Divergence Theorem Flux Numeric

Problem

Compute the outward flux of F = [a*x + d, b*y + e, c*z + f] through the surface of the unit cube [0, 1]^3 numerically.

Sample each face on a 2x2 midpoint grid and add F dotted with the outward normal times the cell area 0.25. For this linear field the midpoint rule is exact, so the result equals the divergence integral a + b + c.

Hint

The constant offsets cancel between opposite faces; only the linear coefficients survive.

Test cases

case 1

in: [1,1,1,5,6,7]

expected: 3

case 2

in: [2,-1,0.5,0,0,0]

expected: 1.5

case 3

in: [0,0,0,3,4,5]

expected: 0

case 4

in: [10,0,-2,0,0,0]

expected: 8

Starter codePython

def flux_cube_numeric(a, b, c, d, e, f):
    # Your code here
    pass

4 test cases · run your code against them in the editor