Governing Equations in Continuous Integral Form

The Navier-Stokes equations may be represented by the following integral equations for continuity and momentum:

(65)

(66)

The terms on the left-hand side of Eqn. 66 are the transient term and the convective flux. On the right-hand side are the pressure gradient term, the viscous flux and the body force terms. is the viscous stress tensor. The body force terms represent the effects of system rotation, buoyancy, porous media and user-defined body forces, respectively.