Working equations of the continuous penalty scheme in axisymmetric coordinate systems

9 Working equations of the continuous penalty scheme in axisymmetric coordinate systems 

After the substitution of pressure via the penalty relationship the flow equations in an axisymmetric coordinate system are written as 

Using a procedure similar to the derivation of Equation (4.53) the working equations of the continuous penalty scheme for steady-state Stokes flow in an axisymmetric coordinate system are obtained as 

10 Working equations of the discrete penalty scheme in Cartesian 

As described in the discrete penalty technique subsection in Chapter 3 in the discrete penalty method components of the equation of motion and the penalty relationship (i.e. the modified equation of continuity) are discretized separately and then used to eliminate the pressure term from the equation of motion. In order to illustrate this procedure we consider the following penalty relationship 

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