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Old   August 4, 2010, 16:19
Question Discretization and convergence
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Karan Anand
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I have a model where the turbine blades are cooled internally. The discretization to NS equation was first performed with 1st order upwind for momentum, energy and viscous model chosen (k-w SST) and standard for pressure. The solution converged with residual set to 1e-4 for all except 1e-6 for energy. I also have mass avrged pressure, velocity and temperature monitors at outlet.

After the solution converged (just with residual criteria, surface monitors are still varying), to get more accurate results, I switched to Second order upwind for all except pressure which was left as standard and reducing the relaxation factors. this time monitoring both residuals and surface monitors. I ran the simulation for a while with 'none' as convergence criteria.

I have a couple of questions:
Firstly, I plotted the residuals and surface monitors. In the velocity monitor, the velocity has almost stabilized, but there exists a few wiggles (extremely minor oscillations). Can I consider the solution to be converged (all other monitors are flat, and converged) ? Is this expected for the discretization method chosen? Also, the residual for energy did not satisfy the 1e-6 mark, can i still say the solution is converged? (I have added a few pics for the grid and convergence history)

Secondly, Could doing this help? ->
Instead of changing the discretization to 2nd order upwind, I first change it to Power law from 1st order upwind. As far as i remember , power law is 1st order accurate but it is way less diffusive and it seems quite similar to hybrid differencing scheme. Is the solution obtained here good enough?
After I switch to power law, I come back to 2nd order, which is a higher order scheme. Could this reduce the wiggles, or help me approach a converged solution? I thought of going for QUICK, but i have a lot of tet meshes.

Other info:
The solver is Steady state -SIMPLE scheme for the staggered grid. The model has no significant curvature , nor high values of natural convection.
Grid is Hybrid with hex core and tetra around. Have a prism boundary layer at the airfoil surface. Entire meshed domain is fluid. Grid is conformal.

Images for grid: (coarse mesh)

Images for convergence (a bit refined mesh and better transition between mesh regions-i didn't add images for them, but you get the basic idea from above)
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