Divergence of Curl Identity Check

Problem

The identity div(curl F) = 0 holds for smooth fields. Verify it numerically for F = [a*y*z^2, b*z*x^2, c*x*y^2].

Compute the curl with central differences (step h = 1e-5), then take the central-difference divergence of that curl. The return value is the residual, which should be near 0.0.

Hint

Two applications of central differences should cancel to within round-off.

Test cases

case 1

in: [1,1,1,1,2,3]

expected: 0

case 2

in: [2,-3,4,-1,0.5,2]

expected: 0

case 3

in: [0,1,0,3,3,3]

expected: 0

case 4

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

expected: 0

Starter codePython

def div_of_curl_check(a, b, c, x, y, z, h=1e-5):
    # Your code here
    pass

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