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October 5, 2010, 13:40	stability analysis and CFL condition	#1
lost.identity Senior Member Join Date: Apr 2009 Posts: 118 Rep Power: 17	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

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