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lost.identity October 5, 2010 12:40

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)
A(|P|) = max(0,1-0.5|P|^5)

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


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