First order in time and Central Difference Convergence problem
Hi all
I am trying to solve compressible flow of gas in a cylinder using NS equations. I have written a code using finite volume method with first order in time and central difference in space. My grid is generated by cylindrical coordinates and the solver in cartesian(meaning grid has concentric circles and radial lines)... I have problem in convergence... the solution oscillates and diverges... I have added artificial dissipation also then I see these oscillations and divergence other wise it only diverges I have tried with various cfl ranging from 0.9 to 0.0001 but failed to get convergence can any body tell what exactly the problem might be.... I have checked the code to see the total flux in the initial condition for all the cells to be zero and ensured proper application of boundary conditions.. any suggestions of what can be checked 
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I am having the exact same problem now. How did you go about resolving it? i will be very grateful for your reply. Thanks 
First of all, I would recommend trying a higher order time integration scheme since the first order scheme coupled with the high order space discretization is generally unstable. The 3stage TVDRK scheme of Shu and Osher or the standard 4stage RK scheme would be good choices.

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@Praveen, I know you are referring to RameshK but I am facing similar issues and will appreciate any help. @DoHander; will try to implement the other methods but will like to debug my program with a simple scheme cos it will be easier to detect bugs in them. I am guessing my problem is not from the time discretisation because the solution did not even converge for the first time step. I am looking at the first step of SIMPLE scheme ie finding velocity with a fixed pressure fields. I hope you can help me. Thanks 
Bug in the program
Hi
Actually there was a bug in calculating the velocity magnitude in the code, fixed it and got the desired convergence. I have solved the same problem for pressure ratio (Po/P)of 1.2 and 1.1 where Po is total pressure at inlet and static pressure at exit, used RK 4 for time integration and solved it. But for convergence I have worked both Euler and Ns equations, for euler the convergnece went all the way to 1e16 but for NS it was oscillating at 1e4. NS code I have run for nearly 3 lakh time steps. 
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