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Orthogonal NS
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The purpose of this document is to present the essential and comprehensive elements required to derive the governing equations for the motion of incompressible Newtonian fluids within general orthogonal coordinate systems.

#. Lower- and upper-case letters are used to represent that the quantities are described on the Cartesian and the general orthogonal coordinate systems, respectively.

#. I do *not* use the Einstein summation rule throughout this document for clarity; the summation symbol :math:`\sum` always precedes when the indices are to be summed.

#. The subscripts are only used to indicate that the quantity is covariant; they are *never* used to represent the exponents.

.. toctree::
   :caption: Prerequisite
   :hidden:

   prerequisite/basis_vector
   prerequisite/transformation/main
   prerequisite/christoffel_symbol
   prerequisite/change_of_basis_vector/main
   prerequisite/nabla

.. toctree::
   :caption: Equation
   :hidden:

   equation/divergence_of_velocity/main
   equation/material_derivative/main
   equation/strain_rate_tensor/main
   equation/divergence_of_tensor/main
   equation/energy_diffusion_and_dissipation/main