CFD Online Discussion Forums - stability analysis and CFL condition

I am trying to do the stability analysis and find the CFL condition for the equations written in the following form

$a_e\widetilde{u}_{e} = a_{e_1}\widetilde{u}_{e_1} + a_w\widetilde{u}_w + b + (\overline{p}_P-\overline{p}_E)$

$a_{e_1} = \left[D_EA(|P_E|) + \text{max}(-F_E,0)\right]$
$a_w = \left[D_PA(|P_P|) + \text{max}(F_P,0)\right]$
$a_e^0 = \overline\rho_e^0\frac{\Delta{r}}{\Delta{t}}\label{eqn:coeffs_mom_c}$
$a_e = a_{e_1} + a_w + a_e^0$
$b = a_e^0\widetilde{u}_e^0 + S_C\Delta{r}$
$S_C = -\frac{\partial}{\partial{r}}\left( \frac{2}{3}\overline\rho\widetilde{k} \right)$

I don't know how to go about doing this when the equations are written in this form of Patankar. Could anyone please guide me?
Thanks