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May 9, 2012, 13:31	fractional step method in cylindrical coordinates, help please?	#1
new_at_this Member Peter Join Date: Oct 2011 Posts: 52 Rep Power: 14	I am trying to solve developing internal flow in a circular duct using a staggered grid and cylindrical navier stokes equations. At the moment I am using a fractional step method with primitive variables but my code is currently wrong and I think it has to do with the pressure correction step and I think I might be using the wrong equations. Please let me know if you see anything wrong. My process is listed below. fractional step for advection terms $U^* = U^n-\Delta t(\frac{\partial UV}{\partial r}+\frac{\partial U^2}{\partial z})$ $V^* = V^n-\Delta t(\frac{\partial V^2}{\partial r}+\frac{\partial UV}{\partial z})$ fractional step for diffusion terms $U^{*} = U^+\frac{\Delta t}{Re}(\frac{1}{r}\frac{\partial U^{}}{\partial r}+\frac{\partial^2 U^{}}{\partial r^2} + \frac{\partial^2 U^{}}{\partial z^2})$ $V^{} = V^+\frac{\Delta t}{Re}(\frac{1}{r}\frac{\partial V^{}}{\partial r}+\frac{\partial^2 V^{}}{\partial r^2} + \frac{\partial^2 V^{}}{\partial z^2}-\frac{V^{}}{r^2})$ pressure correction $U^{n+1} = U^{} - \Delta t(\frac{\partial P}{\partial z})$ $V^{n+1} = V^{} - \Delta t(\frac{\partial P}{\partial r})$ where Pressure is calculated by $\frac{1}{r}\frac{\partial P}{\partial r}+\frac{\partial^2 P}{\partial r^2}+\frac{\partial^2 P}{\partial z^2} = \Delta t(\frac{U^{}}{r}+\frac{\partial U^{}}{\partial r}+\frac{\partial V^{*}}{\partial z})$

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