1_shape   { shape of surface 3 in sphere 1}  

      layer 2 void  

      surface 2 value(u)=V1   { specify sphere1 voltage on top and bottom }  

      surface 3 value(u)=V1  

      start  (x1+R1,y1)  

  arc(center=x1,y1) angle=360  


  limited region 3 { sphere 2 }  

      mesh_spacing = R2/5   { force a dense mesh on the sphere }  

       zbottom = Z2-sphere2_shape { shape of surface 2 in sphere 2}  

       ztop = Z2+sphere2_shape   { shape of surface 3 in sphere 2}  

      layer 2 void  

      surface 2 value(u)=V2   { specify sphere2 voltage on top and bottom }  

      surface 3 value(u)=V2  

      start  (x2+R2,y2)  

  arc(center=x2,y2) angle=360  




    grid(x,z) on y=y1  paintregions as "Y-cut through lower sphere"  

    contour(u) on y=y1 as "Solution on Y-cut through lower sphere"  

    grid(x,z) on y=y2  paintregions as "Y-cut through upper sphere"  

    contour(u) on y=y2 as "Solution on Y-cut through upper sphere"  

    grid(x*sqrt(2),z) on x-y=0  paintregions as "Diagonal cut through both spheres"  

    contour(u) on x-y=0 as "Solution on Diagonal cut through both spheres"  

    glsurface(u) on x-y=0