def f2(z, t):
"""2x2 system for sphere with Re-dependent drag."""
zout = np.zeros_like(z)
v = abs(z[1])
Re = v*d/nu
CD = cd_sphere(Re)
alpha = 3.0*rho_f/(4.0*rho_s*d)*CD
zout[:] = [z[1], g - alpha*z[1]**2]
return zout
def f(z, t):
"""4x4 system for smooth sphere with drag in two directions."""
zout = np.zeros_like(z)
C = 3.0 * rho_f / (4.0 * rho_s * d)
vrx = z[2] - vfx
vry = z[3] - vfy
vr = np.sqrt(vrx**2 + vry**2)
Re = vr * d / nu
CD = cd_sphere(Re) # using the already defined function
zout[:] = [z[2], z[3], -C * vr * (CD * vrx), C * vr * (-CD * vry) - g]
return zout
def f(z, t):
"""4x4 system for smooth sphere with drag in two directions."""
zout = np.zeros_like(z)
C = 3.0*rho_f/(4.0*rho_s*d)
vrx = z[2] - vfx
vry = z[3] - vfy
vr = np.sqrt(vrx**2 + vry**2)
Re = vr*d/nu
CD = cd_sphere(Re) # using the already defined function
zout[:] = [z[2], z[3], -C*vr*(CD*vrx), C*vr*(-CD*vry) - g]
return zout