I am trying to calculate the divergence of a 3D velocity field in a multi-phase flow setting (with solids immersed in a fluid). If we assume u,v,w to be the three velocity components (each a n x n x n) 3D numpy array, here is the function I have for calculating divergence:
def calc_divergence_velocity(df,h=0.025):
"""
@param df: A dataframe with the entire vector field with columns [x,y,z,u,v,w] with
x,y,z indicating the 3D coordinates of each point in the field and u,v,w
the velocities in the x,y,z directions respectively.
@param h: This is the dimension of a single side of the 3D (uniform) grid. Used
as input to numpy.gradient() function.
"""
"""
Reshape dataframe columns to get 3D numpy arrays (dim = 80) so each u,v,w is a
80x80x80 ndarray.
"""
u = df['u'].values.reshape((dim,dim,dim))
v = df['v'].values.reshape((dim,dim,dim))
w = df['w'].values.reshape((dim,dim,dim))
#Supply x,y,z coordinates appropriately.
#Note: Only a scalar `h` has been supplied to np.gradient because
#the type of grid we are dealing with is a uniform grid with each
#grid cell having the same dimensions in x,y,z directions.
u_grad = np.gradient(u,h,axis=0) #central diff. du_dx
v_grad = np.gradient(v,h,axis=1) #central diff. dv_dy
w_grad = np.gradient(w,h,axis=2) #central diff. dw_dz
"""
The `mask` column in the dataframe is a binary column indicating the locations
in the field where we are interested in measuring divergence.
The problem I am looking at is multi-phase flow with solid particles and a fluid
hence we are only interested in the fluid locations.
"""
sdf = df['mask'].values.reshape((dim,dim,dim))
div = (u_grad*sdf) + (v_grad*sdf) + (w_grad*sdf)
return div
The problem I'm having is that the divergence values that I am seeing are far too high. For example the image below showcases, a distribution with values between [-350,350] whereas most values should technically be close to zero and somewhere between [20,-20] in my case. This tells me I'm calculating the divergence incorrectly and I would like some pointers as to how to correct the above function to calculate the divergence appropriately. As far as I can tell (please correct me if I'm wrong), I think have done something similar to this upvoted SO response. Thanks in advance!
