File: sphere.fe

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// sphere.fe

// Spherical tank partially filled with liquid with contact angle.

SYMMETRIC_CONTENT   // natural for a sphere 

parameter rad = 1.00    // sphere radius
parameter angle = 45    // contact angle, in degrees

// cosine of contact angle 
#define  WALLT  cos(angle*pi/180)

// density of body  
#define RHO   1.0

// Various expressions used in constraints
#define wstuff (rad^2*z/(x^2 + y^2)/sqrt(x^2+y^2+z^2))
#define gstuff (G*RHO/8*rad^4*z^4/(x^2 + y^2)*(x^2+y^2+z^2)^2)
#define gapstuff (G*RHO*rad^4/8*z^2/(x^2+y^2+z^2)^2)

constraint 1 convex   // the sphere, as wall for liquid 
formula:    sqrt(x^2 + y^2 + z^2) = rad
energy:
e1:  WALLT*wstuff*y - gstuff*y + G*RHO/8*y*z^2 - gapstuff*y
e2: -WALLT*wstuff*x + gstuff*x - G*RHO/8*x*z^2 + gapstuff*x
e3:  0
content:
c1:  -rad*wstuff*y/3
c2:   rad*wstuff*x/3
c3:   0

constraint 2    // the sphere, for display only
formula:    sqrt(x^2 + y^2 + z^2) = rad

vertices:
1   rad  0   0   constraint 1
2    0  rad  0   constraint 1
3  -rad  0   0   constraint 1
4    0 -rad  0   constraint 1
5    0   0  rad  constraint 2 FIXED   // to show back hemisphere
6    0   0 -rad  constraint 2 FIXED
7    0  rad  0   constraint 2 FIXED
8  -rad  0   0   constraint 2 FIXED
9    0 -rad  0   constraint 2 FIXED

edges:
1    1  2     constraint 1
2    2  3     constraint 1
3    3  4     constraint 1
4    4  1     constraint 1
5    5  9     constraint 2  FIXED // to show back hemisphere
6    9  6     constraint 2  FIXED
7    6  7     constraint 2  FIXED
8    7  5     constraint 2  FIXED
9    5  8     constraint 2  FIXED
10   9  8     constraint 2  FIXED
11   6  8     constraint 2  FIXED
12   7  8     constraint 2  FIXED

faces:
1    1 2 3 4
2    5 10 -9  constraint 2 density 0 FIXED   // to show back hemisphere
3   -10 6 11  constraint 2 density 0 FIXED
4   -11 7 12  constraint 2 density 0 FIXED
5    8 9 -12  constraint 2 density 0 FIXED

bodies:  // start with sphere half full
1    1    volume 2*pi*rad^3/3  volconst 2*pi*rad^3/3  density RHO

read

// Typical short evolution
gogo := { g 5; r; g 5; r; g 5; r; g 10; conj_grad; g 20; }


// Command to print out coordinates of points along cross-section
// of the surface.  This starts at vertex 3 and follows edges that
// point in the positive x direction.
section := {
   thisv := 3;
   nextv := thisv;
   do
   { printf "%9.6f %9.6f %9.6f\n",vertex[thisv].x,vertex[thisv].y,
            vertex[thisv].z;
     foreach vertex[thisv].edge ee do
     { if ee.x > 10*abs(ee.y) then
       { nextv := ee.vertex[2].id;
         break;
       }
     };
     if nextv == thisv then break; // done
     thisv := nextv;
   } while 1;
}