# Filter size of large eddy simulation with Smagorinsky sub-grid stress model

I am trying to implement Large eddy simulation for solving air flow simulation with large Reynolds number using Smagorinsky sub-grid stress model. I read that the filter size should be calculated based on the grid size: $$\Delta=(\Delta_x\Delta_y\Delta_z)^{1/3}$$

Could you please let me know that shall I calculate this $$\Delta$$ for every cell of the mesh? Or is it ok to calculate only for the smallest cell and use delta as a constant?