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Old   April 12, 2004, 12:48
Default Convergence problems
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I am modelling 2D supersonic flow on a wing section and am having difficulty obtaining convergence.

I am using a coupled implicit solver, and inviscid solution.

I am able to obtain convergence using a first order discretization scheme and Courant number of 5. Once I reach this point I then apply the second order scheme to allow further extension of the shock waves as this is more accurate. I require the shocks to reach the pressure far field boundary at 10 lengths from the wing as I intend to measure the pressure signature.

For the first order scheme the solution converges at 477 iterations running at M2.01. I am unable to achieve second order convergence. The residuals remain level for over 1000 iterations.

I am using a fine mesh of 60000 faces, and the plots of static pressure do show shock propagation. However I can't get the solution to converge.

Also after the 1000 iterations there is little change in the static pressure plots, so does this suggest convergence?

And are there other methods of judging the convergence rather than relying on the FLUENT print out?

What is the minimum distance a pressure far field can be applied and would this affect the convergence? I have set the inlet of my domain 5 lengths from the wing section.

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Old   April 12, 2004, 18:03
Default Re: Convergence problems
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When you say you have converged solution at I = 477, can you elaborate further? What are your residuals (10e-3, 10e-4 or what)?

I am not a fluent user, so I don't really know if the residuals shown in the monitor is L2 norm or not. But If it is, then at any location in the domain, if there is a node with a exceptionally large residual, it will blow up your L2 norm (root mean square). If you can obtain the location (x,y,z) or node number of the node with the max residual, maybe you can do mesh refinement on that region to see if your L2 norm will decrease. Again I don't know if you write UDF or do something in Fluent or not for that! If the pressure plots (I assume this pressure plot is the average values of pressure for all nodes in the entire domain) is flat, then based on what i know, indeed the solution is converged. But having a converged solution doesn't mean the solution is even closed to the RIGHT answer.

So when you say the residuals remain level, still how big are those residuals?

And what is it you want from the solution, CL CD CM on the wing or just the flow visulization on the shock?

Good Luck
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Old   April 15, 2004, 00:52
Default Re: Convergence problems
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Hi! A good criteria of convergence is the plots of integral (typical) parameters of flow (for example, such as mass flow rate, Cx, Cy, Cm, total pressure or total temperature on outlet boundaries). Also good practice is to set several points in a domain and monitor them during your solution (for example, plot static pressure). In general, there are only two cases (both for steady and unsteady flows). Process is converged with a good degree of accuracy if the plots are flat or on a self-oscillatory mode.

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Old   April 15, 2004, 19:13
Default Re: Convergence problems
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Thanks for the advice. I have managed to reach a converged solution using a second order differentiation scheme, by reducing the Courant Number whenever the residuals begin to level out.

I have plotted the residuals for continuity, x and y velocity and energy. My flow is in the x direction.

The residuals decreased and then remained level for around I=200 at a value around 1e-02.

The plots I refer to are the diagrams showing the pressure contours of the flow around the object. I thought that because there were no visual changes in these contours after the 200 iterations, that the flow had converged.

Something I find strange is that I had to decrease the Courant Number for the residuals to drop in order to reach convergence. I thought that increasing the Courant number increased convergence :S :S

I will try setting several points in the domain to check for the changes you have described.


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