Incompressible flows are that in which the specific mass does not depend on pressure. So the state equation is used to evaluate r, which depends only on T, , and T is calculated by energy equation. Then we have, in the state equation, an expression to r. Notice that pressure does not have a progressive equation although its influence is detected by the existence of its gradient in the motion equations. The gradients of the two directions should be combined in order to evaluate pressure. So we must extract P from motion equations to make the velocities obtained satisfy the mass equation.

The mass equation does not serve as a progressive equation to any variable, and it becomes a constraint to the velocities field.

So the goal in coupling is to determine the pressures field, which when inserted in motion equations, gives us a velocities field that satisfies the mass equation. In other words, the fact that r does not variate with P introduce a strong coupling between pressure and velocity, this causes great difficulties to solve the system of equations.

The case in which r is neither a function of P nor of T is the particular case solved by csfl-lib-1.0, considering that this software does not have the state equation coupled to the system of equations. Notice, however, that the cases and constant can be treated in the same numerical way.